topic: Music that not focused around melodic and harmonic structures
Essay
Double space/2 pages
Chicago form
require Bibliography
I also provide my writing sample which is the pdf Answer2 , please try to write a similar writing style.
Answer2 (Q: Women composers throughout the 20-21C)
Pauline Oliveros is widely regarded as one of the most influential American
composers in the 1920s. In the 20th century, she encouraged in-depth listening, was open
to what was happening, and actively founded participating communities throughout her
life. Oliveros was born in 1932. She is a composer, performer, writer and philosopher.
She has been active in the forefront of many music movements. Growing up in Houston,
she listened to metropolitan opera’s radio broadcasts Philharmonic and NBC. She also
indicated that her mother was one of the first people to influence her creative thoughts
and ideas. After studying at the University of Houston for three years, she went to San
Francisco State University to study deeper in composition. After her graduation, in 1957,
she and her classmates Terry Riley and Loren Rush began to try improvisation. She
explained that “while the convention music circles of the 1950 s were not exploring
music in this man. The Jazz World was exploring the Breadth of Improvisation SoundsIn
the mid-1960s,” she expanded her scope of creation by collaborating with dramatic
works, such as Elizabeth Harris, Anna Halprin, Merce Cunningham and others who were
dancers and choreographers.
Just like John Cage, he has given “music”, “composer” and “quiet” new definitions.
Oliveros has also expanded the definition and attention of the sonic environment, and the
total environment is equally important to her. At the same time Oliveros began to try a
sound meditation practice, which became the label for her in the future. Sonic
Meditations, which she created in 1974, is also one of her greatest works. Oliveros
encourages the listeners to listen to their own voices and the surrounding environment
deeply, which plays a certain role in the construction and rehabilitation of music
psychology. In the United States and abroad, she is one of the most famous and popular
advocates for training listening awareness. She regularly returns to various parts of the
world to teach and perform. Oliveros was the first director of the Tape Music Center of
Oakland Mills College. California, which is the Center for Contemporary Music right
now, and she is also an outstanding music professor of RPI. She did not get a doctor’s
degree that was very important as a professor in college at that time. for Pauline Oliveros,
she has been focusing on listening to everything around her all her life. she said in the
magazine American music that she grew up in the rural areas of Houston, so she adapted
to the sound of the natural environment at an early age and was influenced by it. She also
thinks that electronic sound is more limited to an audio range than natural sound, but
natural sound is not.
The four sources of Oliveros’s music material are: 1. All the music she has heard; 2.
All the sounds she has heard from nature (including her own internal physiological
sounds); 3. All the voices she heard in the technological world; 4. All the voices she
imagined. But she also has some electronic works, such as her Alien Bog. She uses some
repeated high pitch sounds as introduction. As the pitch drops, Oliveros adds various
sounds to the music, influenced by the frog sounds she heard in studio at Mills. These
sounds also seem to come from all directions, such as horn sounds, chirp sounds, bubble
sounds and rumbling sounds. However, she did not record the croaking of frogs, nor did
she translate the croaking of frogs into the specific pitch of music. Her aim is also to give
the audience more imagination space in such a whole voice.
In addition, most of Oliveros’s works are based on her integration into the natural
environment. No matter where she is, she enjoys and freely experiences her environment
and listens to all the voices around her. Oliveros himself explained: “All is nature that
supports life forms of all kinds; humanity is the body of life forms called humans. . . The
relationship is symbiotic.” This is why she pays attention to meditation and total
environment in his music composition.
Bibliography
Glahn, Denise Von. “Pauline Oliveros.” Essay. In Music and the Skillful Listener
American Women Compose the Natural World, 102–28. Indiana University Press,
2014.
Kelly, Jennifer, and Pauline Oliveros. “Pauline Oliveros.” Essay. In In Her Own Words:
Conversations with Composers in the United States, 152–74. Urbana, IL:
University of Illinois Press, 2014.
Boydell & Brewer
University of Rochester Press
Chapter Title:
STEVE REICH (1936)
Chapter Author(s): STEVE REICH
Book Title: Three Questions for Sixty-Five Composers
Book Author(s): Bálint András Varga
Published by: Boydell & Brewer, University of Rochester Press. (2011)
Stable URL: https://www.jstor.org/stable/10.7722/j.ctt1x71xw.51
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Forty-Seven
STEVE REICH (1936)
In my mind’s eye, I can see the composer on stage, participating in a performance of his
Clapping Music (1972). The piece is performed by two, facing each other, clapping
increasingly intricate rhythmic patterns which appear to require the highest degree of
concentration. What could be more basic to music than two people clapping? And yet it
is immensely thrilling, you respond to it with your body as well as with your mind and
the tension in you leaves you perhaps nearly as exhausted as the two performers must be
feeling, even though the exercise only lasts for fi ve minutes at the most.
At the other extreme, there is Tehillim (1981) for voices and ensemble. I have
not heard it for decades but its majesty still haunts me. It is a setting in Hebrew of
Psalms 19, 34, 18, and 150; whether or not it is an expression of Reich’s faith is
immaterial. If it is true that “beauty is in the eyes of the beholder,” I suppose you can
also claim that the “message” of music is in the mind of the listener.
I.
I have had no experience that is the same as Lutosławski’s, but I have had a
number of experiences with music that may be somewhat similar.
A. When I was fourteen years old, I heard a recording of Le Sacre du Prin-
temps for the first time. I had never heard anything like it. (In fact, at
that time I had not heard any Stravinsky, Bartók, Schoenberg, Berg, or
Webern.) It made an enormous impression on me and I believe that the
seeds of my desire to become a composer were planted at that moment.
B. In the same year—when I was fourteen—I also heard my first jazz
recording. It was by Charlie Parker, Miles Davis, Kenny Clarke, and oth-
ers. It also made a huge impression on me and I decided to begin study-
ing snare drum with Roland Kohloff (formerly timpanist with the New
York Philharmonic) that same year. I would say that my drumming stud-
ies and the rhythmic impulse in me that was touched by Stravinsky, jazz
and, later that same year, by my first hearing of the Brandenburg Concerto
No. 5 formed the basic musical energy in me which is still at work in my
own compositions.
C. In 1957 I studied composition privately with Hall Overton in New York
City and he had me return to playing simple music at the piano, in par-
ticular, the first two books of Bartók’s Mikrokosmos. In these pieces I first
clearly understood the different modes beyond major and minor. Even
more importantly I became clear about the nature of canons as a basic
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208 • S t e v e R e i c h ( 1 9 3 6 )
compositional technique. Canons at the unison have since formed the
basis of almost all my music. The entire “phasing” technique discovered
with tape loops in It’s Gonna Rain (1965) and then transferred to musi-
cal instruments with Piano Phase of 1967 can be correctly seen as a form
of canonic procedure where the subject is short and the rhythmic dis-
tance between the two or more voices is constantly changing.
D. In 1962, via a talk by Gunther Schuller, I examined A. M. Jones’s book
Studies in African Music which, together with my work with tape loops
in 1963, made me aware of the repetition of short patterns with their
downbeats in different places as a new and radically different composi-
tional technique. A few years later I encountered another book, Music in
Bali by Colin MacPhee, which showed me, in notation, music made of
repeating patterns played simultaneously in different note values so that
one could hear rapid interlocking eighth notes, slower moving quarters,
still slower half notes, and one huge gong which played only once per
cycle of 64 beats.
E. While a composition student at Juilliard and later while studying with
Berio at Mills College in California in the early 1960s, I used to spend
many evenings at jazz clubs listening to John Coltrane. I also listened
frequently to many of his recordings. One recording in particular, Africa
Brass, capsulizes what I and many others learned from Coltrane: over
one single harmony, maintained for as long as half an hour, many notes
or even noises can be played. On Africa Brass the entire harmony stays
rooted on the low E of the double bass, yet over it Coltrane, Eric Dolphy,
and others play notes inside or outside the key of E minor as well as
french horn glissandos, and shrieks on their saxophones.
F. In 1964 I helped Terry Riley put together the first performance of his
In C. I suggested that he put a “pulse” in the piece to keep the players
together, which he did using drummed out high Cs on the piano. The
piece showed me one way that repetition of short patterns could func-
tion as a compositional building block. The influence Riley’s piece had
on me was similar to the influence La Monte Young had on Riley several
years earlier in Berkeley and was also similar to the influence I had on
Phil Glass in 1967 when he heard and studied my music for the first time
in New York. Still later my Drumming, plus Riley and Glass had a for-
mative effect on John Adams, Louis Andriessen, Michael Nyman, Gavin
Bryars, and eventually many others, some in the world of pop music.
II.
Your question strikes me as very European. You say that everyday sounds
either “inspire” a composer or they leave him “completely cold.” My answer
is: neither of the above. I fi nd some natural sounds—particularly rain on
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S t e v e R e i c h ( 1 9 3 6 ) • 209
a roof, and nearby running streams or ocean surf, cicadas or crickets, and
birdsongs among others, to be—at one time or another—comforting, fas-
cinating, or mysterious. City sounds I fi nd generally irritating—especially
if I am trying to sleep. When I fi rst did tape music in the early 1960s, I
found natural and machine sounds interesting, but not nearly as interest-
ing as human speech, which I used to make my early It’s Gonna Rain and
Come Out. Basically, I get musical inspiration not from “sounds” but from
music—notes, rhythms, and timbres. I should add that in Different Trains of
1988 I was inspired to combine the speech melody I had discovered in It’s
Gonna Rain and Come Out with real musical instruments, namely the strings
in the Kronos Quartet.
In City Life of 1995 I did use sounds I recorded in New York including
car horns, boat horns, subway chimes, door slams, and many others includ-
ing human voices. My primary idea was to “marry” the sounds to an appro-
priate instrument. Bass drum and door slam, car horn and amplifi ed oboe,
air brakes and cymbal, voices and strings, etc. After pieces using sampling
like Different Trains, City Life, The Cave, and Three Tales I felt a need to return
to instrumental music from 2002 until 2009 when I am now, once again,
turning to sampled speech to match with the Kronos Quartet.
III.
Individual style is the revealing of one’s musical intelligence and emotions in
concrete works. This revelation continues, and hopefully develops, through-
out one’s lifetime. Self-repetition begins when musical intelligence and emo-
tions cease to develop and one nevertheless continues to grind out music.
Such self-repetition is earmarked by techniques which appear in earlier
works and reappear in new works with no further signifi cant development
in terms of harmony, counterpoint, rhythmic structure, orchestration, etc.
One can fi nd poor works within an oeuvre where self-repetition begins,
only to fi nd them followed by a fi ne work that breaks new ground. Break-
ing new ground should not be confused with mere novelty, and develop-
ing a preexistent style should not be confused with self-repetition. Bartók’s
String Quartet No. 5 develops the new ground broken by his String Quar-
tet No. 4, and he then goes on to break further new ground in his (para-
doxically more “conservative”) String Quartet No. 6.
The distinction between novelty and radical development on the one
hand and self-repetition and development within a style on the other is dif-
fi cult to make, but a composer must be able to make such distinctions in
his own work—or suffer the consequences.
1983/2009
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Steve Reich: Music as a Gradual Process: Part I
Author(s):
K. Robert Schwarz
Source: Perspectives of New Music, Vol. 19, No. 1/2 (Autumn, 1980 – Summer, 1981), pp.
373-392
Published by: Perspectives of New Music
Stable URL: https://www.jstor.org/stable/832600
Accessed: 11-05-2020 01:44 UTC
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STEVE REICH: MUSIC AS A
GRADUAL PROCESS
PART I
K. Robert Schwarz
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374
It may appear inappropriate to some for musicology to journey into the
realm of progressive trends in new music. Such areas of concern have been
more traditionally left to the composers and critics to discuss. Yet too many of
these commentators approach their subject with pre-determined biases that
highly color their reporting, and our subsequent understanding, of the trends
being described. It therefore seems imperative that musicology assume the
task of objectively assembling, chronicling, and analyzing recent developments
in new music, so that scholars of the next generation will have an adequate as
well as accurate source basis with which to work. Rather than waiting to view
recent trends in retrospect, we might instead function from the alternative
position of attempting to explain and catalogue new developments as they
occur. The risks involved -those of hasty analysis and inaccurate judgment,
caused by the loss of historical perspective–are great, but the benefits gained
may prove to far outweigh the dangers.
The young, progressive composers, those that depart most significantly
from the mainstream, have been the prime victims of our reluctance to apply
to new music the same standards of objectivity and accuracy that we demand
of historical scholarly research. Steve Reich, an American composer of so-
called “progressive” inclinations, is a fine example of this phenomenon; his
work has been unduly neglected by serious American researchers, and con-
sequently by scholarly American journals. It has fallen to the Europeans,
particularly the British and the Germans, to write about Reich’s music with
the respect it deserves.’ One cannot help but feel that his output merits similar
serious attention by Americans.
Reich’s neglect by American scholars is especially ironic, as he is a rare
example of a young composer who has developed a massive public following.
The academic and musicological community’s silence in the face of this public
acclaim makes it appear that we consider a composer of such popular appeal to
be by definition a less than serious figure. Perhaps we assume that such music
will be facile and unoriginal, that its composer will have compromised his
ideals to gain success. The truth, however, is that a composer need not work in
isolation; there is no reason for us to suppose that Reich’s popularity and
commercial success brands him as a cult figure unworthy of our attention.
Composers such as Steve Reich, Philip Glass, Terry Riley, and others,
are the antithesis of a personality like Milton Babbitt, who wrote that “the
composer would do himself and his music an immediate and eventual service
by total, resolute, and voluntary withdrawal from this public world into one of
private performance and electronic media, with its very real possibility of
complete elimination of the public and social aspects of composition.”2 Reich,
on the other hand, refuses to alienate himself from the public. His works very
consciously belong to the domain of the people. Reich has said:
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375
I believe that music does not exist in a vacuum. One mode of
feedback I rely on most is the popular, naive reaction…. A critic
is often politically biased, for or against a composer…so the
public’s reaction can be a better weathervane of the music’s basic
health…. My work, and that of Glass and Riley, comes as a breath
of fresh air to the new music world… . This basic feeling is very
healthy. It’s a feeling of moving.back away from a recondite and
isolated position, toward a more mainstream approach.”3
Without pandering to popular taste, Reich has molded a style of personal
integrity. His gradual, methodical process of style change has led him, in a
brief sixteen years, to forge a musical language uniquely his own out of the
impersonal minimalism of the mid-1960’s. Reich’s music is worthy of our
closest examination, and it is just such a study that will be attempted here.
There is an immense amount of primary and secondary source material
concerning Reich at the researcher’s disposal. Much of Reich’s music is
recorded on widely distributed major record labels,4 and recently Universal
Edition has released the first commercially available publications of his works.5
In addition, the researcher rapidly finds him or herself deluged by a massive
number of essays, articles record notes, and interviews written by or conducted
with the composer. Few young composers have written so copiously and
cogently concerning their own music as has Reich. At each step of his
compositional development, Reich has made a conscious effort to explain
various aspects of his creative processes in a manner that will bridge the gap
between the composer/creator and the listening public. His admirable little
volume of collected essays, Writings About Music (1974), illustrates these
desires; in this book, he succeeds in describing his own music with a clarity
and honesty that mirrors the structurally lucid aesthetic he favors in his
compositions.
Yet aside from the material that Reich himself has created, very little
other serious work concerning his music has appeared in American journals.
The general press coverage of Reich’s music, however extensive, has for the
most part consisted of concert or record reviews, frequently uninformed and
therefore often unhelpful to the scholarly researcher.6 This study aims to fill
the obvious gap: it will attempt to survey Reich’s stylistic traits, his life, works,
and achievements, and his significance for our time.
Steve Reich is an example of what the recording industry describes as a
“crossover phenomenon”: his music addresses the tastes of jazz, rock, tradi-
tional Classical, as well as new music audiences. He was not only the first
living “serious” composer to sell out Carnegie Hall in a program devoted
exclusively to his own works (Feb. 19, 1980), but also the first “serious”
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376
composer to sell out the New York rock/jazz nightclub, The Bottom Line.
Between 1971 and 1980, Steve Reich and Musicians (the composer’s repertory
ensemble) gave eleven European and American concert tours, a total of more
than two hundred concerts of Reich’s music.7
What sort of music is this that breeds such public acclaim? Reich’s
output has alternately been described, by critics and listeners of various
persuasions and biases, as minimalistic music, hypnotic music, trance music,
pulse music, and phase music. Though Reich has in the past rejected the
application of the label “minimalism” to his own music,8 the term can viably
be applied to aesthetic, at least through the works of 1971. Minimalism,
whether in art, music, or theatre, is an aesthetic which deliberately and
severely restricts the materials and resources that the artist, composer, or
dramatist employs in his conceptions. It is an art which focuses on small
details of structure or concept, and then magnifies these to form the basis of
an entire work. As Reich has said, “By restricting oneself to a single,
uninterrupted process, one’s attention can become focused on details that
usually slip by.”‘ The resultant art is one in which contrast and change, and
even the progression of time itself, can only be appreciated at a much slower
rate than that to which we are normally accustomed. For the sake of attempting
to make some stylistic generalizations about the music of Reich, we will accept
the label of “minimalism” for his work, but with one important qualification:
most of the following generalizations concerning minimalism, while applicable
to Reich, are only viable in relation to the music he composed up to 1971.
Since then, as will be repeatedly underscored here, Reich has turned away
from the severely austere minimalist aesthetic, in favor of a new richness of
content and texture, a beauty of sound, and a loosening of structure.
Many aspects of Reich’s early minimalist period can be viewed as direct
rebellions against the various factions of the post-war avant-garde, as reactions
against serialism, free atonality, and aleatory. Reich desired an immediate
clarity of structure, and he therefore employed musical/compositional processes
that precisely governed the entire course of a composition. Just as the ultra-
rationality and total control of post-war serialism led to a Cageian reaction
involving improvisation, chance, and formlessness, so Reich has rejected the
lack of composer-organized structure in aleatoric music in favor of scores that
are meticulously worked out in advance, down to the smallest detail. For
Reich, the intricacies of serialism were unappealing, as they involved nothing
more than convoluted, hidden structural devices which were rarely apparent
to anyone beyond the composer and his privileged circle. Reich’s aesthetic
required that the structural process be clearly perceived by the listener:
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377
John Cage has used processes and has certainly accepted their
results, but the processes he used were compositional ones that
could not be heard when the piece was performed. The process of
using the I Ching or imperfections in a sheet of paper to determine
musical parameters can’t be heard when listening to music com-
posed that way. The compositional process and the sounding
music have no audible connection. Similarly in serial music, the
series itself is seldom audible…. What I’m interested in is a
compositional process and a sounding music that are one in the
same thing.10
The above quotation comes from one of Reich’s most important essays,
“Music as a Gradual Process” (1968). The essay, as well as Reich’s chosen
process of “phasing,” will be discussed in full later in this article. For now,
suffice it to say that this primacy of structure, apparent to some extent in all of
Reich’s music, is the aspect of his work that most gives in an intellectually and
analytically challenging character. In Reich, structure cannot be a framework
which supports an unrelated facade of sounds; rather, sound and structure
must be identical.
An additional aspect of the minimalist rebellion against the “establish-
ment avant-garde” is exemplified by Reich’s embracing of an exclusive tonal
and/or modal (and chiefly consonant) harmonic vocabulary. Yet Reich’s “new
tonality”, as it has been called,” is much different from traditional tonality.
The tonal/modal gamut of a Reich work is established at the outset, most
typically by the insistent repetition of a brief rhythmic/melodic pattern which,
while tonal, may or may not be linked to an explicitly stated harmonic
structure. In Reich, tonality is therefore only asserted by repetition, as is
Stravinsky’s tonality, which is a prime influence on the younger composer.
There are no dominant/tonic polarities, no hierarchy of harmonies within a
key; only infrequently does one find functional chord progrerssion, and even
these are rarely the motivating force in the particular work.12 Neither is there
such a concept as modulation: when Reich wishes to shift tonal centers in a
work, he does so abruptly, by merely justaposing the new tonality alongside the
old one. Yet this method implies no functional relationships between the two
tonalities involved, nor do any functional polarities exist within either of
them.
Along with this new employment of tonality comes Reich’s belief in a
repeated, steady, driving pulse. The composer himself prophetically predicted
in 1970: “The pulse and the concept of clear tonal center will re-emerge as
basic sources of new music.”‘3 The rhythmic animation of Reich’s music
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378
provides an urgency, an accessibility, and a unifying force that always continues
unabated throughout a composition. Most importantly, Reich’s embracing of
steady pulse introduces an entirely new element into contemporary “serious”
music,14 an element that can be viewed as a reaction against the dissolution of
regular metrical rhythm that was so typical of the post-war avant-garde. Reich
considers a clear rhythmic pulse to be one of the prime elemental forces shared
by all world musics-whether African, Indonesian, Indian, jazz, or Western
Baroque–and he feels it is an essential element of his musical style.
Other aspects of Reich’s compositional style are inherent in the term
“minimalism”. Reich severely limits his musical material by the reliance on a
single dynamic, textural, timbral, harmonic, melodic, or rhythmic level for
sections or entire works (though this observation is often invalid after 1971).
A single set of musical parameters are established at the outset of a piece
which either remain unvaried for the length of the composition, or are altered
only in a very gradual and subtle manner. In this way, the premise of the work
is clearly apparent at the opening, and thus the element of conflict or dualism
is rejected. Clearly related to both the limitation of means and lack of contrast
is Reich’s use of repetition. Coupled with unvarying rhythmic pulse, repetition
satisfies the minimalist ideal of forcing the mind inward on small structural
details, while simultaneously becoming the prime unifying force.
Such repetition, however, also has a rather unusual effect on the
listener’s comprehension of the passage of time. Our experience of music as
sound in time is highly subjective and therefore difficult to discuss at all
precisely; in addition, the element of alteration of consciousness (so clearly
implied by any change in our perception of time) is awkward to deal with
objectively. Reich himself strongly denies that his music aims to create a
trance-like change in consciousness on the part of the listener: “There’s no
intent on my part to create anything like a trance. A lulling into unconscious-
ness would be the worst possible result. What I hope my music summons up in
more attention to detail.. .”. “” While not disagreeing with Reich’s statement,
one could argue that the lengthy contemplation of small details is in itself both
consciousness-altering as well as time distorting. Despite the constant pulse, a
sense of a lack of awareness of the passage of time is experienced by many
listeners to Reich’s music. How paradoxical it is that “this music, which
proceeds so tonally pleasantly, obstructs the “tonal” understanding of time.”’16
Related to Reich’s desire for an immediate clarity of structure is his
dislike of anything improvisational, which could serve only to conceal the
basic framework. Reich demands the subjection of the free expression of the
individual performer to the common goal of group expression. His musical
structures, or “processes” as he refers to them, are rigorously planned in
advance. Though some elements of performer choice enter into these scores,
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379
most are carefully determined in rehearsal, so the performance of a given piece
is as controlled and precise as clockwork. The only spontaneous element added
during the performance situation involves the decision of how many repetitions
there will be of a given musical section. In Reich’s recent works even this
parameter is determined in advance, but in earlier compositions (such as
Drumming, 1971) the number of repeats was decided in performance via an
elaborate system of visual cueing which had the additional advantage of
forcing the members of his ensemble to rely on each other for musical
direction, thereby enhancing the close-knit feeling of the group.
Closely connected to the subjugation of individual expression and the
distrust of improvisation is the question of the impersonality and objectivity of
Reich’s musical processes. Reich clearly stated in his esay of 1968, “Music is a
Gradual Process:” “Though I may have the pleasure of discovering musical
processes and composing the musical material to run through them, once the
process is set up and loaded it runs by itself.”‘7 Combined with the fact that
Reich’s musical ideas are less uniquely personal statements than manifestations
of concepts which are common musical property, his music has as a result
often been branded as lacking “inspiration”, “imagination”, and “expression.”
We must again force ourselves to set aside the nineteenth-century credo of
originality being the prime essential in composition, and realize that much
Western music, from the cantus firmus and parody masses of the Renaissance
through the Baroque and Classical eras, has not always placed originality as
the foremost goal of composition. Rather, what was done with the idea was
important: the germinal cell itself may have been common property, but the
“inventio” of the the work bore the composer’s unique stylistic seal. Such is
the case with Reich; it is only in the working out of the musical process that
the composer’s personal statement becomes evident. However, the mechanical
efficiency of Reich’s performing ensemble tends to lend credence to charges
that the composer’s musical processes are inexpressive and impersonal. One
could therefore say that it is less the musical content itself than the performance
situation demanded by the music which is impersonal; this observation is
bolstered by Reich’s own statements concerning the nature of his ensemble’s
performances:
The attention that mechanical playing asks for is something we
could do with more of, and the “human expressive activity” which
is assumed to be innately human is what we could do with less of
right now. That ties in with non-Western music-African drum-
ming or the Balinese gamelan -which also have an impersonality
to them as the participants accept a given situation and add their
individual contributions in the details of the working-out.’8
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380
This brings us to the important question of non-Western influence in
the music of Reich. Reich has been profoundly affected by his studies of non-
Western techniques and structures, and has undergone vast changes in his
personal style as a result. Reich’s training in African drumming (Ghana,
1970), Balinese gamelan (Seattle and Berkeley, 1973-4), and Hebrew scriptural
cantillation (New York and Jerusalem, 1976-7) has contributed not only to
alterations in his musical aesthetic during the last ten years, but also to his use
of new constructive procedures. For Reich believes not in imitating the sound
of non-Western musics (“What I don’t want to do is to go and buy a bunch of
exotic-looking drums and set up an Afrikanische Musik in New York City.”19),
but rather in learning the structural principles which govern the construction
of foreign musics, and applying these to one’s own personal style. A myriad of
Reich’s stylistic traits may either be derived from or encouraged by non-
Western influences; these include his polyrhythmic structures, constant
repetition, driving pulse, use of tonality/modality, absence of modulation,
slowness of rate of change and lack of dualism, and penchant for rigorously
worked out non-improvisatory structures. All of these aspects of non-Western
influence in Reich’s style will be discussed more fully in the analysis of his
1971 work Drumming (q.v.), along with the more complex question of how
the composer chose to emulate non-Western structural principles within his
own music.
Popular music, expecially jazz, has also influenced Reich. Reich idolized
Miles Davis and Charlie Parker in his youth, and was a jazz drummer himself;
later he became enamored of John Coltrane and his remarkable expansion of
simple two-chord structures. A concentration on percussion (stemming not
only from popular influence, but also from his own personal interest as a
drummer as well as non-Western studies) and his inclusion of such instruments
as small electric organs and saxophones belie popular influence in instrumenta-
tion. In addition, Reich’s use of amplification via individual microphones for
each instrument, and his employment of repetitive rhythms, clear tonality, and
driving pulse may all be related superficially to his knowledge of popular
music.
