Working Terminology for Minimal Music
by Dan WARBURTON
The following article was originally written
for and published in a magazine called Intégral (Vol.2, 1988), edited
by then Music Theory students at the University of Rochester (NY)'s
Eastman School of Music. It was extracted in part from my ESM Doctoral
Thesis from the year before. Scouting around the Internet (as one does..),
I realised recently that this article has been referred to quite frequently
by graduate students working in the domain of minimal music (which is
gratifying, as that's precisely what I intended), but as the original
issue of Intégral itself is presumably long out of print and relegated
to a dusty corner of a reference library somewhere, I'm taking the opportunity
to post it here on Paris Transatlantic. Apart from rewriting the third
footnote, I haven't had to make any changes, and it seems to be just
about as relevant now as it was nearly sixteen years ago. I hope you
find it useful. DW
music has come of age: it is now nearly a quarter of a century since
Terry Riley assembled an ad hoc group of friends to perform what on
paper looked a modest little composition entitled "In C", and some twenty
years have passed since the Reich and Glass ensembles played to single-figure
audiences in draughty New York lofts. By what seems to have been a shrewd
marketing strategy, Philip Glass has now succeeded in capturing the
attention, prestige, and wealth of the operatic community on both sides
of the Atlantic (and is closely being followed it seems by John Adams),
while Steve Reich has been rediscovering and redefining the potential
of the symphony orchestra. Add to this the enormous demand for recordings
of minimal music (thanks in no small part to the efforts of prominent
1970s rock musicians like Eno and Bowie in demonstrating its "crossover
potential"), and it is easy to see why the more reticent "uptown" community
of academics and old-style avant-garde composers have tended to view
this music with mild disdain (tinged with a little jealousy?) bordering
on polite contempt.
their part, the minimalists have shown little interest in wooing this
more exclusive market - unlike as was the case with the Darmstadt avant-garde,
the emergence of minimal music was not accompanied by a flood of polemical
rhetoric - and the academics have accordingly given them little analytical
attention. With the possible exception of Reich's "Writings" (1) and
specifically "Music as a Gradual Process" (which is more philosophical
credo than