In recent years, however, Reich has been turning less towards non-
Western and popular musics and more towards the Western Classical heritage
for inspiration and guidance. Early in Reich’s career, Western influence was
restricted to Medieval and Baroque music. In 1971, Reich voiced the opinion
that, while he admired Bach, he felt that Perotin and the Notre Dame School
were “a kind of high point” in music history.20 Perhaps Reich was drawn to
certain aspects of the Perotin generation’s style that, in gross historical
retrospect, seem almost Reichian: the repeated, ostinato-like rapid rhythmic
patterns in the upper voices, the drone-like supporting cantus, the static
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381
modality, and above all the lack of directionality and climax. Fellow minimalist
LaMonte Young echoes Reich’s love for medieval music when he says, “I feel
that in most music peculiar to the Western hemisphere since the thirteenth
century, climax and directionality have been among the most important
guiding factors, whereas music before that time, from the chants through
organum and Machaut, uses stasis as a point of structure a little bit more the
way certain Eastern musical systems have.”21 Reich was also attracted to late
Baroque music’s unflagging rhythmic propulsion, the same reason he admired
jazz–and Stravinsky. Indicative of Reich’s recent stylistic maturation, however,
has been his re-studying of the remainder of the Western heritage. This
renewed interest in the Western tradition has profoundly affected the composer,
and will be discussed more completely in relation to three of Reich’s newest
works, Octet (1978), Music for a Large Ensemble (1978) and Variations for
Winds, Strings, and Keyboards ( 1979).
Reich’s relationship to electronic music has been an ambivalent one; he
has swayed between wholeheartedly endorsing the use of tape devices, as
exemplified by the speech-based tape pieces so typical of the earliest stage of
his career, and to an equally wholehearted rejection of every last vestige of
electronic means, as he did in 1969. Not content merely to set aside electronic
techniques within the context of his own music, he vigorously predicted the
disappearance of electronic means within new music in general: “Electronic
music as such will gradually die and be absorbed into the ongoing music of
people singing and playing instruments,”22 Reich said in 1970. More recently
(1977), Reich elaborated about why he disdains not only electronic music, but
even the use of electronic instruments within a live ensemble. He stated that,
in his opinion, the deadness in character of electronically generated sounds
(such as the quality of electric organs) was incompatible with the nature of his
music. Reich felt that in compositions such as his, which depend on repetition
and steady pulse, the vitality of character gained by using live instrumentally-
produced sounds was absolutely essential to avoid monotony of tone quality.23
Yet Reich’s decision to abandon electronic means was apparently not
binding. Variations for Winds, Strings and Keyboards (1979) again employs
electric organs within the live ensemble, for the first time since Music for
Mallet Instruments, Voices and Organ of 1973. Even more surprisingly,
Reich’s most recently premiered composition, My Name Is: Ensemble Portrait
(1980) is a pure tape piece, of the same speech-based type as those that began
his career. Reich’s earliest significant works, It ‘ Gonna Rain (1965) and
Come Out (1966) were tape compositions utilizing the verbal material of
human speech as their subject. My Name Is returns to similar methods, as will
be demonstrated at the end of this article. The composer is able to accept his
earliest tape pieces, as well as to rationalize his recent return to tape devices, by
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382
realizing that in a sense these are not electronic works at all. They are all
speech pieces, and are therefore based entirely on actual vocal sounds, not on
electronically produced tones. Reich stated recently:
In a nutshell, all the bad things I’ve had to say about electronic
music have to do with electronically generated sounds, have to do
with oscillator-based music…. I still use electric organs, but they’re
always mixed with instruments or voices. I have no such ambiguity
about [using] the voice.24
Reich’s distaste for electronically generated sounds, combined with his love for
live performance instilled by interests in jazz and non-Western music, has led
to his formation of a permanent repertory ensemble dedicated to the perform-
ance of his music. Steve Reich and Musicians, as his performing group is
called, began in 1966 with three musicians and has grown in numbers over
the years depending on the requirements of each new composition; it reached
twenty-seven members for Music for a Large Ensemble (1978). Significantly,
despite his self-acknowledged limitations as a percussionist and keyboard
player, Reich decided that in one capacity or another he would perform in all
his compositions. “It seemed clear [to me] that a healthy musical situation
would only result when the functions of composer and performer were
united.”25 The result has been an emotional and psychological bond between
composer and performers that makes the ensemble’s concerts into riveting
experiences for participants and listeners alike.
At this juncture, it may be useful to relay some biographical material
concerning Steve Reich, along with the telling evidence of diverse compo-
sitional influences it provides. Reich’s approach to composition and his stylistic
maturation has progressed in gradual, purposeful steps over the past sixteen
years; consequently, a combined recounting of Reich’s life with a detailed
discussion of the composer’s major works will be attempted here.
Steve Reich was born on October 3, 1936 in New York. His youthful
musical training included studies in piano and percussion, the latter under
Roland Koloff, now the principal tympanist of the New York Philharmonic.
By the time Reich was a teenager, his lifelong musical tastes had begun to
form, revealing a distinct predeliction for music with an unvarying pulse and a
clear tonal center; he was especially enamored of Bach, Stravinsky, Miles
Davis, Charlie Parker and Kenny Clarke. From 1953 to 1957, Reich was a
student at Cornell University, majoring in philosophy. At Cornell, he enrolled
in several courses taught by William Austin, and as a result was exposed to a
wider variety of twentieth-century music and jazz, as well as being introduced
to non-Western musics. To his credit, Austin repeatedly encouraged his young
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383
student to pursue composition as a career, a goal Reich evidently desired but
also feared, feeling he was too old to start studying music on a full-time basis.26
After graduating from Cornell, Reich began private composition lessons
in New York with Hall Overton, which lasted from 1957-1958. Reich
enrolled at the Juilliard School in 1958 as a composition student, studying
with William Bergsma and Vincent Perischetti. His early Juilliard works were
in the conventional free atonal idiom of the time. In 1961, Reich left Juilliard
to study composition at Mills College in California, where he worked with
Luciano Berio and Darius Milhaud. During his studies of serial technique with
Berio, conflicts arose between Reich’s love for tonality and steady rhythmic
pulse on the one hand, and the need to write in the accepted serial idiom on the
other. Berio saw that Reich did not transpose, invert, or retrograde his rows,
but that he merely repeated them with rhythmic re-groupings. Says Reich:
“Berio noticed that I was repeating this particular twelve-tone row over and
over and letting it evolve into a static thing, and he said to me one day, ‘If you
want to write tonal music, why don’t you write tonal music?’ ” Reich continues:
That was a very helpful remark for me, because I saw I was
doing what I intuitively wanted to do. As a child, I’d listened to a
lot of pop music, and in my teens to a lot of jazz – … music that I
found extremely attractive but which was obviously and unabash-
edly tonal.. . .I remember, when I first went to Juilliard, feeling a
distinct pull between the kind of music offered me as a model-
atonal, whether twelve-tone or freely atonal–and on the other
hand, music of let’s say John Coltrane, music essentially built up
of one or two chords. What moved me emotionally was always
music built around one tonal center.27
Twelve-tone technique had taught Reich to respect a “systematic, rigorous
approach to composition”,28 but when Reich graduated from Mills College
with his Master’s degree in 1963, he finally knew his skill lay in writing music
with a clear tonal center.
Reich’s career as a composer began in San Francisco in 1963. His early
compositions included several film soundtracks for filmmaker Robert Nelson
(The Plastic Haircut and Oh Dem Watermelons), a work for a production of
the San Francisco Mime Troupe (Ubu Roi), and tape pieces performed at the
San Francisco Tape Music Center. The latter, all based on sounds of the
outside world rather than on electronically sunthesized materials created in
the studio, indlude a collage-like tape work called Livelihood, which utilized
street and passenger noises recorded while Reich was driving a taxicab around
San Francisco.29
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384
Reich’s first two important works were both tape pieces, It’s Gonna
Rain (1965) and Come Out (1966). Both were based solely on recorded verbal
material, in It’s Gonna Rain the voice of a Black street preacher warning of the
dangers of the impending Flood, in Come Out the voice of a Harlem ghetto
boy. Early in 1965, Reich discovered that, by making tape loops of these
already remarkably melodious voices, he could both heighten the musical
quality of the speech, as well as intensifying the meaning of the words. This
was manifested in sound, of course, as incessant repetition. It was no accident
that Reich came to employ the technique of constant repetition; though he had
already been working with tape loops, the final impetus resulted from the
assistance he provided Terry Riley in the latter’s premiere of In C (1964). In C
is certainly not a Reichian work, due to its use of unstructured improvisatory
elements and performer choice, but its employment of a constant unvarying
pulse, its prolonged rhythmic/melodic repetitions, and its static tonality must
all surely have impressed Reich. But Reich’s problem was to find his own way
of approaching repetition as a musical technique, without merely imitating
Riley’s breakthrough. Reich’s revelation occurred as follows:
I discovered that the most interesting music of all was made by
simply lining the loops up in unison, and letting them slowly shift
out of phase with each other. As I listened to this gradual phase
shifting process, I began to realize that it was an extraordinary
form of musical structure. This process struck me as a way of
going through a number of relationships between two identities
without ever having any transitions. It was a seamless, continuous,
uninterrupted musical process.30
Reich had stumbled across the technique of “phasing”, the particular
musical process that was to hold his attention to such an extent that every
composition written between 1965 and 1971 (except Four Organs, 1970)
employs the phasing technique in one way or another. In phasing, two or more
identical melodic and/or rhythmic patterns very gradually change in their
rhythmic relationships to one another during the course of the work. Even-
tually, as the process progresses, new patterns evolve of their own accord.
In It’s Gonna Rain, completed January 1965 and based entirely on the
words of the black street preacher, Brother Walter, the phasing process is first
applied. The preacher’s unusually expressive, almost melodic enunciation of
the title phrase in itself resembles the musical line of Example 1. Beginning in
unison, two tape loops of this same verbal material eventually move one beat
apart, then two, and so on as they gradually go “out of synch” with each other.
As the process of phasing progresses, new and unexpected polyrhythmic
configurations, resulting harmonic combinations, and melodic patterns evolve,
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385
since the two channels of tape constantly change their relationship to one
another.
It’s Gonna Rain is two parts, the first taking the title phrase from a
unison synchronization of two channels through a complete shift of phase,
and then back to the original unison again. Part Two is made from a
considerably longer tape loop, which begins with two unison channels
pronouncing a continuation of the title phrase. But in Part Two, Reich divides
the channels into four and finally eight voices as the phase shifts. These
multiple lines, all moving in and out of phase with one another, produce a
dizzying combination of new resulting harmonic, melodic and rhythmic
patterns far more complex than those of Part One, as well as heightening the
already present speech elements. By the end of the work we are, in essence,
listening to a kaleidoscopic, subtly shifting drone of sound.
Reich’s next work, Come Out (1966) is essentially a refinement of the
same phasing process employed in It ‘s Gonna Rain. Composed for a Town Hall
benefit given to help six boys arrested in the 1964 Harlem riots gain a retrial,
it is based upon the inherently musical vice of Donald Hamm, one of the six
involved. As in the case of Brother Walter, Hamm’s pronunciation of the
phrase “come out to show them” already contains within it a distinctive
rhythmic/melodic profile (See Example 2).
Come Out is similar in conception to It ‘s Gonna Rain, beginning with
two unison channels but soon allowing one of the parts to phase forward.
Later, as the phasing process progresses, Reich divides the two channels into
four and finally eight voices, all phasing against one another. The myriad of
resulting harmonic, melodic, and polyrhythmic combinations, mostly unfore-
seen by the composer, demonstrates that the musical process of phasing, once
set into motion, progresses entirely on its own. “The experience of that
musical process is, above all else, impersonal; it just goes its [own] way… . Once
the process has been set up it inexorably works itself out.”31 Come Out has
been likened by some critics to the “aural equivalent of op art.”32 Just as in op
art our eyes perceive visual illusions which are not present in reality, such as
reversing cubes, three-dimensional effects, and perspective shifts, so too in
Come Out our ears psycho-acoustically fixate upon various transitory patterns
which arise out of the phasing process. It is the presence of these dazzling,
constantly shifting figures that makes the early tape pieces interesting to hear
over and over again. Reich calls these “resulting patterns”, and they are of
great significance for his later compositional development.
In 1966, Reich composed the last of his early tape pieces, entitled
Melodica. It uses the same phasing process as Come Out, but here, instead of
phasing verbal elements, musical pitches are employed. Named after the
plastic toy recorder on which the pitches were played, Melodica, according to
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386
Reich, at the time “felt like a transition from tape music to instrumental
music.”” Yet, in 1966, the composer had reached what must have seemed to
him an impasse: how could he transfer the electronically discovered phasing
process to live musicians?
Nineteen sixty-six was a very depressing year. I began to feel
like a mad scientist trapped in a lab: I had discovered the phasing
process of Come Out and didn’t want to turn my back on it, yet I
didn’t know how to do it live, and I was aching to do some
instrumental 34
The solution to the problem came late in 1966. Reich made a tape loop
of a brief, repetitive piano pattern, and then attempted to play the same figure
on the keyboard against the tape loop. Just as he had done in Come Out, he
tried to phase gradually ahead of the constant unvarying loop pattern–yet
here, the challenge was to see if a life performer could accmpplish what had
been so easy to do electronically. “I found to my surprise, that while I lacked
the perfection of the machine, I could give a fair approximation of it [the
phasing process] while enjoying a new and extremely satisfying way of
playing .. ..”I3
The obvious next step was to see if the phasing process could be
accomplished without any electronic means whatsoever. Early in 1967, Reich
and a friend, sitting at two different pianos, attempted to duplicate the phasing
process: one performer remained on a fixed rhythmic pattern while the other
performer gradually phased forwards, one beat at a time. The result was the
first live phase composition, Piano Phase (1967).36 In this work (Example 3),
two performers begin in unison playing the identical rhythmic/melodic pattern.
As the first performer’s pattern remains unvarying, the second pianist increases
his tempo very slightly (this gradual phasing process is indicated in Reich’s
scores by dotted lines between measures) until he is finally one sixteenth note
ahead of the unchanged figure of the first pianist. The phasing process pauses
at this point, as the newly shifted rhythmic configuration is repeated several
times. Soon, however, the second pianist again moves slowly forward of the
first, finally ending two sixteenth notes ahead of the original pattern. This
sequence of gradual phase shift and repetition is repeated until the two pianists
are back in unison; at this juncture the pattern changes and the whole process
begins anew.
Finally successful in his transference of phasing to live music, Reich
began to see his earlier tape pieces in a different light. He realized that they
were indicative of a trend that was to occur several times in his career -the
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387
exchange of ideas from electronic music to live performance. Reich now
viewed It ‘s Gonna Rain, Come Out, and Melodica as “realizations of an idea
that was indigenous to machines, and on the other hand, the gateway to some
instrumental music I would never have come to by listening to any other
Western, or for that matter, non-Western music.”37 This cross-fertilization of
instrumental music by ideas generated in the electronic studio becomes
apparent once more in Reich’s Four Organs (q.v.) of 1970.
Reich’s next live phase composition, Violin Phase, was completed in
October 1967. Scored for four violins, or one live violin plus three channels of
taped violin, Violin Phase adds two new refinements to the phasing process:
firstly, four voices rather than two are now phasing against each other;
secondly, Reich now begins to make conscious use of the entirely unexpected
“resulting patterns” that arise out of the phasing procedure. In the manner in
which Violin Phase is most frequently performed, the live violinist plays
against one, two, and finally three pre-recorded tapes of himself. The same
twelve-beat rhythmic/melodic figure is recorded on all three tape channels,
but in different phase positions (i.e., the same pattern but with three different
downbeats): Track One is four beats behind Track Two, while Track Two is
eight beats behind Track Three. Besides the different stationary phase positions
of the tape, the performer himself carries out a live phasing process by playing
the same figure as that of the tapes, but moving slowly ahead of the various
channels.
Most significant in Violin Phase is Reich’s conscious employment of
the unexpected resulting patterns. These figures, unforeseen polyrhythmic,
melodic, and harmonic combinations that occur as a result of identical material
being phased against itself, are constantly in a state of flux. In two sections of
the piece the live violinist momentarily doubles some of the pre-existing
resulting patterns that have arisen due to the phasing process progressing in
the three taped channels. Several of the doubled patterns are actually suggested
by the composer, while others are chosen by the performer in rehearsal. The
score itself (see Example 4) is notated in such a way that the three tape tracks,
besides being indicated on separate staves, are also written on one staff in
composite form; the latter version allows the live violinist to see the various
possible resulting patterns more clearly. The live violinist’s process of “pointing
out” the resulting patterns guides the listener’s perceptions and opens up the
listener’s ears to melodic combinations he or she may not have heard: the
effect is almost that of bringing a transitory aural illusion into the realm of
reality.
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r +-s ,>-, ,
Example 1. Steve Reich, It’s Gonna Rain (1965).
Approximate transcription of title phrase of tape.
Come oat to show them)
Example 2. Steve Reich, Come Out (1966).
Approximate transcription of title phrase of tape.
1 “J. 2. hose II i Pp
‘7H …. . …….. W-2 = n …. pf”01
‘iA f# -W F t f tti 4 O 4-t i ad 4r eccooa ja – Ks k H ” “A 0 a4 u . T~q wC~q P’am”Sc Itckves kts +Cf 2( al 4f c
iz?081(1 W uto 0 ‘ d Ie -first Ad( (s&7 i” Ac-70 M&Ovl?) Ae 14 &w sief-aA X?? 04-.4A Jf u 1. ‘ r4e dO (00 jit~t 4is Ik4wt( MowoV w .c -ft 5ec I*C? dA4 ? k C” Ad -trFa tof eme -tV 4& 4t4 5C f OA4* ffrrl
Example 3. Steve Reich, Piano Phase (1967), mm. 1-3.
Copyright 1967 by Steve Reich.
Used by permission.
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I+-,” !I ANN
v~otil i
r7in ..
,, ? IL. [
iio%.”3 IIi i I Iip ii _.ml I _i . i
4k 8
9 9
–4L
? mdPr4 oI Y 44?J5 r 2r43 is ~~ ‘. dL( d 3 r Nt*ii oJG a8 sfd -f to & tioi1 q. – SL -VI” 4 5″4L Spike4Pet
Example 4. Steve Reich, Violin Phase (1967), m. 16.
Copyright 1967 by Steve Reich.
Used by permission.
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NOTES
‘A representative sampling of some of the more important European articles
concerning Reich’s music would include the following: Clytus Gottwald, “Signale
zwischen Exotik und Industie: Steve Reich auf der Suche nach einer neuen
Identitit von Klange und Struktur”, Melos/Neue Zeitschrift fir Musik, (January-
February 1975), pp. 3-6; Clytus Gottwald, “Tendenzen der neuen Musik in den
USA: Gy6gy Ligeti im Gesprach mit Clytus Gottwald”, Musik und Bildung, VIII
(February 1976), pp. 57-61; Michael Nyman, Steve Reich: Interview with Michael
Nyman”, Musical Times, CXII (March 1971), pp. 229-231′; Michael Nyman,
“Steve Reich: Interview with Michael Nynam”, Music and Musicians, XXV
(January 1977), pp. 18-19; Michael Nyman, “SR–Mysteries of the Phase”,
Music and Musicians, XX (February 1972), pp. 20-21.
2 Milton Babbitt, “Who Cares if you Listen?”, in Contemporary Composers on
Contemporary Music, ed. Elliott Schwartz and Barney Childs (New Yoirk, 1967),
p. 249.
3David Sterritt, “Tradition Reseen: Composer Steve Reich”, Christian Science
Monitor, 23 October 1980, p. 20.
4 The following is a brief discography of recordings of Reich’s music available in
America, here listed chronologically according to date of release: Come Out, in
New Sounds in Electronic Music, Odyssey, 32-16-0160, 1967; It’s Gonna Rain
and Violin Phase, in Live/Electric, with Paul Zukofsky for Violin Phase, Columbia
MS-7265, 1969, since deleted; Four Organs, with Michael Tilson Thomas, Ralph
Gierson. Roger Kellaway, Steve Reich, Tom Raney, Angel, S-36059, 1973;
Drumming, Music for Mallet Instruments, Voices and Organ, Six Pianos, with
Steve Reich and Musicians, Deutsche Grammophon Gesellschaft, 2740-106,
1974; Music for Eighteen Musicians, with Steve Reich and Musicians, ECM
Records, ECM-1-1129, 1978; Octet, Music for a Large Ensemble, Violin Phase,
Shem Guibbory for Violin Phase, Steve Reich and Musicians, ECM Records,
ECM-1-1168, 1980.
‘Universal Edition published the following Reich works in 1980, here listed
chronologically by date of composition: Piano Phase (1967), UE 16156; Violin
Phase (1967), UE 16185, Pendulum Music (1968), UE 16155; Four Organs
(1970), UE 16183; Phase Patterns (1970), UE 16184); Clapping Music (1972),
UE 16182; Music for Pieces of Wood (1973), UE 16219.
6 Occasionally, one will stumble across a fine article dealing with Reich in the
mass media; a selected few are listed here chronologically: Donal Henahan,
“Reich? Philharmonic? Paradiddling?”, The New York Times, 24 October 1971,
sec. 2, pp. 13-14; Kenneth Terry, “Steve Reich”, Downbeat, 11 August 1977, pp.
38-40; Nicolas Kenyon, “Spaced Out”, The New Yorker, 10 March 1980, pp.
124-127; Gregory Sandow, “Steve Reich: Something New”, The Village Voice,
10 March 1980, p. 74; Joan LaBarbara, “Three by Reich”, High Fidelity/Musical
America, June 1980, pp. MA 12-13.
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391
7 According to promotional material kindly provided by Reich’s management,
Lynn Garon Management of New York.
8 In a letter to Eric Salzman, he chose to characterize his music as being
“structural”, rather than “minimal”.
9 Steve Reich, Jacket Notes, Come Out, in New Sounds in Electronic Music,
Odyssey, 32-16-0160, 1967.
10 Steve Reich, Writings About Music (Halifax, N.S. and New York, 1974), p. 10.
11 Tom Johnson, “The New Tonality”, The Village Voice, 16 October 1978, pp.
115-116.
12 An exception to this statement would be the chaconne-based composition,
Variations for Winds, Strings and Keyboards ( 1979, q.v.)
13 Reich, p. 28.
14 Other composers also played a role in re-introducing “pulse” into contemporary
music as an important parameter; Terry Riley’s In C (1964) was an especially
seminal work in this respect.
“‘Sterritt, p.21
16 Gottwald, “Signale zwischen Exotik und Industrie”, p. 6.
17 Reich, p. 9.
18 Nyman, “Reich: Interview” (1971), p. 230.
19 Nyman, p. 230.
20 Henahan, sec. 2, p. 13.
21 Richard Kostelanetz, The Theatre of Mixed Means (New York, 1968), p. 188.
A useful interview with LaMonte Young, conducted by Kostelanetz, is included in
pp. 183-218 of this book.
22 Reich, p. 28.
23 Terry, p. 39.
24 From a personal interview with the composer, conducted by the author on
January 2, 1981.
25 Reich, p. 45.
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392
26 This entire biographical summary of Reich’s early career is based upon material
in Wayne Alpern, “An Interview with Steve Reich”, New York Arts Journal,
XVII (January 1980), p. 15; “Interview: Steve Reich:, EAM Accents (European-
American Music Corporation), Spring-Summer 1980, p. 5; Terry, pp. 38-39;
promotional material provided by Lynn Garon Management.
27 Henahan, sec. 2, p. 14.
28 “Interview: Steve Reich,” EAM Accents, p. 6.
29 Catherine O’Neill, “A Modern Composer Whose Rhythms Ride the Ages”, The
Chronical Review, 13 November 1978, p. 21.
30 Reich, p. 50.
31 Reich, p. 50.
32 Myron Bennett, “Music as Furniture”, High Fidelity, February 1972, p. 64.
33 Reich, p. 51.
34 Nyman, “Reich: Interview” (1971), p. 230.
35 Reich, p. 51.
36 For a description of the origin and structure of Piano Phase, see Reich, pp. 51-
52.
37 Reich, p. 53.
[To Be Continued]
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- Contents
- Issue Table of Contents
p. [373]
p. 374
p. 375
p. 376
p. 377
p. 378
p. 379
p. 380
p. 381
p. 382
p. 383
p. 384
p. 385
p. 386
p. 387
p. [388]
p. [389]
p. [390]
p. 391
p. 392
Perspectives of New Music, Vol. 19, No. 1/2 (Autumn, 1980 – Summer, 1981) pp. 1-570
Front Matter [pp. 1-513]
For Aaron Copland at 80
Aaronesque [pp. 2-3]
An Improvisation for A. C. [pp. 4-7]
For Aaron from Bill [pp. 8]
A. C. [pp. 9]
Three Variations on Simple Gifts [pp. 10-12]
For Aaron [pp. 13-14]
Ode [pp. 15-17]
A Roust [pp. 18-19]
For Aaron an Offering [pp. 20]
A Reminiscence [pp. 21]
Light and Splendour [pp. 22-30]
Aaron Copland and American Music [pp. 31-33]
Footnote to Futurism (For Aaron) [pp. 34]
For Aaron, with Admiration &Affection [pp. 35]
To Aaron at Eighty: A Toast for the Banquet That Didn’t Take Place [pp. 36-39]
Short Pieces for Piano (For Aaron) [pp. 40-42]
Variations for a Quiet Man [pp. 43-45]
Sketch/Interlude for Aaron [pp. 46]
A Note for Aaron [pp. 47]
Autumn Pastorale: For Piano [pp. 48-50]
All’s in a Name. Aaron by Any Other Name Might Sound Less Suite. And Ned Could Fade Away Entire….. [pp. 51]
Aaron Copland [pp. 52-53]
A. C. 80 [pp. 54-57]
Fantasy quasi Theme and Variation: Inspired by the Piano Variations of Aaron Copland [pp. 58-65]
To Aaron Copland [pp. 66]
Copland’s Style [pp. 67-89]
A Reflection: Copland at Eighty [pp. 90]
Prayer from Voices of Peace [pp. 91]
Persistently Pastoral: Aaron Copland [pp. 92-96]
A San Diego-Centered Anthology
Foreword [pp. 101-110]
The Percussion Console [pp. 111-114]
The Dissimulated Voice [pp. 115-133]
Writing [pp. 135-162+164-183]
The Composer Seduced into Programming [pp. 184-198]
In Re: Collaboration [pp. 200-211]
The Futures of Music [pp. 212-226]
An Open Letter to Governmental Arts Agencies and Private Arts Foundations [pp. 227-265]
Composers
Earl Kim: Earthlight [pp. 269-277]
An Anatomy of Intentions: Observations on Seymour Shifrin’s Responses, for Solo Piano [pp. 278-304]
Remembering Seymour Shifrin (1926-80) [pp. 305-307]
Charts [pp. 309-331]
Musical Essence and Perception [pp. 333-349]
John Cage’s Variations II: The Morphology of a Global Structure [pp. 351-371]
Steve Reich: Music as a Gradual Process: Part I [pp. 373-392]
Rochberg the Progressive [pp. 395-407]
The Theory of Sonic Awareness in the Greeting by Pauline Oliveros [pp. 409-416]
Events/Reviews
Darmstadt 1980 [pp. 420-441]
Computer Music Conference in New York, 1980 [pp. 442-448]
Women’s Music in New York, 1981 [pp. 449+451+453-462]
Stravinsky Pre-Centenary [pp. 464-477]
1981 A. S. U. C. Festival/Conference [pp. 479-482]
Bowling Green State University Second Annual New Music Festival: A Review [pp. 483-490]
Review: untitled [pp. 491-500]
Review: untitled [pp. 501-506]
Review: untitled [pp. 507-511]
Colloquy
Project: A Piece in Three Movements for One Speaking Voice [pp. 515-518]
10 Sound Texts [pp. 520-529+531]
A Tombeau for John Lennon 1940 – 1980 [pp. 532-535]
Back Matter [pp. 536-570]
Steve Reich: Music as a Gradual Process Part II
Author(s):
K. Robert Schwarz
Source: Perspectives of New Music, Vol. 20, No. 1/2 (Autumn, 1981 – Summer, 1982), pp.
225-286
Published by: Perspectives of New Music
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STEVE REICH: MUSIC AS A
GRADUAL PROCESS
PART II
K. Robert Schwarz
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In 1968, Steve Reich codified his compositional aesthetic in the single
most important essay he has ever written, “Music as a Gradual Process.” This
article, which has been reprinted several times,38 must be examined in detail,
as it is here that Reich clarifies all the trends that have been developing in his
music since 1965, and sets the direction for the future.
The terse, inexpressive wording of “Music as a Gradual Process”
serves to reinforce four important points in the concisest of manners. First of
all, Reich is concerned with clarity of structure, which he feels can only be
achieved by creating compositions in which structure (“process”) and musical
content are identical. He has no use for hidden constructive devices that serve
to obscure a musical process. Secondly, musical processes, once set into
motion, have a life of their own, and need no further meddling from the
composer to progress; they are impersonal and objective procedures. Thirdly,
improvisation can play no part in a musical process; on the contrary, one must
subvert one’s own feelings and allow the inexorable forward thrust of the
process to take charge. Lastly, no matter how objective the process, unexpected
events will still occur: these are the resulting patterns.
To appreciate these concepts in Reich’s own distinctive wording,
excerpts from “Music as a Gradual Process” are quoted below. One should
realize, however, that Reich has since disavowed many of these viewpoints, at
least for his own recent compositions. Nevertheless, this essay provides a
framework for our understanding of Reich’s music through 1971.
I do not mean the process of composition, but rather pieces of
music that are, literally, processes. The distinctive thing about
musical processes is that they determine the note-to-note … details
and the overall form simultaneously. (Think of a round or infinite
canon)…. One can’t improvise in a musical process-the concepts
are mutually exclusive….
I am interested in perceptible processes. I want to be able to hear
the processes happening throughout the sounding music. To
facilitate closely detailed listening, a musical process should happen
extremely gradually… so slowly and gradually that listening to it
resembles watching the minute hand on a watch -you can perceive
it moving after you stay with it a little while….Though I may
have the pleasure of discovering musical processes and composing
the musical material to run through them, once the process is set
up and loaded, it runs by itself….
What I’m interested in is a compositional process and a sounding
music that are one and the same thing….The use of hidden
structural devices never appealed to me. Even when all the cards
are on the table and everyone hears what is gradually happening in
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227
a musical process, there are still enough mysteries to satisfy all.
These mysteries are the impersonal, unintended, psycho-acoustic
by-products of the intended process. These might include sub-
melodies heard within repeated melodic patterns, stereophonic
effects due to listener location, slight irregularities in performance,
harmonics, difference tones, etc….
While performing and listening to gradual musical process one
can participate in a particularly liberating and impersonal kind of
ritual. Focusing in on the musical process makes possible that
shift of attention away from he and she and you and me outwards
(or inwards) towards it.
The years 1968-9 saw a short-lived revival of Reich’s interest in
employing electronics to perform the phasing process. Pendulum Music,
completed in August of 1968, involves allowing four suspended microphones
to swing freely over four upturned loudspeakers. The result is a series of
loosely phased feedback pulses, which gain in intensity as the microphones
swing closer to their respective loudspeakers. As the precise phasing of the
pulses produced by the swaying microphones is largely uncontrollable, this
work has strong overtones of random elements-chance-making it atypical
of Reich’s output as a whole, surrounded as it is by rigorously structured
musical process compositions.39
At the same time that Reich was working on Pendulum Music, he
began to become fascinated with the idea of developing and constructing an
electronic device that would be designed specifically to carry out the phasing
process, a device that could be “played” in a performance situation to simulate
a particular variety of phasing activity. The phasing process desired here was
not the earlier type which had involved changing the rhythmic relationship
between two identical melodic patterns. Instead, Reich was now interested in
starting with a chord, and then very gradually shifting individual tones from
within the sonority out of phase one at a time, so that what began as a vertical
harmonic entity would eventually end up as a series of infinitely changing
horizontal melodic patterns (Example 5). Between February 1968 and early
1969, with the assistance of electronic engineers from New Jersey Bell
Laboratories, Reich constructed a device that would be capable of such a
musical process. The finished product, grandly called “The Phase Shifting
Pulse Gate”, is described in great detail by Reich,40 and will not be discussed
from a technical viewpoint here. Reich unveiled his new invention on May 27,
1969 when, as part of an artistic and musical exhibition entitled Anti-Illusion,
he performed using the “Pulse Gate” at New York’s Whitney Museum.
Despite a year and a half of devoting all his energies to working with
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Example 5. Steve Reich, Pulse Music (1969) for Phase Shifting Pulse Gate. This content downloaded from 130.166.3.5 on Mon, 11 May 2020 01:45:47 UTC 229
electronics, Reich returned home from the Whitney Museum sorely disap- The “perfection” of rhythmic execution of the Gate… was stiff Reich’s conclusion was: “I felt very clearly then that I did not wish to
have any involvement with electronic music again.”42 However, as was noted Though he probably did not realize it in 1969, the energy invested in not been employed in any of his electronic compositions (i.e., the aspect of the
Gate that controlled the duration of individual pulses), and apply it to live horizontal bar graph in time.”44 Therefore, Four Organs, like Piano and from electro-mechanical devices and processes to instrumental music has ideas for the ongoing history of instrumental and vocal music.”45
Four Organs is a gradual process piece, yet of all the works Reich This content downloaded from 130.166.3.5 on Mon, 11 May 2020 01:45:47 UTC 230
is stated at the outset (see Example 6a). It is perhaps Reich’s ultimate changes of pitch, texture, timbre, or dynamics. All alterations consist of This simplistic concept results, surprisingly enough, in a work of that none of the early phase pieces possess. Four Organs is one of the clearest Almost immediately after Four Organs was completed in 1970, Reich
composed another work for four electric organs, this time without maracas. (consisting here of the alternation of the left and right hands of each player in
the sequence L-R-L-L-R-L-R-R) becomes the single unchanging rhythmic basis the by, extremely interesting. I guess I’m a better percussion player than a In June of 1970, one of the great turning points of Reich’s career and to experience drumming as a serious music.”47 Once in Ghana, Reich African music.50 He realized that African rhythmic procedure consisted of
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Example 6a. Steve Reich, Four Organs (1970), mm. 1-4. * 4. &- W 4* O- 0.
:-: ::. – I t t T I I t r ‘t Trf t 1 – – r’ ~ ~ ? 0 B y i? – ‘ , i a o 4. I . 4. 2 – r o + 9 * t * * t *** 1 t + + *? e.* 1. 7 + . 1 t
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20 1 Io ^ t o S + + 1 .9 + . 4 l( + * ^ 1+c* 10. v – ?- V. 4-j -1- II’ 4 to + 1 -4 1+f IL 4 * Io 4 + 2 0 + + lo +4 70 + 4′ * * It I + 10 ( -o )tv(5 + *e)+(4 I s)-v .0 Example 6b. Steve Reich, Four Organs, m. 42. 1
4. –
4
“7-“‘- . .. > r -7 – 7 ‘ – ~~~~~~~~~~~”- ~ -‘ I – – – -‘ ” – ‘ –
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“several repeating patterns of the same or related lengths and each with its Reich was also intrigued by the African method of organizing the Master drummer switches to a new pattern, the other drummers change to a
different appropriate response figure. This structure of statement-response Lastly, Reich was encouraged by the presence in Africa of musical improvisation on the part of the performers. All members of the African framework of a live group performance. In addition, the patterns themselves, Immediately upon returning from Africa, Reich began to work on his instruments could be used to produce music that was genuinely richer in Before analyzing Drumming, it would be wise to deal with the difficult
problem of how non-Western music in general has influenced Reich’s style. To and Berkeley in the summers of 1973 and 1974, under the auspices of the that of Ghana or Bali, could honestly employ non-Western techniques. In This content downloaded from 130.166.3.5 on Mon, 11 May 2020 01:45:47 UTC 234
worthy efforts, but neither involving composition. Alternatively, one might The least interesting form of influence, to my mind, is that of Alternately, one can create a music with one’s own sound that is Beginning with Drumming, and extending through Music for Mallet composer’s own personal style. Many of these non-Western techniques had techniques may derive as much from Reich’s youthful jazz studies as from his
African journey; it is often difficult to decide where popular influence ends point to Reich’s static non-modulatory structures. The idea of stasis itself, of a This content downloaded from 130.166.3.5 on Mon, 11 May 2020 01:45:47 UTC 235
be related to non-Western attitudes towards time. In his choice of instruments
and timbral combinations, and in his predilection for percussion (including,
besides drums, the mallet instruments and metallophones so typical of the Drumming makes use of most of the above techniques and, as a result longer the principal structural device that it was in earlier pieces. Within the Drumming utilizes three new techniques, each of which becomes of for beats) within a constantly repeating rhythmic cycle.”55 Reich calls these
two opposite procedures, respectively, “rhythmic construction” and “rhythmic
reduction”; they are the means by which the process of phasing is introduced, from what may begin as a single beat within a cycle of rests (see Example 8). one at a time, for beats, and the pattern is dismantled step by step in a mirror has taken place in several voices, one of the performers may begin the familiar The second innovation of Drumming involves new experiments with This was necessary, says Reich, as “the phasing process is only clearly audible and therefore combine to form one complete resulting pattern in the ear.”56 Here we have clear evidence of Reich’s new willingness to compromise This content downloaded from 130.166.3.5 on Mon, 11 May 2020 01:45:47 UTC ? HIRD STtlgs
.’ ?^lR I _’ ot J’ 7,
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[ ; ^ 7 hu bNIAt ORCS f S i&M ets tq d s setxl v e lt L P.2 q I u (.US) a Example 8. Steve Reich, Drumming (1971), mm. 1-8. This content downloaded from 130.166.3.5 on Mon, 11 May 2020 01:45:47 UTC 237
-in favor of a new richness of sonority. The method of introducing new The third and final innovation of Drumming involves “the use of the
human voice to become part of the musical ensemble by imitating the exact Phase emphasized the resulting patterns which arose from the three taped most closely with the timbres of the various instrumental families employed in
Drumming. Part One of Drumming is scored for four pairs of tuned bongo Here, Reich employs whistling to blend with the glockenspiel’s lower range, three sections of the work, also combines all the above vocal techniques, each The four sections of Drumming are not separated by any change of The process of rhythmic construction can be seen most clearly at the a time, construct the twelve-beat pattern which serves as the rhythmic basis
for the entire ninety-minute composition. Once the pattern has been completely unusual amount of performer choice involved in Drumming-during the This content downloaded from 130.166.3.5 on Mon, 11 May 2020 01:45:47 UTC 238
forward to the next stage in pattern formation (i.e., the addition of a new beat)
at the same time. And throughout the work, the number of repeats to which a
given pattern is subjected is decided by the performers.
Within any one of the four sections of Drumming, contrasts in texture
may be introduced by adding performers, by rhythmic reduction (resulting in a
simultaneous reduction in the instrumental forces) and a subsequent repetition The previously described “timbral modulation” links the four sections the truly progressive portion of the work in terms of Reich’s later output, for
here Reich freely intermingles the various tone colors provided by the three hearing the same rhythmic pattern for over an hour. In Part Four, significantly,
the phasing process becomes nearly impossible to follow, due to the luxuriant clarity of structure and audibility of procedure, as demanded in “Music as a full sonorous texture, with beauty of sound more important than structural Six Pianos (1973), Reich’s next significant composition, at first glance Four of Drumming. Again, as in earlier works, an ensemble of identical upright spinet pianos were chosen rather than grands, as the small instruments intrusive resonance of grand pianos, while at the same time the pianists could
sit physically close to one another and be able to perceive the musical process If Six Pianos is not a timbral advance over Drumming, it does however
utilize some of Drumming’s structural innovations. Six Pianos marked the the process of rhythmic construction (the formation of a pattern by substituting
beats for rests) that was employed in Drumming.62 However, the method in This content downloaded from 130.166.3.5 on Mon, 11 May 2020 01:45:47 UTC 239
underlying accompaniment of any kind during the drummer’s construction the rhythmic construction takes place against several other performers already
playing the identical rhythmic pattern in another metric position (see Example
9). The constructed rhythmic figure, built up one beat at a time by two of the
pianos, is two eighth notes apart from the existing four-piano pattern. Once
the construction is complete, the effect is that of an identical pattern being arriving at the result are entirely different: “instead of slow shifts of phase, achieving the effect of having constructed a canon (phased) is much less Six Pianos ‘chief advance over Drumming is in its harmonic framework.
The composition is divided into three sections, each of which is delimited by a traditional means of sustaining a lengthy work; the employment of contrasting
keys is certainly more typical of Western music than the prolonged “mono-
tonal” state of Drumming. Yet there is no modulation in Six Pianos: tonality progression, the new key simply being juxtaposed alongside the previous one. merely a refinement of the method of “drumming on the keyboard” that Reich
employed in Phase Patterns. Again, the pianos are regarded as sets of “tuned
drums”, and the musical material, with its division of the basic rhythmic output, due to its consistent application of the principle of rhythmic construc- It is difficult, no matter who the composer, to describe style change compositions assigned to the style periods on either side. Yet it seems clear This content downloaded from 130.166.3.5 on Mon, 11 May 2020 01:45:47 UTC Example 9. Steve Reich, Six Pianos (1973), mm. 1-8. This content downloaded from 130.166.3.5 on Mon, 11 May 2020 01:45:47 UTC 241
lessening of concern in the surface clarity and audibility of the musical reflect Reich’s shift away from his dogmatic, austerely minimal earlier aesthetic. Depending on one’s point of view, Music for Mallet Instruments, Voices and Mallet has been described as a breakthrough piece, combining for the
first time the rhythmic intricacies of works such as Drumming and Six Pianos
(both of which primarily had employed notes of short time values) with the tion as used in Six Pianos, namely “that of constructing, beat by beat, a the remaining glockenspiel and marimba commence a gradual process of 10). Meanwhile, an independent second process takes place in the voices, Four Organs but here, rather than prolonging one note at a time as in the The most interesting factor about these two processes is how the instruments as the various phase positions are formed, acts as a triggering This content downloaded from 130.166.3.5 on Mon, 11 May 2020 01:45:47 UTC 1 ‘I p* “-J6, Wi $ i
“L’ ^^rt tTLriL Example 10. Steve Reich, Music for Mallet Instruments, Voices, and Organ f, -11=. I ^-j
This content downloaded from 130.166.3.5 on Mon, 11 May 2020 01:45:47 UTC 243
By the middle of each of the four sections of Mallet, the various phase positions and into phase unison, thus triggering a sympathetic reaction in
the female voices, organ and metallophone: just as the rhythmic construction the slow process of augmentation, here the sudden shift to rhythmic unison in
the mallet instruments triggers the voices to begin a slow process of diminution.
In essence, the second half of each of the four sections of Mallet is in many rhythmic unison. “This paired process of rhythmic construction/augmentation
(first half of each section) followed by rhythmic unison/diminution (second key and meter.” Section One of Mallet is in F dorian (3/4), Section two is in Despite the seeming complexity of this lengthy description, Mallet’s Drumming, Reich is obviously less concerned now that all the elements of a as a gradual process work is not to be denied, yet the complexity of the texture Mallet enlarges upon the timbral device we observed in Drumming; short, repeating melodic patterns.” This concept, employed in both works in This content downloaded from 130.166.3.5 on Mon, 11 May 2020 01:45:47 UTC 244
move towards sustaining multiple layers of timbre throughout a composition sections by clear changes of key and/or meter. Again as in Six Pianos, the of statement/response he observed in Ghanaian music. one work, Music for Eighteen Musicians. This composition clearly delineates
the beginning of a new style period within Reich’s output; it is also the work principles that Reich had stated in “Music as a Gradual Process” that one changed. This question and others were discussed with Reich in an important ways in which his attitude towards composition has changed. No longer must At the time of writing “Music as a Gradual Process” in 1968 There was a great difference between chance and choice and This content downloaded from 130.166.3.5 on Mon, 11 May 2020 01:45:47 UTC 245
Music for Eighteen Musicians I have made a great deal more …In a sense, I’m not as concerned that one hears how the What I was really concerned with in Music for Eighteen I
wasn’t as concerned with filling the structure as I was ten years I agree, as the texture gets more filled up, as it gets richer, it The old austerity, the need for the bare bones of a composition to be short, much of what earlier in this article was described as being characteristic
of “minimalism”-have disappeared. To someone not acquainted with Reich’s apparent that this is no sudden style change, no gross gesture for popular Music for Eighteen Musicians (hereafter referred to as Eighteen) is This content downloaded from 130.166.3.5 on Mon, 11 May 2020 01:45:47 UTC 246
acoustical; there are not even the electric organs which were still present in simultaneously in Eighteen. The first of these is the clearly stated, steady epilogue of Eighteen, as well as the middle portions of each of the eleven These performers, using the length of their breath as a guide to how long they
should sound, either sing or play pulses on their assigned pitches “for as long falling (< >) pattern, as “gradually washing up like waves against the The harmonic structure of Eighteen is, for the first time in a Reich Musicians than in any other complete work of mine to date.”74 Eighteen is pulsing pitches within each of the eleven chords; instruments which do not next chord in the sequence is introduced. The chord progression itself is by no What follows is indicative of the new importance Reich assigns to the ensemble returns to the first sonority, which is sustained by pianos and piece of about five minutes in length is built upon the sonority. At the end of original sequence, and an independent little piece is constructed over that This content downloaded from 130.166.3.5 on Mon, 11 May 2020 01:45:47 UTC tL j – – -* j- 4t0 – BS – m F4w4Y Example lla. Steve Reich, Music for Eighteen Musicians (1976). Introductory ‘t, it- -WEI IM m Im 1-9-i
This content downloaded from 130.166.3.5 on Mon, 11 May 2020 01:45:47 UTC Example llb. Steve Reich, Music for Eighteen Musicians (1976). Chord [J as it This content downloaded from 130.166.3.5 on Mon, 11 May 2020 01:45:47 UTC 249
Reich views this type of harmonic organization as being reminiscent of as a single note in a cantus firmus or chant melody of twelfth century But Reich’s use of the chordal cycle differs from most traditional remain constant when the pulsing chords return during the course of the deliberately modal and therefore ambiguous as to tonality. Thus, once the he merely alters the bass beneath the pulsing middle-register sonorities. This general, overall structure of Eighteen is clearly audible even to a blend of instrumental and vocal timbres almost entirely obscures the structural techniques and procedures utilized in previous compositions. Many of the downbeats. A process of augmentation of brief two-chord “cadential” progres- each of the eleven sections, the rising and falling chordal pulse (whose mood of the introductory chordal cycle of the composition. Lastly, voices are This content downloaded from 130.166.3.5 on Mon, 11 May 2020 01:45:47 UTC 250
timbres and textures, a masterpiece of sheer aural magnificence. Who would Reich employs a cueing system in Eighteen that is clearly reminiscent will call for changes of pattern in West African music.”76 This cueing system One last structural technique remains to be discussed in relation to heard.”77 Reich accomplishes this technique by utilizing the two-chord it a two-chord “cadential” figure is repeated at irregular intervals with the shifting harmonic accents will be superimposed upon the unvarying melodic rhythmic construction occurring within individual pieces, the pulsing tones of “cadential” progressions which accompany the constructed melodies. career began to gain momentum as never before. He received three important completed December 1978), Octet (commissioned by Radio Frankfurt, com- This content downloaded from 130.166.3.5 on Mon, 11 May 2020 01:45:47 UTC 251
in 1979). But such recognition did not deter Reich from continuing to learn personal style. Consequently, in 1976, upon realizing that he knew compara- Musicfor a Large Ensemble (1978) is in many ways a hybrid, consisting enriched by two female voices, two violas, two cellos, two basses, clarinets, more than in Eighteen, the structural backbone of the work is difficult to Music for a Large Ensemble (hereafter referred to as Large) is con- as was the case in Mallet. Large employs an even more important technique of of diminution to their original length, at which point a new section begins. closer to Eighteen than to Mallet. Reich employs this augmentation/diminution
process in such a manner as to lend a constantly shifting harmonic accent to All four sections of Large employ the process of rhythmic construction
in the mallet instruments (i.e., substituting beats for rests in order to form This content downloaded from 130.166.3.5 on Mon, 11 May 2020 01:45:47 UTC 252
function of the trumpets to enter at the middle of each of the four sections and
to play four sustained chords; these chords rise and fall with the breath in Eighteen, four distinct levels of rhythmic activity occurring simultaneously: constant pulse maintained in the mallet instruments, the gradual process of There is, however, one important innovation added in Large. Towards These lengthier melodies are constructed in typical Reichian fashion; they are melodic line.”80 But the sheer existence of them is an extremely significant to his studies of Hebrew scriptural cantillation, “the technique of which is the Reich’s next composition, Octet, is viewed by the composer as a One is immediately struck by the virtuosity of the two-piano writing of
Octet, surely this is the most challenging piano technique that Reich has ever so that there is some rather complex rhythmic interlocking going on between This content downloaded from 130.166.3.5 on Mon, 11 May 2020 01:45:47 UTC 253
composition and continue unabated through the end of the work.
Structurally, Octet is divided into five sections, some of which are such a way as to obscure the exact moment of transition from one portion to point of section-change, and therefore overlapping of these voices and their processes and sub-structures of individual sections may be obscured, the blends due to the use of only eight musical lines (a far cry from the coloristic Most significant in Octet is the extension of a technique we first resulting patterns as it does from his study of scriptural cantillation. For the
lengthy ornate melodies of Octet, found primarily in the flutes and piccolo, are of the canonic rhythmic processes in the piano, and then connecting these flute and/or piccolo in Sections One, Three and Five of Octet, however, begin one can begin to speak of the composer conceiving of a melody as an entity All five sections of Octet begin with rhythmic construction of a One, but in a different metrical position. This rhythmic construction procedure
in Piano Two is highlighted by the wind instruments, most commonly clarinets This content downloaded from 130.166.3.5 on Mon, 11 May 2020 01:45:47 UTC *. – . . ,I 4 * & 4 -a .f : $ , 4 4 t ) C?t –
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Example 12. Steve Reich, Octet (1979), Section , 3C, Flute only. Copyright 1979 This content downloaded from 130.166.3.5 on Mon, 11 May 2020 01:45:47 UTC 255
this highlighting process in the winds involves the doubling of only an jagged, rhythmically charged interjections.
In Octet, the strings are employed to gradually augment repetitive of Section One, gradually augments to ten measures in length by the end of The overall structure of Octet gives evidence of the composer’s concern
for symmetry. Sections One, Three, and Five display more animated rhythmic Three, and Five involves an enormous five-fold expansion of an initially brief interjections in the winds which are tied more to doubling resulting patterns only a doubling of a four-chord progression; simultaneously, the cello is submediant chords. Section Five combines all of the techniques used in earlier
portions of the work: the brief two-chord pattern in the upper strings which bass clarinet, and the independent, melodically significant lines in the flute Before discussing the last of the three commissioned works, Variations
for Winds, Strings, and Keyboards, it seems important to emphasize several and timbre due to the employment of larger groups of performers, and a
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lessening of interest that process be immediately apparent. Other trends, one might point towards a new concision of structure and an almost Classic aesthetic of so many earlier compositions; Music for a Large Ensemble Reich himself is well aware of his new respect for the Western heritage.
He no longer considers Perotin to be the high point in Western music as he of the Western tradition. The composer stated (1980):
There was… a period in which I was very interested in non- Variations for Winds, Strings, and Keyboards is perhaps the most sioned by the San Francisco Symphony Orchestra, is the first Reich work that oboes, three trumpets, three trombones, two pianos, and three electric organs). players; this is the arrangement performed by Reich and his ensemble on their Reich himself admits that Variations is so different from his earlier
works that a listener “might not perhaps be completely sure that I was the tempo ( J = 120-132) than earlier pieces, resulting in a moderate rather than
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hyperactive pace, as well as allowing light, rapid notes to emerge more lyrically
in performance. Secondly-and most significantly- Variations is built upon a melodic processes. The harmonic pattern of Variations is a slow and lengthy composition. Reich describes how the changes from one chord to the next Instead of moving from one chord to the next, the movement Reich insists that this chordal suspension technique was derived from studying For the first time in many years, perhaps due to the orchestral nature of
the Variations commission, Reich uses no percussion whatsoever in this work, and specifically the “tart clarity of the oboes.. ., provide an analogue in Variations is constructed in three sections, each over one broad petitive rhythmic/melodic figure changing to match the harmonic progression This content downloaded from 130.166.3.5 on Mon, 11 May 2020 01:45:47 UTC 258
melismatic, developed melodic vocabulary than [in] any work of mine to Variations for Reich’s output as a whole is its vast increase in the importance
of the melodic parameter of musical composition. The endless, shimmering the composer’s style (see Example 13). the melodic development, is the new use of harmony as the prime structural method of maintaining the chaconne’s harmonic progression during its remained fixed, so too in Variations Reich retains only the tonally ambiguous well as to modulate, without disturbing the integrity and consistency of the
chaconne’s harmonic sequence. the sustained, suspended harmonies of the strings and third electric organ, has
a significance even beyond its structural harmonic importance. For Reich section enter to sustain structurally important tonic, sub-dominant and are silent for the remainder of the composition; the effect of their entrance is
similar to that of the swelling trumpets in Music for a Large Ensemble. In the third electric organ) enters at important moments to sustain structural Lastly, one might note that again, as in Octet, the composer no longer This content downloaded from 130.166.3.5 on Mon, 11 May 2020 01:45:47 UTC or92
ViE.
Example 13. Steve Reich, Variations for Winds, Strings and Keyboards (1979), This content downloaded from 130.166.3.5 on Mon, 11 May 2020 01:45:47 UTC 260
is of prime importance. In actuality, the lengthy rhythmic/melodic patterns Reich’s next composition, My Name Is. Ensemble Portrait (1980), is, Why would Reich return to electronic music after so many years away in such a way as to enhance and ingeniously transform both its meaning and The new work, My Name Is: Ensemble Portrait, 93 is based upon a piece
dating back to 1967. In the earlier composition, the names of members of the phase relationships between the various names by using three small portable This content downloaded from 130.166.3.5 on Mon, 11 May 2020 01:45:47 UTC 261
Recently, it occurred to Reich that in this long-forgotten concept there
might lie the kernel of a new composition. Instead of using the audience’s The result was My Name Is: Ensemble Portrait, premiered at the My name is Virgil. My name is Chris. My name is Ruth”). The tape piece through a series of complex phase relationships. Immediately after a name is trend we have repeatedly observed in his recent live compositions to tape composer is more interested in the coloristic end result of the multiple phasing
procedures than in the process itself occurring so slowly as to be clearly rhythmic chatter; it is on these timbres that the composer lingers, not on the Compositionally, My Name Is is simply constructed. A voice fades in,
introducing the first name, but rapidly shifts out of phase and into a lengthy first voice moves back into phase unison and fades out. This overlapping of Yet Reich feels that My Name Is, as it was performed at the Whitney This content downloaded from 130.166.3.5 on Mon, 11 May 2020 01:45:47 UTC 262
ways upon the processes used in My Name Is. First of all, instead of employing
voices known only to the composer, it would use voices known to the general
public (such as, perhaps, Roosevelt, Truman, or Hitler). Secondly, such voices What finally convinced Reich to pursue this project seriously was the electronics. We have already noted the inherent musicality of the speech the instrumental music would be able to develop of its own accord. Reich electronics. Such a procedure struck Reich as being a way to “go back into my
own past, to rejuvenate something that I actually enjoyed doing (tape music), electronic music, because I didn’t see any way to incorporate it in any My Name Is-and why I insist that is just a sketch-is because the important larger piece, which is what I really conceive of it to be.”95 application of phasing principles, looseness of process and denseness of texture,
and projected combination with live music, is but a logical (though admittedly As significant a departure as it marks, the new directions heralded by Reich’s this composition will mark the beginning of a new style period for Reich, as it
gives evidence of a style change even more astounding than that which we This content downloaded from 130.166.3.5 on Mon, 11 May 2020 01:45:47 UTC 263
Tehillim, commissioned jointly by West German Radio (Cologne), the composer has chosen to set a text to music in the traditional manner, or destroyed their essential speech rhythms. Yet in Tehillim, the composer creating music for a written text. The fact that the text itself is in Hebrew from the text is gained as well. In addition, there is no surviving Western Inextricably linked to Reich’s new use of a written text is the enormous
expansion of the melodic parameter that is evident in Tehillim. Selecting without being the consequence of either doubling resulting patterns arising in This content downloaded from 130.166.3.5 on Mon, 11 May 2020 01:45:47 UTC 264
substance of the rest of the ensemble, yet the melodic lines were still constructed
of shorter repetitive modules, strung together to create longer phrases. Tehillim
takes the next logical step: the melodic material is neither made up of Ultimately the melodic material achieves complete primacy in Tehillim,
a primacy closely connected to Reich’s concern for proper text declamation. line and verse structure controls phrasing and sectionalization, and occasionally
the exigencies of tone painting dictate the melodic contour. Thus the Psalms Yet not only the melodic parameter establishes Tehillim as a major structural plan of the composition. The basic harmonic technique of Tehillim chordal cycle, established near the outset of a section, undergoes subsequent
permutations which consist chiefly of altering the bass line, while the middle modulatory scope and frequency (and consequent variety of permutations to create longer more enriched chordal sequences. Most significantly, all the more varied in modulatory range and sheer number per movement than was
previously the case in Reich. concern with creating an appropriate setting for the Psalms has led to numerous
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modifications of his musical aesthetic. Meters now change in practically every
measure, though throughout the entire work the metric patterns may be note pulse itself is unvarying. The metric fluctuation allows for a precise Advances may also be noted in instrumental technique, especially the string
writing, which retains its old function as the purveyor of the chordal cycle but
increasingly takes part in the motivic fabric. The strings now contribute Tehillim-both within sections and between movements-are astounding in a warm, expansive new lyricism utterly alien to Reich’s earlier compositions. repetition in the sense that we know it from his previous work. Though the rhythmic chatter that is familiar from Reich’s previous compositions.
Tehillim, not surprisingly, also shows many links with Reich’s earlier for the two constructive types used in Tehillim (canon and variation) may be of the Psalms is conceived as an independent canon with the metrical position This content downloaded from 130.166.3.5 on Mon, 11 May 2020 01:45:47 UTC 266
multiple canonic lines which are all at the same pitch level. For what were the distinction between such early canonic techniques and Tehillim is the fact that
the phase pieces, both electronic and live, included metrically irrational Tehillim s harmonic techniques similarly point back to many earlier With their bass root removed, the middle and upper registers consist either of
triadic chords with many added pitches or modal sonoroties; both are unclear
tonally. Thus a newly added root can substantially alter the direction of the materials progress from seven-note scale patterns at the outset of the movements
to ambiguous four-note scale patterns for the final verses (verses three and inherently unclear tonally owing to their four modal pitches, that Reich As we observed repeatedly in Musicfor Mallet Instruments, Voices and
Organ, Music for Eighteen Musicians, Music for a Large Ensemble, and Octet, nution to alter the temporal span of his chordal cycles. The effect of these
expanding and contracting harmonic cycles beneath relatively constant melody
is to superimpose a wide range of shifting harmonic accents upon the melodic stantly changing relationship between melody and its harmonic underpinning. tation, recall previous compositions. We have already noted the similarities to
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and differences from earlier string writing, the relationships of the vocal the vocal lines are almost constantly doubled by other instruments -clarinets oboes (the melodic soloists) were doubled respectively by two pianos/electric fact, Tehillim s rhythmic vitality and steady pulse are essential in allowing the
work to burst forth at the listener as a prolonged, joyous affirmation of faith.
With Tehillim Reich continues his long return to the Western tradition
that we have previously noted in Music for a Large Ensemble, Octet, and solution, one that abandons repetitive modules in favor of lengthy melodic repetition rejected, the musical materials are finally able to unfold freely and addition to the percussion that Reich has often used before (maracas, marimbas,
vibraphones, and hand clapping), Tehillim adds two new instrumental types: clearly: “In spite of the use of these instruments, Tehillim has no musicological This content downloaded from 130.166.3.5 on Mon, 11 May 2020 01:45:47 UTC tb mf utjr Yr-cJJ2JI P1 jLr j i tj ^ lg$FL I -1 r 6 T i – Hl>j. XUtL j b j y | J i E ^ X r^ rt J i 1; r 1 i i ,J ko-q.e-ki( A – – rz – I+zo k-v, -Tv,’k -zJ y-v,;( ie- hew. ge-lti> 1-
Example 14: Steve Reich, Tehillim (1981), Part I, Section A, verses 1-4, voice This content downloaded from 130.166.3.5 on Mon, 11 May 2020 01:45:47 UTC 269
Tehillim is a complex work of immense variety and any analysis new melodic style and several constructive techniques are combined into a melodic material (see Example 14), which provides all the music for the After the opening solo vocal section, the entire four verses are repeated
once more, now with the clarinet doubling the vocal line and an added second stated canonically, the two-voice canon is repeated with the chordal cycle in begins (Example 15), again with an independent canon built upon the melodic and the maracas begin their chater; here the maracas are not merely an four, Reich capitalizes on the modal ambiguity of the melodic material and, by
changing the bass line, allows the chordal cycle to modulate to G Major while Once the four-voice canons have concluded, Reich returns to a reduced
texture for a restatement of verses one through four; here a single voice is This content downloaded from 130.166.3.5 on Mon, 11 May 2020 01:45:47 UTC a^cIW r 15 ; -1- p- l Ji1 r l.Ka-s4iA-y-;v M6-sws-PAe4-ruek ka-vokd Kai I-rma-a – 5y ya-dl’e jA-
1.^ -5-s- >y- ? , m-m-uq – -A -rtee k4-vod Kai A- t-
+i – – g I:J j Example 15. Steve Reich, Tehillim (1981), Part I, Section F, verse 1, voice parts l.Ha-s This content downloaded from 130.166.3.5 on Mon, 11 May 2020 01:45:47 UTC 271
out, leaving the principal voice to be accompanied solely by tambourines, Parts Two and Three of Tehillim differ from Parts One and Four in
that they abandon the canon as a constructive technique and instead turn to which occurred towards the end of Part One; here a principal voice is Variation One consists of the addition of a string chordal cycle beneath maintained, despite the fact that the text and the principal melodic material Variation Three returns us to a texture and instrumentation identical
to that before the interlude; here, however, the original melodic material and
the accompanying chordal cycle are greatly elongated (compare Example 16b without any melody whatsoever functions as Variation Five, maintaining the permutations of this movement’s harmonic sequence. Finally, Reich returns to This content downloaded from 130.166.3.5 on Mon, 11 May 2020 01:45:47 UTC iP r Pi r U ^1-J lr1 G l]- 1 f J ‘l1 MJj jgn^jL91 .\ rS parts only. Copyright 1981 by Steve Reich. Used by permission.
n . AP – E i –I J
1.i;- a – eek c-a- f-yt c^- yeer ol- cl^v – t&., le-e . -e ‘t v ? 2. ,e-
Example 16b. Steve Reich, Tehillim (1981), Part II, Section D, verse 1, voice j rb ; Z :: l |i ii i ‘ 1* 1 ^4. Iudc lz i , ^ . -.’ ‘ c6Y y – h – – strft kb? . e –
1JI’^Ji,-:l,.l J ‘~’ $-T I – parts only. Copyright 1981 by Steve Reich. Used by permission. 273
Seven of the movement, a coloratura line is added above the previous melismatic
duet texture, just as was done in Variation Four. Thus, Part Two, like any Part Three functions as a predominantly lyrical slow movement, vocal lines are accompanied throughout by an interlocking rhythmic pattern
in the marimbas and xylophones. Part Three opens in C# Dorian, but the “perverse” (ee-kaysh) and results in both a tritone with the C# of the Part Three, like Part Two, is constructed as a variation set, but features
more subtle alterations in its five variations than did Part Two. The develop- from variation to variation; note values are also lengthened, mimicking the beneath both the principal voice and the lower answering line, resulting in a is constantly varied, with new bass pitches and enriched upper registers Most significant in Part Three is the vastly expanded role that the This content downloaded from 130.166.3.5 on Mon, 11 May 2020 01:45:47 UTC 1.TJ-c -sealk- TseA – var- faJ –MeeI
tl~~~~~$~~~~C~~~IF~~~~~( I~~~~~~- F~~~~~ ~~~III-~~~~~~LEl} B10 1IC v l Btt g Tt-c l-. jit Tch– aAs –
Example 17. Steve Reich, Tehillim (1981), Part III, Section A, verse 1, voice parts I 275
formation (from highest to lowest), gradually thickening the texture; and they
provide timbral variety, especially in the lengthy pizzicato pedal points which,
descending by half step from D# to C to begin the chordal cycle of the finale, of the method that linked the various sections of Drumming, here the Part Four combines the constructive techniques (canon and variation), Opening with the homophonic duet texture that occurred in both thoroughly reshapes it to meet the requirements of the new text. Each verse of
Part Four can be viewed as a free melodic variation on the respective verse of
Part One (compare Example 18a to Example 14). Even the opening chordal Once the three verses have been stated the homophonic duet texture Up to this point, it is Part One that has been the prime influence on instrumental interlude, utilizing only the chordal cycle in the manner of
Variation Five of Part Two, follows. Finally, as in Part Two, a vastly expanded high soprano line is immediately added above the other vocal parts. Despite all This content downloaded from 130.166.3.5 on Mon, 11 May 2020 01:45:47 UTC 1. 14-(- le- hI- u bt-af L- – h4-Vck Ha-Ie- lu -u ba-mi;-tm V4– a.v.
l1sr rcft^ll^&i 1 115′ i r| i S .r L ,,i – -i. r -I- 4in i Lir-‘ 1- – yJ IV- l e- (4- y .i
Example 18a. Steve Reich, Tehillim (1981), Part IV, Section A, verses 1-3a, ^ : i It r iJ r irrtiUl , 1. IrL2 I’! 4- ^hl n – ” – ?a ?
Example 18b. Steve Reich, Tehillim (1981), Part IV, Section 0, verse 1, voice 1 This content downloaded from 130.166.3.5 on Mon, 11 May 2020 01:45:47 UTC 277
“inverted pyramid” entrances, brief rhythmic punctuations, and pizzicato A grand increase in instrumentation demarcates what is essentially the addition, all the previous vocal doubling instruments (electric organs, clarinets,
oboe, English horn) are now employed simultaneously. The musical material of Part Four. Structurally, the coda demonstrates in a microcosm many of the techniques used in earlier parts of Tehillim are also reunited in the coda: not
only do all of the doubling vocal instruments appear together for the first time,
but the string writing (with its pyramided entrances from upper to lower throughout most of the work.
Harmonically, the coda fluctuates repeatedly between the major and verse three of Part Four. The chord cycle itself begins as an altered version of
that of Parts One and Four; soon, however, it returns to its starting pitch (Bb) first time in a work of Reich, it is the bass itself-not the middle and upper still employing the “Hallelujah” motive. The final burst of sonority-the This content downloaded from 130.166.3.5 on Mon, 11 May 2020 01:45:47 UTC 278
sound. Tehillim stands as a jubilant affirmation of God, peace, and life itself; By now, it should have become apparent that a discussion of any given as new, unprecedented developments that offer raw material for the future. the way. Each new work appears to capitalize on techniques used in immediately
preceding compositions, but also adds novel ideas which will in turn stimulate etc.; the technique of rhythmic construction of Six Pianos resulted in Music likely to continue to evolve in new and unexpected ways.
In conclusion, it is tempting to try to place minimalism, and Reich’s minimalism was a rebellion against many aspects of the establishment avant- This content downloaded from 130.166.3.5 on Mon, 11 May 2020 01:45:47 UTC 279
manipulations of serialism, which placed intellectual complexity on a higher Yet beyond the simplistic aspect of rebellion against several existing it is a consequence of the condition of mankind in an increasingly complex and “clearly, minimalism is a reaction to twentieth-century information overload, must certainly be emphasized; its conscious restriction of the material employed
can easily be viewed as an extreme response to the complex incomprehensibility that, in one sense, this type of response is no more than an escape, yet, escape had a lasting power, despite the many cultural changes that have occurred The second most obvious aspect of minimalism is perhaps its desire
for a clarity of structure coupled with rigorously planned processes, its assertion that composer intervention is necessary to regain control over an increasingly basis for an entire composition, rather than any developmental or directional Reich’s personal style is a mirror of the stylistic eclecticism of the
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contemporary music scene. Such eclecticism has become the norm since the tonality. Eastern philosophical thought, with its rejection of both goal-direction
and Western notions of progress and development-and a consequent aspect number of options available to today’s composer of new music. that a variety of aesthetics can be drawn upon for the development of one’s traditional goal-directed developmental forms. Reich asserts that all musics malists, and especially Glass and Reich, derive less their sonic models than world music, allows the Western heritage to be perceived as only one possible
source among many others. This denial of the primacy of Western culture apparent in recent years not only in the arts but also in international politics, One last aspect of Reich’s style should be discussed briefly, as it is so noting Reich’s use of the term “pattern” when referring to motives within his This content downloaded from 130.166.3.5 on Mon, 11 May 2020 01:45:47 UTC 281
of contemporary culture.’03 One cannot help but feel that the underlying century ideal that established originality and personal expression as the prime Steve Reich has revitalized contemporary music in a way that would to the primal forces of metrical rhythm and clear tonality that the avant-garde
had cast aside. Yet he has done this without compromising his own beliefs, and
has maintained an admirable stylistic continuity and musical integrity throughout
his career. Most importantly, he has re-introduced new music to a mass public The audience at a sold-out Carnegie Hall in February 1980 rose to its in modern society-Steve Reich deserves our recognition and our praise.
This content downloaded from 130.166.3.5 on Mon, 11 May 2020 01:45:47 UTC ACKNOWLEDGEMENTS
Special thanks is due to those who made a study of this scope possible. This content downloaded from 130.166.3.5 on Mon, 11 May 2020 01:45:47 UTC NOTES
38 Reich, pp. 9-11; Source, V, No. 2 (1971), p. 30; Liner Notes, DGG 2740-106, 39 For a discussion of Pendulum Music in its revised version (1973) see Reich, 40 Reich, pp. 17-24.
41 Reich, p. 25.
42 Reich, p. 55.
43 Reich, p. 25.
44 Reich, p. 25.
45 Reich, p. 55. Four Organs was derived from several electronic techniques, only 46 Reich, p. 55.
47 Henahan, sec. 2, p. 14.
48 Reich, p. 56.
49 Reich, p. 57. For a detailed description of Reich’s African journey, see Reich, 50 Reich’s interest in African music dated back to 1963, when he became acquainted This content downloaded from 130.166.3.5 on Mon, 11 May 2020 01:45:47 UTC 284
51 Reich, p. 32.
52 Reich, pp. 35-36.
53 Reich, p. 58.
54 Steve Reich, “A Composer Looks East”, The New York Times, 2 September 55 Reich, p. 58.
56 Reich, p. 61.
57 Reich admits that Webern’s concept of “Klangfarbenmelodie” was influential 58 Reich, p. 58.
59 Reich, pp. 61-62.
60 Michael Nyman, “SR-Mysteries of the Phase”, p. 20.
61 See Reich, p. 67. Six Pianos was even rehearsed in a New York Baldwin Piano 62 Aside from Clapping Music (1971), Drumming had been Reich’s last work to 63 Reich, pp. 68-69.
64 According to the analysis by Reich, Liner Notes, DGG 2740-106, 1974.
65 Terry, p. 39.
66 Reich, p. 69.
67 Whenever “cadential” is placed in quotes in this article, it is used to refer to a 68 Reich, Liner Notes, DGG 2740-106, 1974.
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69 This analysis of Mallet has been based on material in Reich, Writings, pp. 69- 70 Reich, p. 71.
71 For some reviews of Music for Eighteen Musicians, see (in chronological 72 Michael Nyman, “Reich: Interview” (1977), pp. 18-19.
73 Both this and the previous quotation are taken from Steve Reich, Jacket Notes, 74 Reich, Music for Eighteen Musicians.
75 Reich, Music for Eighteen Musicians
76 Reich, Music for Eighteen Musicians
77 Reich, Music for Eighteen Musicians
78 The dates for Reich’s cantillation studies, as well as the dates and origins of the 79 “Semi-functional” because, while the resolution of dominant to tonic (in 80 Alpern, p. 17.
81 Alpern, p. 17.
82 Alpern, p. 17.
83 Reich states concerning the piano writing of Octet: “It’s a piece which I do not This content downloaded from 130.166.3.5 on Mon, 11 May 2020 01:45:47 UTC 286
84 Alpern, p. 17.
85 Alpern, p. 19.
86 Alpern, p. 17.
87 Alpern, p. 19.
88 “Interview: Steve Reich”, EAM Accents, p. 7.
89 Sandow, p. 74.
90 Alpern, p. 18.
91 Alpern, p. 18.
92 See the quote concerning electronic music to which note 24 refers.
93 Much of the following material concerning My Name Is: Ensemble Portrait is 94 Such as the process embodied in the 1967 work Slow Motion Sound; i.e., 95 From a personal interview with the composer, January 2, 1981.
6 Reich, Writings, p. 49.
97 From a personal interview with the composer, January 2, 1981.
98 Personal interview, January 2, 1981.
99 Charles Ward, “Reich Premiere to Reveal Composer’s Non-repetitive Side,” 100 The Rothko Chapel (Houston), Program Notes for Tehillim, 21 and 22 101 “Steve, parlez-nous de votre derniere oeuvre, Tehillim”, Libgration, 23 September 102 Eric Salzman, Twentieth-Century Music: An Introduction, 2nd ed. (Englewood 103 Clytus Gottwald, “Tendenzen der neuen Musik in den USA: Gyorgy Ligeti im This content downloaded from 130.166.3.5 on Mon, 11 May 2020 01:45:47 UTC image 1 Perspectives of New Music, Vol. 20, No. 1/2, Autumn, 1981 – Summer, 1982
Analysis of Emergent Beat-Class Sets in Steve Reich’s “Clapping Music” and the Yoruba Bell
REFERENCES
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This content downloaded from 130.166.3.5 on Mon, 11 May 2020 01:50:40 UTC Analysis of Emergent Clapping Music and the Justin Colannino, Francisco Gomez, 1. Introduction
The history of music is often the history of humanity’s reactions to it. A good example of this may be observed in Minimalism. Since the This content downloaded from 130.166.3.5 on Mon, 11 May 2020 01:50:40 UTC I I 2 Perspectives of New Music
indeterminacy, where Cage is its most notable figure. Although the term particular composer, but minimalist works share concern for non It is probably Reich who most unhesitatingly repudiates the Western In his essay “Music as a Gradual Process,” Reich states his principles This content downloaded from 130.166.3.5 on Mon, 11 May 2020 01:50:40 UTC Analysis of Emergent Beat-Class Sets I I 3
phases. First, a melody is played by two or more players, and after a These ideas are fulfilled in many of Reich’s works composed between This paper is concerned with a mathematical comparative analysis of musical styles, which influenced his music. Such an influence is most This content downloaded from 130.166.3.5 on Mon, 11 May 2020 01:50:40 UTC I 14 Perspectives of New Music
2. Clapping Music
Clapping Music is a phase piece for two performers clapping the same play the pattern in unison. interest. First of all, Clapping Music constitutes a synthesis and a modulation) elucidates the musical structure of the piece.7
3. Measuring Features of Clapping Music
When one listens to Clapping Music, a question that arises naturally is V? VI V2
“**” [?9r r r’ r r * s’ r r ‘ |r r r’ r r * b ‘ r r’ |r r r’ r r * s’ r r’
Vlt vu vu
P1 |?r r r * r r * t1 r r’ |r r r * r r * t’ r r * |r r r * r r * t’ r r *
example 1: the first and last few bars of clapping music
This content downloaded from 130.166.3.5 on Mon, 11 May 2020 01:50:40 UTC Analysis of Emergent Beat-Class Sets I 15
the pattern is defined, however, the rulebook does not allow us to One mystery in Clapping Music is how Reich was able to find a African drumming in Ghana.9 In particular, we note an extraordinary two years after travelling to Ghana to study African drumming, but Clapping Music [] ^ ppp?pp^p^pp7 EXAMPLE 2: THE PATTERN OF CLAPPING MUSIC AND THE YORUBA CLAVE
This content downloaded from 130.166.3.5 on Mon, 11 May 2020 01:50:40 UTC i i 6 Perspectives of New Music
Reich used in Clapping Music. It appears that Reich considered the The Yoruba people live on the west coast of Africa, mainly in Nigeria, Clap 1-j-j-j cpsITTjOTX: EXAMPLE 3: MUSIC FROM THE LALA PEOPLE
EXAMPLE 4: RHYTHMIC PATTERNS FROM DESERT MUSIC
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diaspora evolved and the descendants of the Yoruba people can also be The clave considered here is widely employed as a timeline in the It might be argued that there may exist other clave patterns very motivation for comparing these two patterns. In fact, an intriguing The musical effectiveness of Clapping Music is due in part to the way 4. Phylogenetic Analysis
Phylogenetic graphs were originally used in biology to determine the we define a new measure of proximity (similarity) between rhythmic This content downloaded from 130.166.3.5 on Mon, 11 May 2020 01:50:40 UTC I I 8 Perspectives of New Music
and other interval sets such as pitch-class sets has received a great deal of Consider first the simpler swap-distance inspired by the most As mentioned before, one of the reasons for comparing the pattern of Music. For each rhythm the bottom of each column of Example 5 This content downloaded from 130.166.3.5 on Mon, 11 May 2020 01:50:40 UTC Analysis of Emergent Beat-Class Sets I 19
Surprisingly, the sums take on only two values, 48 and 74, where Vo, V3, Whereas traditionally, phylogenetic graphs have been used in the marked with black dots) approximates as closely as possible the distances Variations I V0 I V1 I V2 I V3 I V4 I V5 I V6 I V7 I V8 I Vg I V10 I Vn Y, I 74 j 48 j 48 j 74 1 48 j 48 j 74 1 48 j 48 j 74 j 48 j 48
EXAMPLE 5: THE DIRECTED SWAP DISTANCE MATRIX OF This content downloaded from 130.166.3.5 on Mon, 11 May 2020 01:50:40 UTC I 20 Perspectives of New Music
Fit= 100% I_I >v_^^rr^^^^^^ V3 ? C2 ^^^^ In addition, the graph also contains nodes (without black dots) that beat-class modulation structure of Clapping Music. For the moment, we trochees. A trochee is a rhythmic grouping consisting of a long note gj j>j j>j j>j t>\
EXAMPLE 7: THE “ANCESTRAL” RHYTHM OF CLAPPING MUSIC
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is a common Afro-Cuban drum pattern, also found in disparate areas of and C4, that can be easily seen in Example 6. When Clapping Music is which goes from V? to V6, variations are still kept away from Vo. In the V10 and V11, tend towards Vo. Lastly, Clapping Music closes by coming graph. All rhythms in clusters CI and C4 are at a distance of 6 from the Clusters || CI | C2 | C3 | C4 _”____t__V5_Ve_ 11 Vn I I I
EXAMPLE 8: CLUSTERING IN CLAPPING MUSIC
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X.XX.XX.XX.X
x x x, x x . x . x x. ^ Tx^TTxTx X . X X X EXAMPLE 9: CONVERTING Vo AND F3 INTO THE CENTRAL PATTERN OF NODE A
Let us now compare the Clapping Music pattern to the Yoruba The graph is a chain with a rather disappointing fit of 89%, with no This content downloaded from 130.166.3.5 on Mon, 11 May 2020 01:50:40 UTC Analysis of Emergent Beat-Class Sets 123
Variations I V0 I Vj I V2 1 V3 I V\ \ Vs \ Vg \ V7 \ Vs I V9 I Vjo I Vii E I 38 I 48 j 48 j 38 I 66 j 36 1 56 1 42 j 43 j 55 | 41 | 66
example 10: the directed-swap distance matrix of the yoruba timeline
Fit=89% – v8 v3 –
example 11: the phylogenetic graph of the yoruba timeline
5. Syncopation Analysis of Clapping Music
The characterizing feature of any definition of syncopation includes a This content downloaded from 130.166.3.5 on Mon, 11 May 2020 01:50:40 UTC 124 Perspectives of New Music
found in the literature, such as the measure proposed by Longuet wider applicability and validity than the others.28 pation of Clapping Music, may be described as follows. We assume that The WNBD measure D(x) of a note x is then defined according to the (1) D(x) = ^ , if note x &a ends before or at a+i. (2) D(x) = ^ , if note x ends after a+\ but before or at a+i.
(3) D(x) = ^ , if note x ends after a+i.
(4) D(x) = 0, if a; = a.
See Example 12(b) for an illustration of this definition. Now, let n ” 1 -4 .-. ,i *_ i+1 ei+2 1 (3) ?*???_Bl I I EXAMPLE 12: DEFINITION OF THE WNBD MEASURE
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Example 13 plots the WNBD measure of the variations in Clapping On the other hand, a look at the graph of the WNBD measure for the 6. Concluding Remarks
Although phylogenetic graphs have already been used for analyzing example 13: the graph of the syncopation measure of CLAPPING MUSIC
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VO VI V2 V3 V4 V5 V6 V7 V8 V9 VIO Vll V12
EXAMPLE 14: THE GRAPH OF THE SYNCOPATION MEASURE OF THE YORUBA CLAVE
transformation of variations, or the structure of the musical form. Our would expect that changing only one note could not make such a The WNBD measure of syncopation produces interesting conclusions combinatorial point of view. In this paper we have added arguments of a measure pose several open problems. For example, one may ask which This content downloaded from 130.166.3.5 on Mon, 11 May 2020 01:50:40 UTC Analysis of Emergent Beat-Class Sets I 27
as well as the pattern used in Clapping Music, or whether one may This content downloaded from 130.166.3.5 on Mon, 11 May 2020 01:50:40 UTC I 28 Perspectives of New Music
Notes
1. Sutherland (1994), 1.
2. Pousseur (1966), 93. For further discussion on these topics, see 3. Reich (2002), 34.
4. Reich (2002), 68.
5. See Cohn (1992), and Roeder (2003).
6. For a discussion of Cohn’s formalist analysis of Reich’s music, and 7. While Clapping Music has received litde musical analysis despite this 8. Sec Toussaint (2003), and Diaz-Banez, et. al. (2004).
9. This interpretation is reflected in Michael Nyman’s article in The 10. See Epstein (1986). Men Rodriguez (1998), Euba (1991), and Pressing (1983).
12. See Men Rodriguez (1998) and Ortiz (1998).
13. Jay Rahn (1987; 1996).
14. See Smith and Honing (2006).
15. The bibliography offered by Kramer (1985) lists several such 16. See Callender, et. al. (2007), Straus (2003), and Tymoczko (2005).
17. See Diaz-Banez, et. al. (2004), and Toussaint (2002, 2003, 2004a).
18. See Callender, et. al. (2007), and Tymoczko (2005).
19. See Diaz-Banez (2004), and Toussaint (2004a).
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20. To obtain precise details about these timelines consult Toussaint 21. For a discussion of the SplitsTree program, see Hudson (1998).
22. See Klower (1997), van der Lee (1995), and Rodriguez (1997), 23. See Hagoel (2003).
24. See Asch (1975).
25. See Toussaint (2005a).
26. Toussaint (2003).
27. See Johnson-Laird (1991), Longuet-Higgins (1984), Smith (2006); 28. See Gomez et al. (2005).
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References
Alen Rodriguez, Olevo. 1998. From Afro-Cuban Music to Salsa. Berlin: Amira, John and Steven Cornelius. 1999. The Music OfSanterta: Tradi Asch, Michael. 1975. “Social Context and the Musical Analysis of Slavey Bettermann H., D. Amponsah, D. Cysarz, and P. Van Leeuwen. 1999. American Physiological Society: H1762-H1770.
Buchler, Michael. 2000. “Broken and Unbroken Interval Cycles and -. 2001. “Relative Saturation of Interval and Set Classes: A New Callender, Clifton, Ian Quinn, and Dmitri Tymoczko. 2007. “General University.
Cohn, Richard. 1992. “Transpositional Combination of Beat-Class Sets Diaz-Banez, Jose-Miguel, Giovanni Farigu, Francisco Gomez, David Eli Rodriguez, Victoria, et al. 1997. Instruments de la Musica Fol Epstein, Paul. 1986. “Pattern Structure and Process in Steve Reich’s Euba, Akin. 1991. Yoruba Drumming: The Dundun Tradition. This content downloaded from 130.166.3.5 on Mon, 11 May 2020 01:50:40 UTC Analysis of Emergent Beat-Class Sets I 31
Gomez, Francisco, Andrew Melvin, David Rappaport, and Godfried T. Haack, Joel. 1991. “Clapping Music?a Combinatorial Problem.” The -. 1998. “Mathematics of Steve Reich’s Clapping Music.” Pro Hagoel, Kobi. 2003. “The Art of Middle Eastern Rhythm.” Kfar Sava, Huson, Daniel H. 1998. “SplitsTree: Analyzing and Visualizing Evolu Isaacson, Eric J. 1990. “Similarity of Interval-Class Content between Jones, A. M. 1954. “African Rhythm.” Africa: Journal of the Interna Johnson, Timothy A. 1994. “Minimalism: Aesthetic, Style or Tech Johnson-Laird, Philip N. 1991. “Rhythm and Meter: A Theory at the Keith, Michael. 1991. From Poly chords to Poly a: Adventures in Music Klower, Tom. 1997. The Joy of Drumming: Drums and Percussion Kramer, Jonathan. 1985. “Studies of Time and Music: A Bibliography.” Lerdahl, Fred and Ray Jackendoff. 1983. A Generative Theory of Tonal Longuet-Higgins, H. Christopher and Christopher Lee. 1984. “The This content downloaded from 130.166.3.5 on Mon, 11 May 2020 01:50:40 UTC I 32 Perspectives of New Music
van der Lee, Pedro. 1995. “Zarabanda: Esquemas Ritmicos de Acorn Marvin, Elizabeth West, and Paul A. Laprade. 1982. “Relating Musical Mertens, Wim. 1983. American Minimal Music. London: Kahn and Morris, Robert D. 1979-80. “A Similarity Index for Pitch-Class Sets.” -. 1995. “Equivalence and Similarity in Pitch and Their Interac Nyman, Michael. 1971 “Steve Reich.” The Musical Times 112 (March): Ortiz, Fernando. 1995. La Clave. La Habana: Editorial Letras Cubanas.
-. 1998. Los Instruments de la Musica Cubana. La Habana: Potter, Keith. 1986. “Steve Reich: Thoughts for his 50th-Birthday -. 2000. Four Musical Minimalists: LaMonte Young, Terry Riley, Pousseur, Henri. 1966. “The Question of Order in the New Music.” Pressing, Jeffrey. 1983. “Cognitive Isomorphisms Between Pitch and Quinn, Ian. 1997. “Fuzzy Extensions to the Theory of Contour.” -. 2001. “Listening to Similarity Relations.” Perspectives of New -. 2006. “Minimal Challenges: Process Music and the Uses of This content downloaded from 130.166.3.5 on Mon, 11 May 2020 01:50:40 UTC Analysis of Emergent Beat-Class Sets I 33
Rahn, Jay. 1987. “Asymmetrical Ostinatos in Sub-Saharan Music: Time, -. 1996. “Turning the Analysis Around: African-Derived Rhythms Rahn, John. 1979-80. “Relating Sets.” Perspectives of New Music 18/1 Randel, Don, editor. 1986. The New Grove Dictionary of Music and Reich, Steve. 1974. Writings About Music. New York: The Press of the -. 2002. Writings About Music 1965-2000. Oxford: Oxford Uni Roeder, John. 2003. “Beat-Class Modulation in Steve Reich’s Music.” Rogers, David W. 1999. “A Geometric Approach to PCSet Similarity.” Scott, Damon, and Eric J. Isaacson. 1998. “The Interval Angle: A Simi Smith, Leigh, and Henkjan Honing. 2006. “Evaluating and Extending Straus, Joseph. 2003. “Uniformity, Balance, and Smoothness in Atonal Sutherland, Roger. New Perspectives in Music. Sun Tavern Fields, 1994. Toussaint, Godfried T. 2002. “A Mathematical Analysis of African, -. 2003. “Classification and Phylogenetic Analysis of African This content downloaded from 130.166.3.5 on Mon, 11 May 2020 01:50:40 UTC I 34 Perspectives of New Music
-. 2004a. “A Comparison of Rhythmic Similarity Measures.” Pro -. 2004b. “A Mathematical Measure of Preference in African -. 2005a. “The Euclidean Algorithm Generates Traditional Musi -. 2005b. “Mathematical Features for Recognizing Preference in Tymoczko, Dmitri. 2005. “Voice-Leadings as Generalized Key Signa Uribe, Ed. 1996. The Essence of Afro-Cuban Percussion and Drum Set. Xenakis, Iannis. 1965. “La crise de la musique serielle.” Gravesaner This content downloaded from 130.166.3.5 on Mon, 11 May 2020 01:50:40 UTC p. [111] Perspectives of New Music, Vol. 47, No. 1 (WINTER 2009) pp. 1-276 Turnitin Report Formatting Title Page Citation Outline
– – – – 7 ) — { 7 ) ) j L1
_…_.. (S,_ttl.-.c…a. ” – J.m ^ –
Copyright 1969 by Steve Reich. Used by permission.
All use subject to https://about.jstor.org/terms
pointed by the results. He stated then:
and unmusical. In any music which depends on a steady pulse, as
my music does, it is actually tiny micro-variations of that pulse
created by human beings, playing instruments or singing, that
gives life to the music.41
earlier, Reich has continued to have ambivalent feelings towards electronic
techniques. Nevertheless, it was not until 1980 that Reich overcame his old
resolve and again turned to electronic music; the result was a work in
progress, My Name Is: Ensemble Portrait (q.v.). It is most significant, though,
that Reich chose to return to a verbally based tape piece with My Name Is-
not to electronically produced musical sounds. One can state that it is unlikely
that music based on electronically generated sonorities will ever interest him
again.
the “Phase Shifting Pulse Gate” had not been wasted. A concept derived from
the “Gate” soon inspired Reich to return to live instrumental composition, and
the resulting work, Four Organs, was completed in January 1970. In Reich’s
“Pulse Gate” compositions, individual notes had been phased out of an
opening simultaneity to produce melodic patterns. Four Organs, however,
would capitalize on the “variable pulse-width aspect of the Gate”,43 which had
performance. The new work would open with a single chord; one beat at a
time from within the sonority would grow gradually longer and longer in
duration, producing a “sort of slow-motion music… .The tones would simply
begin in unison in a pulsing chord, and then gradually extend out like a sort of
Violin Phase several years earlier, is an instrumental piece derived from ideas
that originated in the electronic studio. Reich states: “This feedback of ideas
brought me to think of electronic music as a kind of interlude filled with new
composed between 1965 and 1971, it is the only one which is not a phase
piece. The composition consists entirely of the gradual augmentation of
individual tones from within the short, repeated dominant eleventh chord that
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minimalist work: in the entire twenty-five minute composition there are no
gradually increasing the rhythmic durations, accomplished by holding down
one, and eventually several, of the notes of the chord beyond the sounding
length of the sonority itself. To enable the performers, playing small electric
organs, to count up to two hundred beats on any one series of sustained tones
(the length to which the augmentation has progressed by the time the work
ends, see Example 6b), another performer maintains a steady eighth-note pulse
with maracas throughout the entire composition.
compelling force and even drama. The expectations of any listener who is
aware of the process involved are constantly drawn toward anticipating the
next step in the augmentation procedure, producing a sense of directionality
statements of Reich’s compositional aesthetic as defined in “Music as a
Gradual Process”; it is also one of his last truly minimalist works.
The new composition, entitled Phase Patterns, utilized an innovative style of
keyboard writing that Reich describes as “drumming on the keyboard”,46
(Example 7). In Phase Patterns, the paradiddle stroke of Western drumming
of the entire composition. Reich claims that the application of such percussive
techniques to the keyboard arose from his own limitations as a pianist: “I had
to come up with a way of playing that is very particular to me but which is, by
piano player….”47 This new type of keyboard writing had important implica-
tions for Reich’s later compositions, expecially Six Pianos (q.v.) of 1973, and
led the composer to view all keyboard instruments as “extraordinary sets of
tuned drums.”48
occurred. The composer flew to Ghana to study African drumming at the
Institute for African Studies, University of Ghana at Accra. According to
Reich: “I went to Ghana to learn African musical structures by playing them,
received daily instruction from Gideon Alorworye, the Master drummer of the
Ewe tribe who was in residence at the University. Reich became especially
fascinated with the polyrhythmic structures which form the basis of so much
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Copyright 1970 by Steve Reich. Used by permission.
1+ -* – + {– * il 11 – 1 + – t o – 4* – + ” a ‘ ‘ * – 4 o * 1-(*( (* t4+ a1
. L -4 * O 4.4-* 4 *-s* ; _
.. _.-. – – – – – – -z – – – – * – — . .
a ~ ~ ~ ~ ~ *, @_
_. 4 _- — – , I. 4 _ -_ _.. . _ . -.
Copyright 1970 by Steve Reich. Used by permission.
All use subject to https://about.jstor.org/terms
Copyright 1970 by Steve Reich. Used by permission.
All use subject to https://about.jstor.org/terms
own separate downbeat”51 -in essence, a polyrhythmic structure not very
different from Reich’s own.
percussion ensemble in performance. In ensembles consisting of drums of
varying sizes and pitches, the Master drummer is in constant control of the
group, indicating to the other performers when it is time to change from one
rhythmic pattern to the next. A particular figure of the Master drummer
elicits an appropriate response from the remainder of the ensemble; when he
continues throughout a work, lending a unity to a performance that makes it
possible to play complex rhythmic structures without the conductor of Western
music.52
structures that are rigorously organized in advance, involving little or no
percussion ensemble must subject their personal expression to the higher goal
of a precise rendition of repetitive, interlocking rhythmic patterns within the
modally based and relying on steady pulse to give them life, served to endorse
Reich’s perceptions of his own music.
magnum opus, a ninety-minute composition entitled Drumming (Fall 1970-
Fall 1971). According to Reich, the African visit’s primary influence on
Drumming was that of “confirmation”. “It confirmed my intuition that acoustic
sound than that produced by electronic instruments, as well as confirming my
natural inclination towards percussion.”53
attempt to answer this question, we must discuss not only his African visit of
1970, but also his study of Balinese gamelan. The latter took place at Seattle
American Society for Eastern Arts. Already after his African visit, and again
during his Balinese studies, Reich began struggling with the thorny problem
of how he, a Western composer brought up in a very different culture than
1973, Reich saw several alternatives available to a composer who wished to
absorb non-Western idioms. One could give up composition and become
either an ethnomusicologist or a performer of non-Western music-both
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continue composing and attempt to absorb one’s newfound knowledge; yet, if
one chose this path, in what way would the composer assimilate foreign
influences? Reich dealt with this question at length in an article published
in The New York Times as well as in his own Writings About Music.54 He
came to the following conclusions:
imitating the sound of some non-Western music. This can be
done by using non-Western instruments in one’s own music
(sitars in the rock band), or in using one’s own instruments to
sound like non-Western ones (singing Indian style melodies over
electronic drones)… Imitating the sound of non-Western music
leads to exotic music; what used to be called “Chinoiserie”.
constructed in light of one’s knowledge of non-Western structures.
… One can study the rhythmic structure of non-Western music
and let that study lead one where it will while continuing to use
the instruments, scales and any other sound one has grown up
with. This brings about the interesting situation of the non-
Western influence being there in thinking, but not in sound. This
is a more genuine and interesting form of influence because while
listening one is not necessarily aware of some non-Western music
being imitated. Instead of imitation, the influence of non-Western
musical structures on the thinking of a Western composer is likely
to produce something genuinely new.
Instruments, Voices and Organ (1973) and Music for Eighteen Musicians
(1976), a myriad of non-Western influences can be noted in Reich’s music, yet
all of these are incorporated, using traditional western materials, within the
been employed by Reich, either consciously or subconsciously, before the
African trip; the journey itself served to a great extent as a confirmation of
paths already laid out. As a matter of fact, most of the following “non-Western”
and non- Western influence begins. Rhythmically, one might mention the use
of a constant unvarying pulse throughout a work, combined with Reich’s
preference for polyrhythmic structures in which several rhythmic patterns of
the same or related material have different downbeats. Tonally, one might
music expanding over lengthy periods without pronounced contrast, may well
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Balinese), Reich shows his affinity to non-Western instrumentation. Lastly,
his devotion to live ensemble playing, his discarding of electronics in favor of
acoustical performance, and his rejection of improvisation with a consequent
turn towards composer-organized processes, were all encouraged by the
virtuoso group performances he observed in African as well as Balinese music.
of its almost ritualistic repetition of drumming patterns, it appears to be
Reich’s most overtly non-Western influenced work. Drumming is the last
work of Reich’s to employ the phasing process extensively, though here it is no
context of Reich’s entire compositional output, Drumming is of tremendous
importance; it is a pivotal, transitional work, standing between the early,
austerely minimal gradual process pieces, and the later, less rigorously
structured, almost luxuriant instrumental tapestries.
great importance for Reich’s later compositional development. Firstly, Drum-
ming introduces “the process of gradually substituting beats for rests (or rests
almost as a substructure, into Drumming. By rhythmic construction, Reich
refers to a process in which a pattern will slowly be formed, one beat at a time,
Rhythmic reduction indicates the reverse process: here, rests are substituted,
image of the way it was constructed. Once the process of rhythmic construction
phasing process.
timbre and texture. One must realize that all of Reich’s music prior to
Drumming was written for ensembles of two or more identical instruments.
when two or more voices moving against each other are identical in timbre,
However, the last of the four parts of Drumming is the first composition by
Reich in which instruments of different timbres are combined simultaneously.
structural clarity-and the listener’s immediate comprehension of the process
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-C
|/A [u e , j7 i 7j p r -r 71
wp ~perefolUar bPis JRA 0 tl?ee d14Uo (OScdliU -fW1i aie M e JLWeO. 1
ki ilo ^^^),l k e ttL s (^ Q syUi AER et4 s 1ual4 s$st & fq k4i a A eA WI. il
AQ (AfM J cWig 04 P A t4 tw 6^ ee W cM g Ae ; all 1C0W4S5 w -Ael
foY tudul w5tw u r t dw
Copyright 1971 by Steve Reich. Used by permission.
All use subject to https://about.jstor.org/terms
timbres is also innovative: instrumentation is gradually changed while rhythm
and pitch remain constant. Instruments enter doubling the existing pitches
and rhythms of the previous performers and, as the former players fade out,
the latter gain in prominence, providing a seamless “timbral modulation.”57
sound of the instruments,”58 a technique Reich returned to in Music for
Mallet Instruments, Voices and Organ (1973), Musicfor Eighteen Musicians
(1976), and Music for a Large Ensemble (1978). The voices do not employ
any text; instead, they are used to double and underscore the various resulting
patterns that arise out of the phasing process, just as the live violinist in Violin
channels. Reich’s challenge was to discover what types of voices would blend
drums; Reich found that here a male voice singing syllables such as “tuk, tok,
duk” would blend most effectively. Likewise, Part Two, scored for three
marimbas, uses female voices singing such syllables as “bou and dou”. Part
Three, written for three glockenspiels, requires different vocal usages, as no
human voice could merge effectively with the high range of these instruments.
and piccolo with its upper range. The final Part Four, previously mentioned
due to its innovative mixture of all the instrumental forces used in the other
paired with the activity of its respective instrumental group.59
key, as would be traditional in Western music, but instead by complete and
highly contrasting changes of timbre. Pitch and tonality are both static
parameters in Drumming, with each performer keeping “to the narrow modal
gamut he begins with, which is just one contribution to the tonal static
harmonic unit.”60
beginning of Drumming’s Part One (Example 8). The work opens with a
single drum beat and eleven beats of rests, within a cycle of twelve-beat
measures. Starting with this solitary beat, the drummers gradually, one beat at
formed, the phasing process begins in one of the instruments. There is an
opening process of rhythmic construction not all the drummers must move
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of the rhythmic construction process, and by the employment of the human
voice. The voices (or voice in Part One) blend almost unnoticed into the
ensemble, doubling resulting patterns arising out of the phasing process.
of Drumming together. It is the last section of Drumming, however, that is
instrumental families. A kaleidoscope of sound is the result-rich, animated,
and hardly ever seeming repetitive, even though the listener by now has been
timbral blend. Here, we have the first occurrence of a turn away from the
Gradual Process.” Reich’s earlier aesthetic is now compromised in favor of a
perceptibility. With this single innovation, more than any other, Drumming
charts the path that Reich was to follow in subsequent compositions.
seems to be a reversion from the textural and timbral variety heralded by Part
instruments is employed. According to the composer, Six Pianos was the
result of an idea of “composing a piece for all the pianos in a piano store.”61 Six
allowed the performers to play rapid, rhythmically complex music without the
accurately.
decisive rejection of phasing as a structural technique; it is based entirely upon
which this process is used here differs from the earlier work. In Drumming,
the performers constructed a pattern, one beat at a time, from what began as a
single beat and eleven rests within a twelve-beat cycle. As there was no
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process, the pattern was literally formed out of complete silence. In Six Pianos,
played against itself, but two beats “out of synch.” Superficially, this may
appear to be the same as the familiar phasing process, but here the means of
there is a percussive build up of beats in place of rests.”63 This new method of
perceptible to the listener, however, and is another sign of Reich’s recent
willingness to compromise his aesthetic of structural clarity.
change of key and mode (Part One is in D Major, Part Two is in E Dorian,
Part Three is in B natural minor).64 This new use of tonality to structurally
define sections of a composition is indicative of a turn back towards more
is established by repetition alone without any semblance of functional harmonic
The keyboard technique of Six Pianos does not break new ground; it is
pattern between alternating left and right hands, reflects this conception. In
spite of its timbral limitations, Six Pianos remains an important part of Reich’s
tion, and its new use of tonality as a structural device.
within one person’s output. It is even harder to parcel off a composer’s work
into neat style periods with clearly defined changes in style occurring at one
precise moment; there often seem to be more transitional works than there are
that Reich was, between 1971 and 1974, moving towards a distinct change of
style, one made manifestly clear by Music for Eighteen Musicians (1976, q.v.).
We have already noted elements of this new style, however, as long ago as Part
Four of Drumming. An interest in beauty of sound as an end in itself, a
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Copyright 1973 by Steve Reich. Used by permission.
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process, a richness of texture and sonority, an expansion of the vocal and
instrumental resources, and a new use of harmony as a structural element, all
Drumming s Part Four and Six Pianos gave evidence of many of these trends,
and Musicfor Mallet Instruments, Voices and Organ (1973) continues them,
further enriching the texture and musical resources employed and providing
the first complete demonstration of the composer’s coloristic imagination.
Organ (hereafter referred to as Mallet) may be considered as the last of the
transitional works, standing between the phase pieces and the richly conceived
later compositions-or as the first example of the new style.
augmentation technique utilized in Four Organs.65 Mallet, scored for four
marimbas, two glockenspiels, a metallophone (vibraphone without motor),
voices, and electric organ, therefore merges two simultaneous interrelated
rhythmic processes. The first process is the familiar one of rhythmic construc-
duplicate of a pre-existing pattern, with the second one or more beats out of
phase with the first.”66 This process is employed exclusively by the marimbas
and glockenspiels and is immediately apparent at the opening of the work: one
glockenspiel and three marimbas begin by playing their fully constructed
rhythmic pattern (as did the four pianos at the beginning of Six Pianos), while
constructing the identical pattern in a different metrical position (see Example
metallophone and organ. This process consists of the gradual augmentation of
a brief two-chord “cadential” progression,67 a procedure perhaps inspired by
earlier work, elongating the entire “cadential” pattern over progressively more
and more measures.
composer interrelates them. The rhythmic construction of the first process,
which naturally involves increasingly animated rhythmic activity in the mallet
mechanism, inspiring further gradual elongation in the voices, metallophone,
and organ. These two processes therefore on one level take place independently,
while on another level also signal each other to proceed to the next stage in the
structure.
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lb Hp, L!” I- ‘U I” kL-J U + 4 > t } tttg 7 T 0 % ‘> W :7>Pr2
(1973), mm. 1-2. Copyright 1973 by Steve Reich. Used by permission.
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rhythmic constructions in the mallet instruments have been entirely formed,
causing these instruments to reach their point of maximum rhythmic activity.
At the same time, the voices, due to the triggering mechanism described
above, have been continuing their augmentation process; by the middle of
each section they have elongated to maximum length (based on the “longest
length of continuous tone a single breath can sustain.”68) At the midpoint of
each of Mallet s four sections-the point of maximum activity in the mallet
instruments and maximum prolongation of the voices’ “cadential” progression
– the lower mallet instruments abruptly move out of their variously constructed
in the mallet parts at the opening of the work had triggered the voices to begin
ways a mirror image of the first half. A step by step compression of the two-
chord “cadential” progression takes place in the voices, organ, and metallo-
phone, until these parts have returned to the opening length of their chordal
pattern. Beneath this process, the mallet instruments maintain their pattern in
half of each section) occurs four times, in sections marked off by changes of
A dorian (2/4), Section Three is in B natural minor (3/4), and Section Four
is on an A dominant eleventh chord (3/4).69
overall structure, that of construction/augmentation vs. unison/diminution,
is readily apparent to the listener. But the sub-structure, namely the mallet
instruments’ construction of identical out-of-phase patterns, gets obscured by
the work’s luxuriant timbral blend. As in Six Pianos and Part Four of
musical process clearly be perceptible. The fact that Mallet is still conceived of
conceals the procedure.
namely, “using the voice to exactly imitate the sound of an instrument playing
the form of voices highlighting instrumentally created resulting patterns, is
“extended in Music for Mallet Instruments, Voices and Organ to a constant
vocal-instrumental blend as one of the basic timbres of the entire piece.”70 The
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serves to obscure the musical process; it also foreshadows the complex
textures of works such as Music for Eighteen Musicians. In addition, Mallet
continues a trend we first observed in Six Pianos, that of structurally defining
tonalities are juxtaposed in abrupt non-functional relationships. Lastly, the
concept we noted in Mallet-that of one musical process triggering an
appropriate response pattern in another instrumental group -is closely related
to Reich’s non-Western studies; it is especially similar to the African technique
From 1974 to 1976, Reich concentrated all his creative efforts upon
that was most influential in establishing Reich’s name before a mass public.71
Music for Eighteen Musicians marked such a radical departure from the strict
might have asked whether the composer’s compositional aesthetic had entirely
interview conducted by critic Michael Nyman.72 In speaking with Nyman,
Reich reflects on the “didactic quality” of his earlier works, noting the many
a work be based on a single, gradual process that is clearly audible to the
listener at all stages of its progression. No longer must a structure be
immediately apparent, nor are structure/process and musical content one and
the same, as they were in 1968. No longer is the process of composition
impersonal; on the contrary, it is now filled with composer and performer
choice. Reich’s new style aims at a richness of texture and sonority, an
expansion of the vocal and instrumental resources employed, and a subse-
quently greater freedom of musical structure. The following paragraphs are
excerpted from the Nyman interview:
the stress in music was on individual expression and free improvi-
sation, and I was trying to divorce myself from that and to show
that one could work in a more impersonal way…. It’s true that the
thrust of the article and very terse wording of it was to drive home
an idea of impersonality which I thought was important at that
time. And now it’s eight years later and I don’t feel like making
that point any more, because it’s so well understood and I have
changed musically quite a bit.
what I was trying to do was to eliminate personal choices. In
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personal choices, but there isn’t one iota more of chance in my
music, and I don’t believe that will ever change….Chance is
something I’ve found is a very unhealthy influence, and it has
produced very poor music…. But the idea of choice is something
quite different and that is something from which I have shifted
position.
music was made as I was in the past. If some people hear exactly
what’s going on, good for them, and if other people don’t, but they
still like the piece, then that’s OK too.
Musicians was making beautiful music above everything else…
ago. On the other hand, although the overall sound of my music
has been getting richer, it has done so without abandoning the
idea that it has to have structure….
becomes less possible and less necessary to follow the process.
There was a didactic quality to the early pieces, and looking back
I’d say that, when you discover a new idea, it’s very important to
present that idea in a very forceful and clear and pared-down way.
…But once you’ve done that, what do you do? Just sit there
cranking out one perfect phase piece after another? Personally, as
a human being, I feel the need to move on, not to sell out or cop
out, but just to move on.
apparent at first glance, the deliberate restriction of available resources-in
total output, the comparison of a work such as Four Organs (1970) with
Music for Eighteen Musicians might lead one to conclude that the composer
had bowed before the temptation of reaching a larger public. However, it is
consumption. Rather, it is the result of a gradual stylistic shift we noted
beginning with Part Four of Drumming, and extending through Six Pianos
and Mallet. Music for Eighteen Musicians merely brings to fruition various
trends which were already well established in Reich’s earlier compositions.
scored for violin, cello, two B-flat clarinets/bass clarinets, four women’s
voices, four pianos, three marimbas, two xylophones, and a metallophone.
Though most are amplified via microphones, all the instruments employed are
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Mallet. Rhythmically, there are several different levels of time occurring
rhythmic pulse which is immediately apparent at the opening of the work in
the pianos and marimbas, and which is maintained unceasingly, in one
instrumental family or another, throughout the entire composition. The
second type of rhythm, new in Reich’s music, is the employment of human
breath as a measure of duration. The entire opening introduction and closing
central sections of the work, utilize pulses played by the voices and the winds.
as their breath will comfortably sustain them.” Reich conceives of these
pulses, which due to the nature of human breath are emitted in a rising and
constant rhythm of the pianos and mallet instruments.”73
work, as important as the rhythmic structure. Reich himself states: “There is
more harmonic movement in the first five minutes of Music for Eighteen
constructed around a sequence of eleven chords which is played at the
beginning of the work as an introduction and which returns once more at the
end as a sort of epilogue. All the instruments and voices play their assigned
breathe likewise follow the breath patterns (< >) of the wind players. Each of
the eleven chords is held for the duration of two breaths, at which time the
means far-reaching; many of the eleven chords are merely inversions or
revoicings of the previous sonority, and there is no modulation (See Example
lla).
harmonic movement in this work. Once the cycle of eleven chords is completed,
marimbas. As these rhythm instruments prolong that single chord, a small
the first section, the rhythm instruments switch to the second chord in the
sonority. This process is repeated over each of the original cycle of eleven
chords, resulting in a composition that contains eleven central sections, plus
the opening introduction and concluding epilogue (these latter two being the
only parts of the work in which the chordal structure is stated explicitly).
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t I PI I
1-9″P
chordal sequence.
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is altered in section V of the work.
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medieval cantus firmus technique: “Each chord that might have taken fifteen
or twenty seconds to play in the opening (introductory) section is then
stretched out as the basic pulsing harmony for a five minute piece, very much
Organum by Perotiil might be stretched out for several minutes as the
harmonic center of a section of Organum.”75
cantus firmus or variation procedure. In Eighteen, the bass line of the chordal
cycle is no more than decorative; it is the middle and/or upper registers which
work. Yet the middle and upper registers, lacking their bass underpinning, are
pulses recur as the subjects for their respective eleven sections, Reich gains
the latitude for modulation as well as re-harmonization of the melodic material:
Comparing Example lla to Example llb demonstrates how, in the fifth
section of the work, Reich is able to modulate to C-sharp minor by maintaining
an approximation of the middle and upper registers but changing the bass
pitches. The composer apparently likes the tonal/modal ambiguity derived
from such a harmonic procedure, as he returned to this type of technique once
more in 1979 as the basis for his Variationsfor Winds, Strings and Keyboards.
fairly casual listener. Within the eleven individual sections, however, the lush
techniques employed. It is the sub-structures of these separate pieces that serve
almost as a summation of Reich’s work from 1965 to 1976, a vast reunion of
small pieces employ rhythmic construction, that of gradually substituting
beats for rests; others use rhythmic construction in connection with a quasi-
phasing process, in which the constructed rhythmic patterns have different
sions is often involved (here usually given to the strings), reminiscent of the
elongation procedures employed by the vocal parts in Mallet. In the middle of
duration is determined by the length of a human breath) returns in the voices
and winds; this gives the effect of a constant reminiscence of the texture and
used to add timbral variety by doubling the rhythmically constructed melodic
patterns. Yet all of these sub-structures disappear as the listener becomes
dazzled by the surface beauty of the work, a sparkling melange of shifting
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have suspected that a tapestry of such sonic variety could have come from the
pen of a previously austere minimalist?
of non-Western techniques, specifically of the Balinese gamelan. The signal to
change from one section to the next, as well as internal changes within
individual pieces, “are cued by the metallophone… whose patterns are played
once only to call for movement to the next bar, much as in a Balinese gamelan
a drummer will audibly call for changes of pattern, or as the master drummer
allows the progression from one piece to the next to be accomplished as
gradually and smoothly as possible; the intention in fact is for one section to
blend almost unnoticed into the following.
Eighteen. Reich frequently employs, within individual pieces, a changing
relationship between harmony and melody. “Specifically, a melodic pattern
may be repeated over and over again, but by introducing a two- or four-chord
cadence underneath, first beginning on one beat of the pattern, and then
beginning on a different beat, a sense of changing accent in the melody will be
augmenting “cadential” progression, just described above as being similar to
the elongation process of Mallet, as the chordal underpinning for a melodic
line. If the melody itself consists of a repetitive rhythmic pattern, and beneath
“cadential” progression itself gradually elongating in length, a whole variety of
line. Thus, we can now return to a comment made at the opening of our
discussion of Eighteen, namely that there are several different layers of
rhythmic activity simultaneously occurring in this composition. We are now
in a position to chart at least four separate levels of musical time in Eighteen.
the steady rhythmic pulse maintained in the mallet instruments, the process of
the winds which rise and fall as a human breath, and the shifting, augmenting
After Music for Eighteen Musicians became generally known, Reich’s
commissions which resulted in three splendid works that will be described in a
moment, Music for a Large Ensemble (commissioned by the Holland Festival,
pleted April 1979), and Variations for Winds, Strings, and Keyboards
(commissioned by the San Francisco Symphony Orchestra and completed late
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more of world music and culture, from absorbing new influences into his
tively little about his own Jewish heritage, he began an intensive study of
Hebrew, the Torah, and scriptural cantillation techniques, culminating in two
years spent learning traditional cantillation systems and their notation (New
York and Jerusalem, 1976 and 1977).78 We shall soon see how Reich’s study
of his Jewish heritage had a profound effect on his musical style.
of techniques borrowed from Music for Eighteen Musicians and Music for
Mallet Instruments, Voices and Organ. It is scored for a core of eleven
percussionists who create and maintain the rhythmic activity of the work
(marimbas, xylophones, vibraphone, pianos); they are harmonized and timbrally
flutes, soprano saxophones, and four trumpets. Though all instruments are
acoustical, the strings, winds, voices and pianos are amplified. Timbrally, the
size and richness of the ensemble has increased to such an extent that, even
discern on the surface.
structed in four sections, each defined by abrupt changes of key and/or meter,
Mallet s, however: this is the utilization of brief two-chord “cadential”
progressions which gradually augment until the middle of each of the four
sections and, once having reached maximum elongation, return by a process
The use to which these lengthening and shortening chords are put, however, is
the rhythmic/melodic figures which are superimposed above it. Harmonically,
Large is much simpler than Eighteen, being closer in its conception to Mallet,
the ascending or descending (and also augmenting or diminishing) “cadential”
progressions provide the sole harmonic movement within each of the four
sections. The effect produced is that of a constant swaying between semi-
functional sonorities within each of the four juxtaposed key areas.79
identical patterns which are metrically several beats apart), as was the case in
both Mallet and Eighteen. Also like Eighteen, Large employs vibraphone cues
to coordinate the ensemble. The most significant application from Eighteen,
however, is the use of the human breath as a measure of duration. It is the sole
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patterns, but do not pulsate as they did in Eighteen. Thus, we have in Large, as
the process of augmentation/diminution of the “cadential” progression, the
rhythmic construction likewise in the mallet instruments, and the sustained
trumpet chords which enter at the midpoint of each of the four sections of the
work.
the middle of each of the four sections, as maximum elongation of the chord
progression approaches and rhythmic construction in the mallet instruments
is complete, there are longer melodic lines stated in the violins and clarinets.
“composed of smaller melodic patterns combined to create a somewhat ornate
development in Reich’s style, one that will have an impact on Octet and
Variations, as the melodies themselves, while initially constructed from
separate repetitive units, are of greater length and more sustained musical
interest than have ever been found in Reich before. Reich’s readoption of the
traditional concept of melody is but another example of his abandonment of
the minimalist aesthetic in favor of a greater abundance of resources. The
composer attributes his newly found method of melodic construction directly
putting together of small motives to make long melodic lines that make sense
of the sacred text.”81
“reaction to constantly working bigger and bigger, and a reaffirmation of the
fact that small pieces are as important as large ones.”82 The work is scored for
two pianos, string quartet, and two woodwind performers; the latter are
expected to play a variety of instruments (clarinets, bass clarinets, flutes,
piccolo) but there are never more than a total of eight musical lines occurring
at one time among all the performers.
demanded.83 Reich views the piano style of this work as “the result of years of
writing for those mallet percussion instruments is transferred to the keyboard,
the two pianos which generates the rhythm for the entire Octet. ,’4 These inter-
locking, canonically constructed piano patterns, which comprise the incessant,
dense rhythmic backbone of the piece, begin immediately at the opening of the
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delineated by clear changes of key and/or texture, while others are elided in
the next. Structural elision is apparently a prime goal in Octet; the musical
processes of some of the instrumental parts are often not completed by the
respective processes into the ensuing portion is inevitable. We have noted
previously, in discussing Mallet, Eighteen, and Large, that while the musical
overall structure of the work and the boundaries between its constituent parts
are still clearly audible. In Octet, for the first time in a Reich composition,
neither the larger structure nor the individual sub-structures of the five
sections are immediately apparent. Despite the reduction of available timbral
luxuriance of Eighteen and Large), Octet is a work in which the composer
seems no longer concerned that the listener comprehend the constructive
basis and musical processes involved.
observed in Large, that of forming lengthy melodic lines by joining together
smaller melodic fragments. In Octet, it becomes apparent that this technique
of melodic construction derives as much from Reich’s own earlier interest in
constructed by the composer selecting resulting patterns that have arisen out
patterns together to form full-fledged melodic lines. The melodies found in the
to assert their independence from the mere doubling of resulting patterns; it is
in these sections of the work, where the lengthiest melodic lines occur, that
unto itself, apart from any dependence on figures which have arisen in other
voices (see Example 12).
canonic relationship between Pianos One and Two. The basic rhythmic
pattern is already fully formed in Piano One at the opening of each section; it
is Piano Two that must involve itself in the process of rhythmic construction,
with the end result being the formation of a pattern identical to that of Piano
and/or bass clarinets (though this varies from section to section). However,
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by Steve Reich. Used by permission.
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incomplete portion of the rhythmically constructed pattern of Piano Two,
resulting in distinctive melodic lines for the woodwinds which consist of brief,
“cadential” progressions. This slow elongation process is similar to the
technique we observed earlier in Mallet, Eighteen and Large. For example, the
two-measure, three-chord pattern, which is found in the violins at the opening
that portion of the piece. As in Eighteen, and Large, the elongating “cadential”
progressions in the strings lend a constantly shifting harmonic accent to the
repetitive melodic lines occurring above them. In Sections Two, Four, and
Five, the cello’s “cadential” bass pattern, repeatedly swaying between semi-
functional tonic and submediant sonorities and simultaneously augmenting as
well, makes the changing harmonic accents particularly noticeable.
activity in the cello and bass clarinet, as well as the previously mentioned
lengthy melodic lines in the flute and/or piccolo which show greater indepen-
dence from resulting patterns than the melodies of other portions of the
composition. The augmentation process of the upper strings in Sections One,
two-chord progression. In contrast, Sections Two and Four favor brief rhythmic
than are the full-fledged melodies of Sections One, Three, and Five. The
augmentation process of the upper strings in Sections Two and Four involves
elongating the shifting “cadential” bass pattern which sways between tonic and
expands to many times its original length, the shifting “cadential” bass figure
in the cello, the rhythmic interjections of resulting patterns in the clarinet and
and piccolo.
points. First of all, these three Reich compositions (Large, Octet, Variations)
display a new turn on the part of the composer back towards his Western
musical heritage, and to a great extent a consequent shift away from non-
Western techniques. We have already noted the vast enhancement of texture
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equally indicative of a rejection of “minimalism”, include lengthy melodic
lines, a new structural importance of harmony, and a sense that the composer
is writing in a more intuitive less impersonal manner than ever before. Lastly,
sense of proportion. Reich appears to have discarded the endless time-distorting
(sixteen minutes long), Octet (eighteen minutes) and Variations (twenty-two
minutes) are never in any way diffuse or verbose, no matter how texturally
dense they may be. Lengthy repetition is curbed in favor of having musical
structures unfold more rapidly and less repetitively.
did in 1971, now finding valuable insights to be gained from much wider scope
Western music and I think that this was an incredibly fertile and
healthy influence that has now become a permanent part of my
vocabulary. At the moment, however,… looking back at older or
recent Western music, like that of Bart6k, has been exceedingly
useful and important to me, and I can see that continuing for
some time…. I would say that it’s important to me to study the
past, particularly that of one’s own traditions.. .not so much to
rehash what has been done better by those that precede oneself, as
to continue to speak in the musical language that one naturally
speaks in at the time that one is alive now, [but] with a better
knowledge of what went on before.85
indicative of this trend towards the Western tradition. Variations, commis-
can be performed by full orchestra (it is scored for strings, three flutes, three
There is also a chamber orchestra version of the composition for twenty-five
recital programs.
composer.”86 Several new features are immediately apparent in Variations
which lend the work its remarkably different sound. First of all, it is slower in
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repeated chaconne-like structure; for the first time in Reich’s music it is fully
functional harmony that has primacy in determining structure, not rhythmic/
one, the chaconne recurring only three times in the entire twenty-two minute
occur within the chaconne’s harmonic progression:
would be via what is traditionally called a suspension; i.e., that all
the notes stay the same, except one, and then another moves and
then another moves and in the midpoint one creates certain
dissonances until finally these are resolved, so one is dealing with
a functional harmonic situation, but a new one, and I believe that,
certainly, functional harmony is not exhausted.87
the second movement of Bartok’s Piano Concerto No. 2 (1931); in other
words, it is a method he learned purely by looking at Western sources. “For
me, it’s a major breakthrough because it (Variations) deals with a harmonic
language implicit in many pieces but never really developed, and unless I had
gone back to some traditional Western sources, I probably would not have
developed it myself.”88
composition. The result is an entirely new, mellow instrumental timbre,
lacking the familiar steady rhythmic chatter of the marimbas and xylophones.
The wind instruments, which carry the melodic and rhythmic material of the
woodwind sound to the absent percussive attack.”89
statement of the harmonically-based chaconne pattern. Within each of the
three sections, the flutes and oboes alternate in presenting the melodic
material. The three flutes are doubled throughout Variations by two pianos
and three electric organs, while the three oboes are doubled only by three
electric organs. It is not until the very end of the last variation that the two
groups are united in playing the melodic material. Each of the three variations
presents a distinctive melodic pattern, with the individual notes of the re-
beneath. The effect, says Reich, is “one of a considerably more florid,
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date.”90 He does not exaggerate: one of the two most significant features of
melodic lines of the flutes and oboes, hovering high above the rest of the
ensemble, signal a stylistic shift as radical as anything we have yet observed in
The other significant feature of Variations, every bit as important as
determinant. Though we have observed shifting, repetitive, semi-functional
“cadential” progressions in Reich’s previous works, as well as the juxtaposition
of static tonalities to delimit sections of compositions, nothing could possibly
have prepared us for the harmonic growth evident in Variations. Yet Reich’s
subsequent statements harks back to earlier techniques. Just as in Music for
Eighteen Musicians only the middle register of the pulsing chordal “cantus”
middle register of the chaconne progression, while changing the bass line
beneath. Thus he is able to reharmonize the melodic material of the winds, as
The chaconne-like progression, occurring slowly but persistently within
capitalizes timbrally on his new-found use of structural harmony: at strategic
intervals within the first and third variation, the double bass and full brass
dominant sonorities. This is the sole function of the brass in Variations as they
second variation, the brass are absent, but the string bass (doubled by cello and
harmonies, as well as to sway back and forth between tonic, sub-dominant and
dominant sonorities in a manner similar to the “cadential” progressions of
Octet and Large. Though the cadential patterns do not augment here as they
did in the earlier works, they can now be understood for the first time in fully
functional structural terms, conceived as they are within a clear, harmonic
hierarchy and tonal framework.
cares to describe the structures of the individual sections, not even the
formation of the rhythmic patterns. It is the basic harmonic progression which
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mm. 321-324. Copyright 1979 by Steve Reich. Used by permission.
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are never constructed during the course of the work: they spring forth, fully
formed, right at the opening of the composition. Reich is well aware of the
radical stylistic shift that Variations and its two new compositional techniques
-a harmonic structural basis combined with lengthy independently conceived
melodic lines-heralds. He states that, unlike Music for Eighteen Musicians,
which was “a summation of what has come before, it (Variations) is very
much an open door leading to a much-enriched harmonic and instrumental
world for me in the future.”91
as of March 1981, still a work in progress. At first, it appears to present
disturbing contradictions for those of us who would wish the composer’s
musical development to progress in a straight, unbroken line. As previously
mentioned, with My Name Is Reich returns to electronic music for the first
time since his decisive rejection of all electronic techniques in 1969. Even
more perplexing is the fact that My Name Is harks back to a still earlier
stylistic aesthetic from within the composer’s output: it is a verbally based
tape/speech composition in many ways very similar to Come Out (1966) and
It s Gonna Rain (1965), Reich’s first two significant works.
from it, and why would he choose to go back to the speech-based tape
aesthetic, in which he had seemingly already lost interest in 1966? The
composer now makes it clear that his earlier rejection of electronic music in
1969 applied only to electronically generated sounds.92 Viewed from this
angle, Come Out, It s Gonna Rain, and My Name Is are not really electronic
works at all: though they use electronic techniques to realize their process,
they are speech pieces pure and simple. Consisting as they do entirely of pre-
recorded verbal material, they are merely tape compositions which use speech
its sonic qualities.
audience were taped as the concertgoers entered the hall. The most interesting
names were then edited and dubbed onto tape loops during the first half of the
Reich and Musicians recital; after intermission, Reich informally improvised
tape recorders. The result was a flexible phase composition, similar in its
almost aleatoric aesthetic to Pendulum Music, compositionally, the effect was
close to Come Out and It’s Gonna Rain, but here the phasing process was
presented in a technically much more fluid and unstructured manner.
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names as the basis for a tape piece, he would use the names of the performers
in his own ensemble. Instead of improvising the phase relationships, he would
meticulously work them out in advance, but using the technologically more
sophisticated equipment made available since 1967, with a consequent greater
complexity of the end product.
Whitney Museum in New York on January 6, 1981. Reich is careful to label
this composition as a “work in progress,” for reasons which will become
evident in a moment. At the Whitney Museum, the eight performers of Octet
first stepped forward to microphones and introduced themselves (“My name is
Ed. My name is Nurit. My name is Shem. My name is Bob. My name is Mort.
began immediately afterwards, with these same introductions repeated in the
identical order. Starting with Ed, Reich puts each of the names, one at a time,
announced, a rapid shift of phase begins; unlike Come Out and It s Gonna
Rain, where the phasing process took several minutes to become audible, in
My Name Is it takes only several seconds for a complete shift of phase to be
accomplished. The rapidity of the phasing process, combined with its loosely
structured application, makes one realize that the composer has transferred a
music: just as live works, such as Music for Eighteen Musicians, placed beauty
of sound and luxuriance of texture over perception of process, here too the
audible at all stages of its progression. And the coloristic effects are indeed
remarkable-resulting patterns, reverberations, drones, chordal combinations,
phasing process itself.
section of coloristic patterning. A second voice eventually also fades in,
introducing the next name, and rapidly shifts out of phase; simultaneously, the
phasing processes is repeated for all eight of the names used in the composition.
and just described here, is no more than a work in progress, a sort of
“notebook sketch” for a much larger composition that would go far beyond the
re-hashing of old tape techniques. The projected work would expand in several
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could be combined with sound film, resulting in a historico-political multi-
media event. Thirdly, rather than having the electronic procedures consist
only of phasing techniques, Reich would submit these well-known voices to a
variety of processes, including some conceived of much earlier in the composer’s
career, but which were technologically impossible to realize at that time.94
realization that his devotion to instrumental music, so apparent since 1969,
would not have to be abandoned as a result of his renewed interest in
material used in It s Gonna Rain and Come Out, as well as the harmonic,
melodic, and rhythmic resulting patterns which arise from the complexity of
the verbal phase relationships. Why would it not be possible to utilize live
instruments in combination with the electronic tape, to imitate the sounds
produced by the rapidly phasing verbal material as well as to complete the
implied harmonic, melodic and rhythmic inferences of the resulting patterns?
Once live instruments were introduced, the tape could fade out, at which point
realized that this combination of verbally-based tape techniques with live
instrumental music would be his ultimate goal in any musical project involving
which I had stopped doing merely as a kind of ongoing movement away from
meaningful manner into what I was doing now. What I would like to do with
part of it is to introduce the instruments…. One would end up with a tape and
a live score. And My Name Is would become a kind of notebook sketch for this
It should by now be apparent that My Name Is, with its coloristic
unexpected) outgrowth of trends already present in Reich’s stylistic development.
most recent composition, a four-part work entitled Tehillim (Hebrew for
“Psalms”), are far more remarkable. It is not an exaggeration to predict that
observed in Music for Eighteen Musicians.
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South German Radio (Stuttgart), and the Rothko Chapel (Houston), consists
of settings of four Psalm texts, in Hebrew. For the first time in Reich’s career,
unlike the speech-based tape pieces which took verbal phrases and made them
into the actual musical material. Reich had always been displeased by his
student attempts of the early 1960’s to set a written text directly to music.96
His initial joy at discovering the tape techniques of Come Out and It s Gonna
Rain derived primarily from his realization that the use of recorded speech as
musical material would solve his problem of how to compose vocal music. For
Reich felt that setting the works of certain American poets (such as William
Carlos Williams, Charles Olsen, and Robert Creeley) directly to music distorted
finds himself, for the first time, entirely comfortable with the process of
gives him two distinct advantages: first of all, Hebrew is not Reich’s native
tongue, and he therefore gains a certain linguistic distance from the material
which he would not have with English; secondly, the Psalms are not in
modern Hebrew but in ancient Hebrew, and therefore a historical distance
scriptural cantillation tradition for the Psalms, as there is for the Torah and
the Books of Prophets. Reich, who has studied cantillation techniques, can
thus feel doubly free in his dealings with the Psalm texts: not only is he
removed from the language, but he can approach the Psalms purely as words
without any background knowledge of cantillation melodies hovering in his
mind.
specific Psalms as subject matter for a composition obviously assumes a
consequent use of musical material that will enhance the meaning of the texts
chosen. Therefore, it must have seemed apparent to Reich that Tehillim could
no longer be constructed around melodically repetitive patterns, as all his
previous compositions had been, without violating the integrity of the text. In
Tehillim, we are dealing with genuine melodic material, spun out independently
other voices, or of joining together repetitive fragments to form a longer
melodic line. We have observed a slow and steady growth of the melodic
parameter in Reich’s recent compositions: the melodies of both Music for a
Large Ensemble and Octet were formed either by using the resulting patterns
from other voices, or by piecing together smaller fragments in the manner of
cantillation technique. Variations allowed the melodic material of the flutes
and oboes to become, for the first time, entirely independent of the musical
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repetitive fragments nor resulting patterns. We are now listening to fully-
formed melody, conceived as an integral, independent entity. In the composer’s
own words, Variations, at least melodically, is “poverty-stricken” compared to
Tehillim.97
For the Hebrew text’s accentuation pattern determines rhythm and meter, its
themselves (and melody, their conveyor in music) govern both the large-scale
form and smaller structural details of Tehillim.
turning point in Reich’s oeuvre; harmony also exhibits a vast expansion in
scope. Though Tehillim was conceived initially as a melodic work, with the
harmonic skeleton not germinal but rather a later addition,98 the several
interrelated harmonic cycles of Tehillim are a prime contributor to the overall
harks back to that which we first observed in Music for Eighteen Musicians: a
and upper registers remain fairly constant. Thus Reich gains the latitude for
eventual modulation, merely placing new bass pitches beneath the original
chordal cycle and removing those notes from the middle and upper registers
which interfere with the revised modulatory plan. However this technique is
used in a much freer manner than it was in Music for Eighteen Musicians: the
required of a movement’s basic chordal cycle) are far greater in Tehillim than
in Reich’s earlier works. Similarly, Reich takes liberties in the manner in
which he relates the various permutations of the harmonic cycle; several
versions may be combined, either by reordering, overlapping, or juxtaposition,
harmonic cycles are now clearly wedded to functional tonality, enabling the
harmonic language to possess a greater sense of direction than ever before.
The chords themselves, chiefly triadic but with many added tones, are similarly
Other aspects of Tehillim point to new directions in Reich’s work. His
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reduced to groups of two or three beats, and within each movement the eighth
declamation of the Hebrew and is in sharp contrast to Reich’s earlier work
which typically maintained a fixed meter for long sections or entire compositions.
rhythmic punctuations, staggered imitative entrances, timbral enrichment,
and further imitation of vocal motives. The timbral and textural contrasts in
their scope and variety, showing the composer’s new concern with diversity,
not unity, of sonic quality. Tempo likewise is employed as an element of
contrast, with the third part functioning as a true slow movement, pervaded by
What is truly unprecedented in Tehillim is Reich’s abandonment of
composer warns us that “while there is no repetition in Tehillim, I do not
mean to say that I’m through with repetitions,”99 Tehillim itself employs
repetition only in the manner that it has traditionally been used in Western
music. Large-scale sections (such as entire Psalm verses) or individual lines of
text may be repeated, but repetition of the earlier Reichian type-the constant
reiteration of small-scale rhythmic/melodic modules -has been almost entirely
rejected. Only the percussive backbone of Tehillim (the tambourine, hand
clapping, marimbas, and vibraphones) retains the sort of incessant, interlocking
work. Structurally, Reich has not abandoned his interest in clarity of process,
discerned aurally by any concentrated listener. The concept of canon in itself
has a long heritage in Reich’s music. Just as phasing was a sort of seamless,
transitionless canonic technique–and as rhythmic construction resulted in
the formation of canonic relationships between two or more instrumental
parts-so too Tehillim depends on the canon in order to combine its new
lengthy melodic material. Part One of the work consists almost entirely of
two- and four-voice canons at the unison sung by women’s voices; each verse
between the voices varying from verse to verse. In this way Tehillim, while
blazing new paths in its melodic construction, can simultaneously have a
satisfying organic connection to Reich’s earlier works, due to its utilization of
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multiple vocal tracks of It s Gonna Rain (1965), or the multiple instrumental
tracks of Violin Phase (1967), if not identical canons at the unison? The prime
transitions between the various canonic positions. Yet the effect of the canons
of Tehillim s Parts One and Four (due to their unison pitch relationship, their
identical vocal range and performing medium, and their pure, non-vibrato
vocal style) is remarkably close to Reich’s early tape music. In essence, the
superimposed vocal tracks of Come Out and It s Gonna Rain have returned in
Tehillim in an utterly different guise, proving once more the fertility of
electronic influence on live instrumental music.
works. We have already noted the origin of Tehillim s chordal cycle in Music
for Eighteen Musicians and Variations. It must be stressed, however, that
Reich’s ability to modulate in Tehillim, as in earlier compositions, derives as
much from the deliberately ambiguous modality of his harmonic materials as
from his alteration of the bass beneath fixed middle and upper register pitches.
entire chordal cycle. Closely connected to the harmonic modality is the
melodic modality of the vocal lines. In Parts One, Two, and Four, the melodic
four in Part One, verse three in Parts Two and Four). It is these verses,
exploits for reharmonization, modulation, and cyclic permutation when they
recur later in their respective movements.
here in Tehillim Reich again employs techniques of augmentation and/or dimi-
materials above. Similarly, the melodies themselves (in Parts Two, Three, and
Four) use augmentation as one of their prime methods of variation, and the
combination of elongated melody with altered chordal cycles produces a con-
Lastly, the sonic quality of Tehillim, its timbres, textures, and instrumen-
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canons to tape music, and the interlocking rhythmic patterns in the percussion.
In Tehillim, one of the most distinctive timbres is derived from the fact that
and later electric organs in Part One; oboe and English horn in Part Two;
oboes, violins, and clarinets in Part Three; oboe and English horn, clarinets,
and later electric organs in Part Four. The almost electronic sonority resulting
from this unison doubling of instrumental and non-vibrato vocal lines is
similar to the timbres produced in Variations, where three flutes and three
organs or simply electric organs. The final textural link to Reich’s earlier
music involves steady pulse: Tehillim, despite its frequent meter change and
timbral/textural contrasts, at no point abandons Reich’s earlier aesthetic
requirement that repeated constant pulse be the backbone of new music. In
Variations. Tehillim finds Reich dealing with the problem of text setting that
Western composers have grappled with for centuries and arriving at a personal
lines that employ traditionally Western canons (though at the unison) and
variations as developmental techniques. The notion of development is in itself
new in Reich, for in Tehillim one feels for the first time that, with constant
develop as the work progresses. Together with its functional harmonic cycles,
typically tonal harmonic vocabulary, and immense variety of contrasting
textures and timbres, Tehillim appears to draw more deeply from the well of
Western tradition than any previous Reich composition. Yet Reich was careful
to include instruments within the orchestral ensemble that would relate both
to the Psalm texts themselves and to their Middle Eastern associations. In
small tuned tambourines without jingles, and crotales (antique cymbals). The
former resemble the small drums described in the Bible (including Psalm 150,
set in Part Four) under the name tof; the latter were widely used in the Middle
East in Biblical times, as were hand clapping and rattles.100 But Reich states
content, and it does not pretend to reconstruct Hebrew music of the Biblical
period.”101
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1. +at-shL- hM-yiM e-ri-peL-ree-m? k-va
k; -ca. 2. Yom-le-yo, ya- ee-aA o/- -er o – Iy- a- – I – l-
^-cha-ve da- -a. 3. A;n oa Aer . o- a;. da-v- ree~ ,e- -elee. h;s&-
1^e ko-fam L4- e-k^Rl k< - ah- r-ez ya- +2z k4-ran u-n/k -*hk-y tiy-v?;l'\e<-l/y-
only. Copyright 1981 by Steve Reich. Used by permission.
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attempted here can only begin to scratch the surface of its riches. Some
analysis must nonetheless be undertaken if only to demonstrate how Tehillim s
coherent whole. Part One sets Psalm 19:2-5 (1-4 in the King James Version).
It opens with a solo voice accompanied only by tuned tambourine and
rhythmically doubling hand clapping. Each verse of the Psalm is given distinctive
remainder of Part One, including the subsequent canons that are constructed
upon the melodies of the opening verses. Part One begins using a seven-note
scale within D natural minor; verses three and four progress to a modal four-
note scale and allow Reich the latitude for later modulation.
tambourine and rhythmically doubling hand clapping. Reich’s devotion to
canon is such that even the two tambourine/clapping lines are now in
rhythmic canon with one another, producing a complex interlocking rhythmic
pattern. A two-part vocal canon at the unison ensues with the metrical
position of the answering voice varying for each of the four verses; a second
clarinet is added to double the answering line. Once all four verses have been
the strings now added beneath, lending entirely new harmonic accentuation to
the previously stated melodic material. Finally a four-voice canon at the unison
material of each of the four verses. Electric organs now double the vocal lines
aesthetic choice, but (as in Four Organs) are essential in clarifying the metric
stress. Five complete repetitions of each verse’s canon occur; beneath the
swirling melodic lines in the voices, the strings play an immensely elongated
and slightly altered version of their earlier chordal cycle. In verses three and
the canons on the original melodies continue above unabated.
again accompanied by doubling clarinet, tambourine, and maracas. This
section is subsequently repeated added the string chordal cycle beneath, now
modulating to an implied D Major. When the four verses are finally complete,
Reich repeats the previous section (with the chordal cycle beginning again) but
now adds a lyrical second voice singing in parallel thirds or sixths beneath the
principal melodic material. Eventually the second voice and string chords fade
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l.Ha-rs- y- ‘i, w4- -peh-reee ka-vohd t;( u- na-a -Say ya^c i-‘A ed Aa –
LA-
only. Copyright 1981 by Steve Reich. Used by permission.
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maracas, and clarinet, thus recalling the vastly reduced texture of the opening
of the movement. Overall, Part One may be viewed as a symmetrical form
progressing from a free melodic style utilizing sparse instrumentation to two-
and finally four-voice canons above rich instrumentation; gradually the
movement returns to a thin non-canonic texture by its end. A seamless
transition between Parts One and Two is provided by the tambourines and
maracas, which blend almost unnoticed into the tambourine and hand clapping
accompaniment that opens the second part.
the variation. Part Two sets Psalm 34:13-15 (12-14 in the King James
Version) and, as Part One, progresses from a seven-note scale (here in Ab
Major) to an ambiguous four-note scale (Ab-Bb-Db-Eb) for the last of the
three verses. The lyrical duet texture that opens Part Two is similar to that
paralleled by a lower line which customarily sings a sixth below the upper
voice (Example 16a). The two voices are doubled respectively by oboe and
English horn.
the vocal duet and its accompaniment; the cycle typically both shifts the
harmonic accent and (for verse three) modulates to B Major. Variation Two is
an instrumental interlude; merely the text and the vocal parts are removed,
while the English horn and clarinet now double one another, playing what in
Variation One was the lower voice’s counter-melody to the principal melodic
line. Both the succession of meters and the versification of Variation One are
have been abandoned.
to Example 16a). Variation Four superimposes a high coloratura soprano line
over the previous duet texture; the new voice is doubled by clarinet and clearly
pierces through the thick orchestral/vocal texture. An instrumental interlude
meter and versification pattern of the previously lengthened melodies of
Variations Three and Four. The percussion are the stars of this section,
accompanied by a string chordal cycle that is an altered composite of all earlier
a duet texture and melismatically ornaments the already extended version of
the melodic material (Variation Six, Example 16c); for the final Variation
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1.. t^ – k. – eetk Iy-cdh – f.z dat- yte, ol- chay yav 4-. lwee -r ‘?v 2. .N-
Example 16a. Steve Reich, Tehillim (1981), Part II, Section A, verse 1, voice
parts only. Copyright 1981 by Steve Reich. Used by permission.
J l.i c – km – eeLk e4 y – c4’ – c ,-ft – yee^ o
lte -j j i il :fJ rr ^E ; ^f . zTz-^
Example 16c. Steve Reich, Tehillim (1981), Part II, Section G, verse 1, voice
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good variation set, mixes a number of developmental techniques-stable
melody with altered harmony, instrumental interlude based on previous vocal
material, elongation and melismatic ornamentation of the vocal line, and
added counterpoint in the high soprano.
providing a respite from the faster tempo and more animated texture of the
other sections. Here the tempo slows from J =144 to J =112, and the
orchestration changes to feature subdued mallet instruments (vibraphones
and marimbas), in contrast to the lively timbres of the tambourines, maracas,
and hand clapping which permeate all the remaining movements. Part Three
sets Psalm 18:26-27 in an imitative duet texture aptly suited to the Biblical
text (see Example 17): the upper voice states the first half of each Psalm line
(“With the merciful… “), and the answering line echoes the musical material
of the principal voice at a lower pitch level (“… .You are merciful”). The two
modality is clouded in the second verse by a melodic shift to G l in the
principal vocal line; this lovely touch of tone painting depicts the word
marimba/vibraphone 1, and a dissonance with the G#of marimba/vibraphone 2.
mental techniques employed consist chiefly of changing the melodic contours
elongation techniques used in Part Two. Simultaneously, the vocal duet is
enriched by adding parallel melodic lines (often at the third, fourth, or fifth)
four-voice texture. The chordal cycle in the strings, as in the other movements,
lending a changing harmonic interpretation to the melodic materials above.
Not only is there modulation, but chord cycles are altered in every possible
manner: by adding or removing chords from the original cycle, by substituting
new bass pitches, and by overlapping or juxtaposing differing versions of the
original sequence.
strings play in the motivic fabric. Here they are not simply relegated to
prolonging chordal cycles: they imitate previously stated vocal motives; they
add brief rhythmic punctuations which momentarily double the rhythmic
patterns in the marimbas and vibraphones; they enter in inverted pyramid
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_E 1 7. -e -_c . c
only. Copyright 1981 by Steve Reich. Used by permission.
This content downloaded from 130.166.3.5 on Mon, 11 May 2020 01:45:47 UTC
All use subject to https://about.jstor.org/terms
assist in the seamless transition to Part Four. Most interesting for those of us
who like to view Reich’s recent works as hybrids of earlier techniques is the
effortless “timbral modulation” that links Parts Three and Four. Reminiscent
marimbas, vibraphones, and strings of Part Three gradually fade out while the
tambourines of Part Four crescendo into the opening of the finale.
melodic materials, chordal cycles, and distinctive textures of all the other
movements of Tehillim. As such, it functions as a gigantic recapitulation,
returning to the original tempo (J =144), key (D minor), and opening
melodic material. Part Four sets Psalm 150:4-6, a text that refers to drums,
strings, winds, and cymbals, all appropriately used within this movement.
Parts One and Two, Part Four takes the melodic material of Part One and
cycle of Part Four is based on Part One, being a composite of two different
versions of the first movement’s harmonic sequence.
changes into a two-voice canon at the unison, again harking back to the
structural techniques of Part One. Continuing the parallel relationship with
Part One, the following section constructs a four-voice canon at the unison
upon the melodic material of each verse. As in the other movements, the
chordal cycle is soon altered beneath the tonally ambiguous melody of the
third verse to allow Reich to modulate to G Major.
Part Four. Once the canons have ended, however, Parts Two and Three
become of greater importance. A variation on the melodic material of Part
Four ensues, utilizing the same elongation technique we observed in Parts
Two and Three (compare Example 18b to Example 16b); even a high soprano
part, reminiscent of Part Two, is now added above the other two voices. An
melismatic version of the already elongated thematic material is introduced; a
the influence of Part Two in the variation techniques, the string writing in
these sections refers back to Part Three, with its more active motivic fabric,
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2. b-lc – 4- – La-+z;l-fw – z ‘ sa-r5 -OLa 1-(e- /u- h f La -Jt- z i-h r t -ac ,
3. K’ol i,a-s/,l-n/ – “a – -/il ya Kta.- 3I – – ..C / 4f ‘ “-S – ” – /,;f
voice 1 part only. Copyright 1981 by Steve Reich. Used by permission.
t. /L – le- (I – hL /c-c- -Wf (u-t a – c4ol / a-(e – l Lu – 1h –
only. Copyright 1981 by Steve Reich. Used by permission.
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pedal points in the bass. Even the chordal cycle itself is now a composite of
that of Parts Two and Three, as if to complete the recapitulatory nature of the
finale.
coda of Part Four, a prolonged joyous affirmation on the single word
“Hallelujah.” The flute (to double voice three), piccolo (to double voice one),
crotales (to imitate or double vocal motives), and vibraphone (to enrich the
percussive backbone and remind one of the timbre of Part Three) are added; in
itself is derived entirely from the “Hallelujah” motive which closed verse three
variation techniques used in the entire work. The “Hallelujah” motive, initially
echoed between pairs of voices in a manner similar to Part Three, soon
elongates until it is several measures in length. Subsequently, it is augmented
even further by the addition of ornamenting melismas. Many of the instrumental
strings, its held chords, and its bass pizzicato pedal point) recalls that of Part
Three. Within the percussion section, the vibraphone joins the maracas and
tambourines to reinforce the interlocking rhythmic patterns that have continued
minor key signatures used in the work’s four parts, mimicking the shifts in
mode that occurred so prominently in verses three and four of Part One and
and begins a series of repeated bass patterns (Bb-A-G). Here, perhaps for the
registers-which is of prime importance, preparing for the closing tonality of
the work, D Major. Upon the final repetition of the bass pattern, the bass
remains on A, the dominant of D. While D Major is never stated (only implied
by its dominant in the bass) it is clearly understood as a result of the
purposeful, functional harmonic progression that has driven inexorably toward
the concluding measures. Meanwhile the vocal parts have abandoned imitative
techniques in favor of a homophonic three-voice (and later four-voice) texture,
thickly textured vocal parts, doubling wind instruments, percussive rhythmic
patterns, repeated chordal cycle in the strings, and high-pitched crotales
ringing out above the entire ensemble-produces an exhilarating tapestry of
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the sheer joy with which it ends overwhelms the listener and performer alike
and cuts across religious barriers to unite us all in a song of praise.
Reich work must end with a multifaceted conclusion which points both
forward and backward. In describing any new composition, it seems one can
never fail to note the structural techniques which reflect earlier works, as well
For this reason, Reich’s compositional development itself, and not just his
early aesthetic of 1968, could be fairly described as “Music as a Gradual
Process”; hence the title of this article. Reich seems to progress in a highly
rational manner from one composition to the next with few deviations along
later development. Hardly anything goes to waste or leads to an unproductive
dead end. The early tape pieces resulted in the live phase works; the “Phase
Shifting Pulse Gate” encouraged the augmentation techniques of Four Organs,
Music for Mallet Instruments, Voices and Organ, Octet, etc.; the timbral and
textural enrichment of Drumming led to Music for Mallet Instruments,
Voices and Organ, Music for Eighteen Musicians, Music for a Large Ensemble,
for Mallet Instruments Voices and Organ, Music for Eighteen Musicians, and
Music for a Large Ensemble, the use of human breath as a duration of length
in Music for Eighteen Musicians was apparent once more in Music for a Large
Ensemble and Variations; the lengthy ornate melodies of Music for a Large
Ensemble found greater expansion in Octet, Variations and finally Tehillim -the
list is endless. All these examples serve to reinforce the impression of a
deliberate, steady progress toward an as yet unrealized (and perhaps uncon-
scious) goal. Thus, it is easy to predict that Reich is one composer who will
never submit to stylistic stagnation: any musician who has undergone such a
vast aesthetic transformation in a mere sixteen years of creative activity is
style in particular, within the broader context of not only new music but also
contemporary society as a whole. Why did minimalism arise in the early
1960’s, and what are the reasons for its continued development? Most obviously,
garde that the progressive younger composers found unattractive. The numerical
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level than listener comprehension, were discarded in favor of a clarity of
structure. The random processes of Cage and aleatoric music in general were
rejected in favor of rigorously structured composer-organized compositions.
Lastly, the requisite atonal idiom was challenged by the notion that tonality-
though, as we have seen, tonality of a vastly different type–could still play a
powerful role in creating new and original music.
aesthetics, minimalism is an art with more profound reasons for its development;
uncontrollable society. Of all aspects of minimalism, it is the deliberate
limitation of the resources employed, the focusing in on minute amounts of
material, that is the most immediately apparent. Eric Salzman has stated that
to the buzzing, blooming confusion.”’02 Such a reason for the rise of minimalism
of both contemporary music and contemporary culture in general. It is true
or not, the music produced has at least two of the marks of artistic value: it has
since the mid-1960’s, and it has had the ability to grow and develop far beyond
its original aesthetic, as the music of Reich and Glass makes apparent.
that the composer’s conscious control over the musical material is still an
important factor to be considered. This is in sharp contrast to the rather
nihilistic Cageian view that either eliminates art altogether, or asserts that all
aspects of our culture deserve equal consideration as art. Here, the minimalists
re-assert that conscious judgement is needed to determine what is viable as art,
unfocused musical scene. It is true that Cage has influenced the minimalist
aesthetic in other ways; at the fine line where minimalism and concept art
merge, it is obvious that the notion of a single idea or activity being valid as the
procedure, clearly stems from Cage’s philosophy. Yet the minimalists’ utter
rejection of random procedures, and their emphasis on an almost dictatorial
domination of the musical material, goes beyond Cage to reflect an urge
present in all of us: the desire to regain control over increasingly elusive social
and artistic processes.
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1960’s; a multiplicity of sources and techniques has replaced the dogmatic
application of selected compositional methods, whether serial, atonal, or
aleatoric. Reich has employed a vast number of widely varied structures and
techniques within his music. We have already noted his roots within popular
music, evident in a steady driving pulse, choice of instrumentation, and use of
of timelessness in the resulting music-has also profoundly influenced the
composer. A wide range of non-Western cultures have provided Reich with
structural models, including Africa, India, Southeast Asia, and the Middle
East. Reich’s embracing of tonality is in itself but another example of the large
But the eclecticism of Reich’s music has its roots beyond the assertion
own compositional style. For Reich simultaneously rejects the exclusive primacy
of the Classical Western heritage, whether recent avant-garde techniques or
and cultures, whether popular, Western, or non-Western, are equally viable as
sources of new music. While contemporary art has long since admitted the
validity of using non-Western sources as structural models, contemporary
music, with the notable exception of such composers as Messiaen, has largely
restricted non-Western influence to exotic, coloristic applications. The mini-
their structural techniques from non-Western music, a type of influence that
can only occur after long study of the foreign cultures involved. Their
declaration of the equal validity of all cultures, their support of the concept of
reflects a general turn against an attitude that asserted the superiority of
Western society; the rejection of such ethnocentrism has become increasingly
with third-world and nonaligned nations declaring the equal worth of their
own native heritages and cultures.
often emphasized by less sympathetic critics and composers. Reich has repeatedly
been accused of composing mechanistic music that requires mechanistic
performances; the composer’s own early insistence on the impersonality and
inexorability of “process” certainly bolstered this judgment. Other commentators,
own music, have viewed Reich’s art as being a reflection of the “industrialism”
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current beneath all these observations is the assumption that music must
make a uniquely personal, expressive statement; if it does not, it is somehow
less valid as art. In effect, this results from expecting new music to live up to
outdated notions of what art should be, notions that stem from the nineteenth-
criteria for art. There is no reason to apply such criteria to minimalism; by
doing so one unfairly imposes the requirements of one aesthetic on another.
Taken on its own terms, Reich’s music most certainly is expressive, even
exhilaratingly so. Yet it is an exhilaration derived less from the character of
the basic material than from the combined effects of a satisfying intellectual
structure, couched in an accessible idiom, and performed by virtuosi who
exhibit evident pleasure in adding their own individual contributions to the
ultimate goal of group expression.
have seemed hardly possible a few years ago. By the 1960’s, the established
avant-garde was in danger of collapsing inwards upon itself, lost in a maze of
structural complexities and techniques, with no one beyond a privileged few
the slightest bit interested in what it was doing. Steve Reich has changed that
situation by re-injecting an element of accessibility into new music, by returning
as the viable, exciting art form it should have been all along. By doing so, he
has challenged the view that the composer must be isolated from the public to
create great art, and signaled a return to the healthier relationship between
composer and society that existed prior to the last one hundred years: the
composer is not only once more part of society as a whole, but in the process of
regaining his place within contemporary culture, he has shown us that
achieving public acceptance cannot be equated with writing music that is of
less than serious artistic value.
feet at the concert’s end, giving a standing ovation to a young composer who
had just presented a program of challenging new works. For making con-
temporary music, and the act of composition, once more powerfully relevant
to the world at large -and for dramatically redefining the role of the composer
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The generosity, effort, and encouragement of Steve Reich himself were
indispensable at every stage of this project, as was the assistance of his
manager, Lynn Garon Management of New York. Above all, credit must
go to Dr. Austin B. Caswell, chairman of the Musicology Department at
Indiana University/Bloomington, without whose constant advice and
guidance–and conviction that new music is an appropriate area of study
for musicology–this article would never have come to fruition.
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1974; Whitney Museum of American Art, Anti-Illusion: Procedures/Materials
(New York, 1969), pp. 56-57. There are some slight differences in orthography,
punctuation, and layout between the various versions; “Music as a Gradual
Process”, as quoted in this article, is taken from Reich, pp. 9-11.
Writings, pp. 12-13; for its original version see Source, V, No. 2 (1971), p. 31;
Whitney Museum, pp. 28-29.
one of which was “The Phase Shifting Pulse Gate”. The impetus for the work also
came from an early concept piece of Reich’s, Slow Motion Sound (1967). The
latter had remained a concept as it was technologically impossible to realize at the
time: its premise was “to take a tape loop, probably of speech, and ever so gradually
slow it down to enormous length without lowering its pitch.” (Reich, p. 15). The
result would be the augmentation of a pattern initially heard in shorter values.
The combination of this concept with the “Pulse Gate’s” unused potential for
gradually drawing out the length of a single tone led to Four Organs. Slow Motion
Sound has again returned to influence Reich in connection with the projected
expansion of his tape piece My Name Is. Ensemble Portrait (see note 94).
pp. 29-37 and 56-58.
with the monograph by A.M. Jones, Studies in African Music, 2 vols. (London,
1959).
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1973, sec. 2, p. 9; Reich, Writings, pp. 38-40. Again, as with “Music as a Gradual
Process”, the two versions differ slightly; the section quoted in this article is from
Reich, Writings, p. 40.
here; however, in Drumming, instrumentation is changed gradually (by fading in
the new instrumental group while the previous one fades out), in contrast to
Webern’s technique.
showroom in 1972-3.
employ a live phasing process. Reich’s most recently completed work, My Name
Is: Ensemble Portrait (1980, q.v.), has returned to the phasing process, but within
the sphere of tape, not live, music.
progression that, while cadential in its sonic qualities, is stripped of any true
cadential purpose by its constant repetition and harmonically non-functional
context.
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71, as well as on the lengthy discussion written by Reich and included in the Liner
Notes to DGG 2740-106, 1974. The latter is reproduced in Boston Symphony
Orchestra, Program Notes, 93rd Season (1973-4), pp. 695-697 (program for
concerts of January 24, 25, 26, 1974).
order): “Radikales Poker”, Der Spiegel, 25 October, 1976, pp. 214-216; Peter
Heyworth, “Mr. Reich’s Revolution”, The Observer Review, 6 February 1977, p.
30; John Rockwell, “Reich in Review”, The New York Times, 18 May 1977, sec.
3, p. 21; Andrew Porter, “Patterns”, The New Yorker, 6 November 1978, pp.
187-188; John Rockwell, “The Pop Life”, The New York Times, 17 November
1978, sec. 3, p. 12; John Von Rhein, “Many-sided Maestro Moves from Minor to
Major Status”, The Chicago Tribune, 4 March 1979, sec. 6, pp. 6-7, 15.
Music for Eighteen Musicians, ECM Records, ECM-1-1129, 1978.
commissions for Reich’s recent compositions, have been derived from promotional
material provided by Lynn Garon Management.
Section Four) is evidence of rudimentary functional harmony, the overall harmonic
context of the work, with its constant repetition and juxtaposed key areas, is non-
functional.
play in because the parts are extremely difficult and I wrote myself out of the
piece.” (Alpern, p. 17.)
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derived from a personal interview with the composer, which took place on January
2, 1981.
gradually slowing down a sound without changing its frequency (see note 45).
The Houston Chronicle, 21 November 1981, sec. 3, p. 7.
November 1981.
1981.
Cliffs, N.J., 1974), p. 186.
Gesprach mit Clytus Gottwald,” Musik und Bildung, VIII (February 1976), pp.
58-59.
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Front Matter [pp.1-1]
Cornelius Cardew (1936-1981): Cardew as Teacher [pp.2-3]
T. S. Monk [pp.4-9]
It’s Monk’s Time [pp.10-11]
Howard Hanson (1896-1981) [pp.12-25]
Robert Miller (1930-1981) [pp.26-27]
Clara Silvers Steuermann (1922-1982) [p.28]
In Memoriam Wilson Coker [p.29]
The Noise Instruments of Luigi Russolo [pp.31-48]
Conversation with Alvin Lucier [pp.50-58]
Conference on the Oral Mode 1981/1982
Intravenal Song [pp.59-65]
The Orality Perspective: The Oral Mode in Contemporary Art and Culture – Voice and Performance [pp.68-74]
Visual Music [pp.75-93]
untitled [pp.94-95]
untitled [p.95]
untitled [p.96]
On Hearing Forum82 at Symphony Space, New York, November 13, 1982, from 3 to 6 P.M. [p.98]
John Cage in a New Key [pp.99-103]
Conversation with Vincent Persichetti [pp.104-133]
Varese, Wolpe and the Oboe [pp.135-148]
Carter’s “Duo for Violin and Piano” [pp.149-168]
An Elliott Carter Discography [pp.169-181]
Boulez’s Third Piano Sonata: Surface and Sensibility [pp.182-198]
Text, Music, and Meaning in the Third Movement of Luciano Berio’s Sinfonia [pp.199-224]
Steve Reich: Music as a Gradual Process Part II [pp.225-286]
In Response [pp.288-329]
Symbolic Extension and Its Corruption of Music [pp.331-356]
Circumscribing the Open Universe [pp.357-362]
Unanswering the Question [pp.363-405]
Getting to Gnaw All about You [pp.406-412]
ForM.(A Music) [p.413]
From A Mozartian Dialectic [pp.414-432]
New Perspectives in Native American Music [pp.433-446]
Music as a Realistic Art [pp.448-463]
If I am a Musical Thinker [pp.465-517]
A Music-Theoretic Proposition of Stephen Dedalus [pp.519-523]
The Investigation [pp.525-559]
untitled [pp.560-567]
A Pyrrhic Victory for Scholarship? The New Grove Dictionary of Music and Musicians [pp.568-591]
The Making of a New Music Ensemble [pp.592-599]
1982 A.S.U.C. National Conference [pp.600-603]
American Society of University Composers Region V Conference. University of Illinois, Urbana-Champaign, November 5-8, 1981 [pp.604-608]
New Music America 1982. Chicago, July 5-11, 1982 [Two Reports] [pp.609-622]
On Electronic Strings in Live Performance: The Design and Construction of an Electroacoustic Monochord [pp.623-639]
Texture as Psycho-Rhythmics [pp.640-648]
Timeshapes [pp.649-650]
Impressions after an Improvisation [p.651]
Back Matter [pp.652-656]
Timeline
Author(s): Justin Colannino, Francisco Gómez and Godfried T. Toussaint
Source: Perspectives of New Music, Vol. 47, No. 1 (WINTER 2009), pp. 111-134
Published by: Perspectives of New Music
Stable URL: https://www.jstor.org/stable/25652402
Accessed: 11-05-2020 01:50 UTC
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Beat-Class Sets in Steve Reich’s
Yoruba Bell Timeline
and godfried t. toussaint
Second World War, mainstream classical music had been dominated by
composers such as Boulez, Berio, Cage, Ligeti, and Stockhausen, among
others. These composers represent postwar Modernism, either through
postserialism, Boulez being its most prominent figure, or through
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Minimalism was originally used for the visual arts, it was later applied to
a style of music characterized by an intentionally simplified rhythmic,
melodic and harmonic vocabulary. Indeed, Timothy Johnson has argued
that the term minimalism may be defined most fruitfully as a technique
rather than an aesthetic or style. The music of LaMonte Young, Philip
Glass, Terry Riley, and Steve Reich represent the major reaction to the
Modernism epitomized by the aforementioned composers. Indeed,
whereas Modernism is decisively atonal, Minimalism is clearly modal or
tonal; whereas Modernism is aperiodic and fragmented, Minimalism is
characterized by great rhythmic regularity; and whereas Modernism is
structurally and texturally complex, Minimalism is simply transparent.
Minimalism has different materializations depending upon the
functional tonality and reiteration of musical phrases, often small motifs
or cells, which evolve gradually. For example, while Young uses
sustained drones for long periods of time, Glass chooses recurrent chord
arpeggios, and Riley and Reich incorporate repeated melodies and quick
pulsating harmonies. No less significant is the fact that minimalist music
possesses almost none of the main features of Western music (at least
since the time of the Romantic period); that is, harmonic movement,
key modulation, thematic development, complex textures, or musical
forms with well-designed structures. On the contrary, this music
deliberately skirts around any sense or awareness of climax or
development, and seems to ignore the dialectic of tension and release, at
least as it is usually posited in the classical music tradition. In the words
of Roger Sutherland, “The listener is invited, not to follow a complex
musical ‘argument,’ but to concentrate upon a slowly changing sound,
and focus with microscopic awareness on different aspects of it.” 1
classical tradition. Reich objects to both European serialism and
American indeterminacy because in these traditions the processes by
which the music is constructed cannot be heard and discerned clearly by
the listener. Before him, Pousseur and Xenakis had already pointed out
that “where the most abstract constructions have been employed . . .
one has the impression of finding oneself in the presence of the
consequences of an aleatory free play.”2
as follows: “I am interested in perceptible processes. I want to be able to
hear the process happening throughout the sounding music.”3 For such
processes to be accessible to the listener, they must flow in an extremely
gradual manner. The process itself must be related to the idea of shifting
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while one of them gradually shifts phase. At the beginning of the
phasing a kind or rippling broken chord is produced; later, as the
process moves forward, the second melody is at a distance of an eighth
note, and a new interlocking melody arises. The process continues until
the two melodies are in phase again.
1965 and 1973. The experimentation started with It’s Gonna Rain and
Come Out (both composed in 1966), where he applied the phasing
process to tape recordings; it continued with Piano Phase (1967), and
Violin Phase (1967), where he experimented within an instrumental
context (no electrical devices); and finally, Reich reached the highest
development in Drumming (1970-71), Clapping Music (1972), and
Music for Mallet Instruments, Voices and Organ (1973), where he incor
porated gradual changes of timbre and rhythmic augmentation, among
other musical resources. By the end of 1972, he abandoned the gradual
phase shifting processes, because “it was time for something new.”4
Clapping Music and the bell rhythmic timelines of West African Yoruba
music. During the summer of 1970 Reich traveled to Ghana, where he
studied African drumming. He learned Gahu, Agdabza, and other
readily perceived in works like Drumming and Clapping Music, where
the phasing is discrete, but still noticeable in his continuous phasing
pieces such as Phase Patterns, Violin Phase, and New York Counterpoint,
where he uses rhythmic ostinatos that are subsets of West African bell
timelines.5 More specifically, we study Clapping Music with regard to
syncopation, inasmuch as it forms an essential part of that piece. Could
not Clapping Music be considered as a piece where the first performer
keeps a fixed metrical context that the second performer contradicts
with a rotation of the same pattern? In other words, we almost have here
the definition of syncopation. The analysis of Reich’s music from the
point of view of the change in rhythmic properties as the piece
progresses in time was pioneered by Epstein, and continued by Richard
Cohn, who analyzed Phase Patterns and Violin Phase focusing on the
cardinalities of the emergent beat-class sets (the number of attacks or
onsets per metric cycle).6 Here we analyze Clapping Music and a Yoruba
bell timeline focusing on the amount of syncopation of the emergent
beat-class sets.
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pattern throughout the duration of the piece. The phasing is discrete,
with one performer advancing an eighth note after several repetitions of
the pattern, while the other imperturbably remains playing the pattern
without shifting. See Example 1 for further details. In the following,
variations produced by shifting are numbered in ascending order as
{Vo, Vi, . . . Vn, V12}, where Vo = V12 indicates that the two performers
This piece, in spite of its apparent simplicity, does not lack musical
refinement of Reich’s ideas by means of a piece with few but well
combined elements. Secondly, Clapping Music enjoys a profound
metrical ambiguity (a common characteristic in Reich’s music) as well as
a great deal of interlocking rhythmic patterns. The analysis of these
interlocking rhythmic patterns as the piece progresses (beat-class
how Reich came to select that particular pattern. As the pattern shifts, a
series of interlocking rhythms emerges, creating great variety. Further
more, there is a sense of balance in the whole piece, between the
resulting variations, as they create and release rhythmic tension. Once
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change it. The beat-class modulation throughout the piece is carved in
stone. Therefore, the pattern must be carefully chosen to begin with.
Phylogenetic graphs have been already used to analyze musical rhythms.
In UA Mathematical Analysis of African, Brazilian, and Cuban Clave
Rhythms,” Toussaint offered a phylogenetic analysis of binary timelines.
Timelines are rhythmic patterns repeated throughout a piece whose
main functions include rhythmic stabilization as well as the organization
of phrasing. Subsequently, such an analysis was extended to ternary
timelines taken from the Sub-Saharan African tradition, and to the
hand-clapping metric rhythms of flamenco music.8 In all cases,
worthwhile conclusions were drawn from these phylogenetic analyses. In
this paper we use phylogenetic graphs to both analyze the structure of
Clapping Music itself and to compare it to the Yoruba rhythmic
timeline.
pattern that works so well within the constraints of process music. There
is no doubt that his inspiration for the pattern came from his study of
resemblance between the pattern of Clapping Music and a bell pattern
used by the Yoruba people of West Africa: only one additional,
seemingly inconsequential, note has been added by Reich. The two
patterns are shown in Example 2.
We should mention that Reich composed Clapping Music in 1972,
became interested in African music through the writings of A. M. Jones.
In 1954 Jones published a comprehensive seminal paper on the topic of
hand-clapping patterns used in African music.10 In this paper Jones
describes a piece of music called Beer Dance performed by the Lala
people of what was then central Rhodesia. This piece has three clapping
patterns performed in unison, shown in Example 3. The resultant
clapping rhythm is in fact the same necklace pattern (rotation) that
Yoruba Clave []ffi|?7p7p^7p7|?^7
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pattern quite successful, motivating him to use it again in 1984 in his
composition Desert Music, where it is played on marimbas (see Example
4).
although they can be found also in the eastern Republic of Benin and
Togo. Because most of the slaves were taken from West Africa, a
Clap 2 – jjj. j j.
Resultant
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found in Brazil, Cuba, the Caribbean, the United States and the United
Kingdom. They are one of the largest cultural groups in Africa, and
musically speaking are of great relevance. Yoruba music has exerted
much influence on the music of the surrounding countries.
sacred music of the Yoruba people.11 Bettermann calls this rhythm the
Omele. It is also found in Cuba, where it is used in several styles like the
rumba Columbia.12
similar to the Clapping Music pattern. See for example the collection of
candidate timelines assembled and discussed by Jay Rahn.13 That this is
not the case is made clear in the following section. Once we formally
introduce the distance function used to measure dissimilarity between a
pair of rhythms, we will verify that the Yoruba clave is the rhythm
closest to the Clapping Music pattern among a great number of African
ternary timeline patterns. These reasons constitute our primary
natural question is whether the Yoruba clave itself works just as well as
the pattern employed in Clapping Music.
in which syncopation is dealt with, thus providing motivation to mea
sure the amount of syncopation of the emergent beat-class sets as a
function of time. The problem of defining a mathematical measure of
syncopation with formal precision has not been addressed until re
cently.14 In their 2005 article, Gomez, et al. reviewed several mathemat
ical measures of syncopation, and proposed a new measure, the weighted
note-to-beat distance measure (WNBD measure from here on). This
measure will be used here to compute the syncopation of Clapping
Music and the Yoruba clave pattern, and thus flesh out their underlying
beat-class modulation structures.
proximity and evolution of species. Biologists measure the degree of
proximity between two species by comparing their genes. In our con
text, rhythmic patterns take the place of genes, and as a consequence,
patterns (measures used in biology are not appropriate in the context of
music). The question of how to define similarity measures for rhythms
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attention in the past.15 More recently, in the area of voice-leading, dis
similarity or distance measures similar to the edit distances used here
have entered the stage.16 A variety of dissimilarity measures have
recently been compared in the context of phylogenetic tree analyses.17
Among the similarity measures compared (Euclidean interval vector
distance, interval-difference vector distance, swap distance, etc.), the
most satisfactory one in these studies has been the directed-swap
distance, which is a generalization of the simpler swap-distance, first
introduced by Jose-Miguel Diaz-Banez. This was the motivation for
using this distance measure in this study.
elementary mutation model used in bioinformatics. Let Pand Q be two
rhythms with the same number of onsets. Positions of the rhythm that
contain an onset will be referred to as occupied positions. The swap
distance is the minimum number of swaps required to convert P to Q.
In this case the solution is simple: the first onset of P must move the
position occupied by the first onset of Q the second to the second, and
so on. This is equivalent to computing the Li norm between the index
vectors of the onsets’ time coordinates of the two rhythms, and
corresponds to the distance measure preferred in voice-leading.18 The
directed-swap distance is a generalization of the swap distance designed
to handle comparison of rhythms that do not have the same number of
onsets. Let P have more onsets than Q. The directed-swap distance is
the minimum number of swaps required to convert P to Q with the
constraints that each onset in P must move to some occupied position of
Q, and all occupied positions of Q must receive at least one onset from
P. For example, the directed-swap distance between Player-1 and
Player-2 in variation Vi is 4, since we have to perform four swaps in
Player-1 at positions 3, 6, 8, and 11 to convert Player-1 to Player-2 (see
Example 1). In our case, since all rhythms have the same number of
onsets, computing the directed-swap distance is easy because it reduces
to the simpler swap-distance and thus the computation of a sum of a
linear number of terms.19
Clapping Music to the Yoruba timeline is that this timeline is the rhythm
closest to it. The distance between them was measured with the
directed-swap distance, and the set of timelines used in the comparison
was taken mainly from well-established African musical traditions.20
The distance matrix corresponding to the directed-swap distance is
shown in Example 5. Box notation is used for the variations of Clapping
indicates the sum of the swap distances to all other rhythms.
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V6 and V9 are the variations that obtain the highest score. Also
noteworthy is the diagonal below the zeros in Example 5, that is, (4, 4,
4, 8, 4, 4, 8, 4, 8, 4, 4). This diagonal gives the directed-swap distances
between consecutive variations. It takes on only two values, 4 and 8, but
these values differ considerably, and change six times over a total of
twelve variations.
analysis of sequence data such as molecular sequences in biology in
order to construct a phylogeny of a group of species, in this study they
are used for analyzing musical rhythms, with the goals of visualization,
cluster analysis, classification, and the reconstruction of “ancestral”
rhythms to determine how useful they are as a new tool for musico
logists. Example 6 shows the phylogenetic graph computed for the
distance matrix. This graph was constructed with the program SplitsTree,
which draws a graph in the plane such that the distances travelled along
the edges of the graph between any pair of rhythm nodes (variations
between the corresponding rhythms in the distance matrix.21 The
program also computes a fitness value, listed as a percentage value,
which shows how well the distances in the graph match those in the
matrix. In our case we obtain a fitness value of 100%, meaning that the
distances in the graph are all exactly the same as in the distance matrix.
Vb=xxx.xx.x.xx. 0
Vl=xx.xx.x.xx.x 4 0
V2=x.xx.x.xx.xx 8 4 0
V3=.xx.x.xx.xxx 12 8 4 0
l/4=xx.x.xx.xxx. 4 2 4 8 0
l75=x.x.xx.xxx.x 8 4 2 4 4 0
V6=.x.xx.xxx.xx ~12 8 4 2 8 4 0
Vr7=x.xx.xxx.xx. 44482480
F8=.xx.xxx.xx.x 8 4 4 4 4 2 4 4 0
V9=xx.xxx.xx.x. ~2 4 8 12 4 8 12 4 8 0
Vio=x.xxx.xx.x.x ~T~ 2 4 8 ~~4 4 8 2 4 4 0
Vn=.xxx.xx.x.xx ~8~ 4 2 ~4~ 4 ~4 4 4 2 8 4 0
THE CLAPPING MUSIC PATTERN
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EXAMPLE 6: THE PHYLOGENETIC GRAPH OF THE CLAPPING MUSIC PATTERN
imply “ancestral” rhythms. The ancestral node of the entire collection of
variations is the center of the graph, in this case the node labelled A.
This phylogenetic graph provides valuable information about the
consider the central node A. Such a node corresponds to an “ancestral”
rhythm, and is also the center of the graph (i.e., it is the vertex that
minimizes the maximum distance to any other vertex in the graph).
Note also that as the variations Vo, Vi, . . . Vu progress throughout the
piece, they exhibit considerable switching from one side to the other
with respect to node A. Therefore, it seems that this central node plays a
key role in the piece. There is as yet no known efficient algorithm to
compute the “ancestral” nodes for rhythms in phylogenetic graphs
constructed with our distance measure. However, in this case, given the
small number of rather short rhythms involved, the “ancestral” rhythm
can be reconstructed by hand without much difficulty. It turns out to be
the rhythm shown in Example 7.
This fundamental rhythmic pattern is none other than a group of
followed by a short note. This “ancestral” rhythm has a strong metric
time-keeping character. The trochee, expressed in box notation as [x.x],
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the globe. For some examples in Latin American music, it is found in
the Chilean cueca, and the Cuban coros de clave.22 It is common in Arab
music, as for example in the Al Tder rhythm of Nubia.23 It is also a
rhythmic pattern of the Drum Dance of the Slavey Indians of Northern
Canada.24 Furthermore, the entire pattern of eight onsets in a time span
of twelve pulses shown in Example 7 is also the Euclidean rhythm E(S;
12), which distributes the onsets as evenly as possible.25
The phylogenetic graph has four distinguishable clusters CI, C2, C3
performed these clusters appear in the order given in Example 8. From
this sequence of clusters we may observe the evolution of the variations
through time. There is a first section formed by variations Vo to V3; in
it, each variation moves further away from Vo. In a second section,
third section, variations V7 and Vs remain around the center of the
graph, and represent a turning-point after which the subsequent varia
tions move towards Vo. The variations in section four, consisting of V9,
back to the main pattern (Vo = V12) played in unison. This evolution
may be detected, although less visually, on the diagonal below the zeros
in the directed-swap distance.
There is another interesting property deducible from the phylogenetic
central node A; those in clusters C2 and C3 are at a distance of 2 from
A. However, rhythms to the left of A are converted into A by
“pushing” their onsets to the right, whereas rhythms to the right of A
are converted into A by “pushing” their onsets to the left. For example,
to turn Vo = xxx.xx.x.xx. G CI into A, six swaps are needed, but all of
them are forward swaps. On the other hand, V3 = .xx.x.xx.xxx E C4 is
converted into A by performing six backward swaps (see Example 9).
11 Vo I Vi 1 V2 1 VT
_’__J___Vs_
_”_V^_^o__Vii__
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Vo Vs
timeline. To start with, we present the swap distance matrix For the
Yoruba bell pattern in Example 10, and its corresponding phylogenetic
graph in Example 11. By looking at the bottom row of the matrix we
see that the sums of the distances take many different values. The most
similar rhythm is Vs and the most different one is V*. That is not
surprising: Vs is the “standard pattern” used in Bembe, a very popular
ternary rhythm.
Toussaint already proved that it is one of the most similar of an
important family of ternary timelines.26 Here we note that the standard
pattern is the most similar rhythm in its own wheel (the wheel of a
rhythm consists of those rhythms obtained by its rotations that begin on
an onset). The diagonal below the zeros is (5, 7, 5, 7, 5, 5, 7, 5, 7, 5,
5). The difference between two consecutive variations is smaller than in
the case of Clapping Music. Changes are more frequent in the case of
the Yoruba clave.
ancestral nodes. Take into account that if the fit is not 100%, reasoning
on the graph does not accurately reflect reasoning on the distance
matrix, and accordingly, neither on the rhythms. For example, on the
graph the distance from Vo to Vi is 2.5, but in the matrix it is actually 2.
The role of A could be played by variation Vs in this phylogenetic
graph. It is the center of the graph, and as before, variations alternately
go from left to right and from right to left around Vs. Nevertheless, this
does not seem to yield any particular insight into the structure of the
Yoruba clave. Hence, there is no remarkable clustering analysis to be
discussed. In addition, the graph does not exhibit special symmetries or
regularities of musical significance. In conclusion, when the musical
process of Clapping Music is carried out on the Yoruba timeline, a rather
awkward result is obtained.
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Vq=x.x.xx.x.xx. 0
Vi=.x.xx.x.xx.x 5 0
V2=x.xx.x.xx.x. 2 7 0
V3=.xx.x.xx.x.x 3 2 5 0
Vi=xx.x.xx.x.x. 4 9 2 7 0
V5=x.x.xx.x.x.x 1 4 3 ~2~~ 5 ~0~
I ()=.x.xx.x.x.xx ~~6 1 8 3 10 5 0
V7=x.xx.x.x.xx. 1 6~ 1 4~ 3 2 7 ~0~
V8=.xx.x.x.xx.x 4 I 6 1 8 3 2 ~5 0
V9 =xx.x.x.xx.x. 3 8 1 ~6 1 1 9 2 7 0
Vjo=x.x.x.xx.x.x 2 3 4 1 6 1 4 3 2 5 0
Vji=.x.x.xx.x.xx j 7 2 9 4 11 6 1 ~8 4 9 5 CT
a v10 vi v6
momentary contradiction of the prevailing meter. Accordingly, the
WNBD measure is based on the durations of notes, and how they cross
over the strong beats of the meter. This measure differs from the others
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Higgins and Lee based on the height of a tree generated by a metrical
grammar, Keith’s measure based on the combinatorial structure of
metrical levels, Toussaint’s measure of metrical-complexity based on the
metrical structure of Lerdahl and Jackendoff, or Toussaint’s off-beatness
measure based on the underlying polyrhythmic group-theoretic struc
ture of the meter.27 Gomez et al. proved the WNBD measure to have
The WNBD measure, which will be used here to analyze the synco
a note ends where the subsequent note begins. Let a, a+i be two
consecutive strong beats in the meter. Also, let x denote a note that
starts after or on the strong beat a but before the strong beat a+\. We
define J[x) = mm{d(x-, a), d(x; ei+i)), where d denotes the distance
between notes in terms of durations. Here the distance between two
adjacent strong beats is taken as the unit, and therefore, the distance d is
always a fraction (see Example 12(a)).
following cases:
2
denote the number of notes of a rhythm. Then, the WNBD measure of
a rhythm is the sum of all D(x), for all notes x in the rhythm, divided by
n.
(a) (b)
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Music with respect to a 12/8 meter. The measure produces only three
different values, namely, 24/8; 21/8 and 12/8, but the graph is quite
revealing about how syncopation works in Clapping Music. Variation Vo
by itself has a high value of syncopation. Two identical ascending
descending cycles, V\?Vi?Vz?Va and Vi?Vs?V6?Vz, follow after
Vo. From Vi, we find a symmetric cycle with respect to the previous
cycle, namely, Vz?Vs?V9?Vio. Finally, we discover an ascending path
to Vu (which is a half of the previous cycle). If variation Vi were moved
after F12, then the resulting graph would have a perfect mirror
symmetry about Vi. Therefore, a strong symmetry in musical form is
evident in Clapping Music.
Yoruba clave, depicted in Example 14, reveals several differences. As in
Clapping Music, the measure only takes three values, namely, 21/7,
18/7 and 15/7. The range of the syncopation values is much smaller
than in the case of Clapping Music, and consequently, so is its rhythmic
variety. The smaller the range of the measure is, the less interesting the
rhythms are from the syncopation standpoint. The graph of the Yoruba
timeline exhibits the same quasi-symmetry about Vi.
inter-relationships within families of rhythms, in this paper we have used
them for studying the modulation of the dissimilarity of the emergent
beat-class sets of process music, in particular Reich’s Clapping Music.
The resulting phylogenetic graph allows us to explore a variety of
musical properties of the piece, such as the classification, evolution, and
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positive results lead us to advocate the use of phylogenetic graphs as a
useful tool for musical analysis in general, especially for musical styles as
characteristic as Minimalism. Reich’s other pieces in this style, such as
Music for Pieces of Wood, would likely benefit from this kind of analysis.
We have compared Clapping Music to the Yoruba bell timeline. One
significant difference in musical terms. Quite to the contrary, as we have
seen, the phylogenetic graph of Clapping Music has a richer structure
than that of the Yoruba clave. This is a consequence of its inherent
musical structure.
as well, mainly that certain features of beat-class modulation such as
rhythmic variety, at least from a syncopation standpoint, can be mea
sured in terms of the range and distribution of the syncopation values.
Previously, Haack proved that Clapping Music is unique from a
geometrical nature to support this conclusion.
The properties exhibited by the phylogenetic graphs and the WNBD
rhythms yield nice graphs, that is, graphs with good properties
(symmetry, clustering, 100% fit, etc.) The WNBD measure gives poor
results when it is used to measure the interlocking melodies (for that we
just use the Clapping Music pattern as the meter, and recompute the
measure). Therefore, finding a function that measures the overall
complexity of the union of two rhythms is an interesting open problem.
Finally, it is not known which other rhythmic patterns would work just
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characterize those rhythms that guarantee musically interesting results
when used in phasing music.
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Mertens (1983;, Sutherland (1994), and Reich (2002).
the redeeming factors of formalist methods applied to process music
in general, see Quinn (2006).
rich structure, Cohn (1992), Haack (1991; 1998), and Toussaint
(2002) have all offered analyses from mathematical perspectives.
Musical Times.
11. For discussion of the Yoruba timeline as used in sacred music see
sources. Additionally, the references included in the current work
provide more recent sources, including the research of Buchler,
Cohn, Morris, Quinn, and others.
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(2003) and the references therein.
respectively.
Keith (1991); Toussaint (2002); Lerdahl and Jackendoff (1983);
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Front Matter
Species Concepts in Biology and Perspectives on Association in Music Analysis [pp. 5-68]
A Mathematical Model for Optimal Tuning Systems [pp. 69-110]
Analysis of Emergent Beat-Class Sets in Steve Reich’s “Clapping Music” and the Yoruba Bell Timeline [pp. 111-134]
Gridless Beats [pp. 135-164]
About Some Music of Thomas Adès [pp. 165-173]
䙩湤楮朠䍡来琠剹ō慮椠周牯畧栠愠剥ⵍ潤敬汩湧映≖慲楡瑩潮猠䥉∠孰瀮‱㜴ⴱ㤲�
Wreath Products in Transformational Music Theory [pp. 193-210]
Stuart Saunders Smith’s “Links No. 6 (Song Interiors)”: How Can I Tell what I Think Until I See What I Sing? [pp. 211-232]
Compositional Parameters: “Projection 4” and an Analytical Methodology for Morton Feldman’s Graphic Works [pp. 233-267]
EDITORIAL NOTES [pp. 268-270]
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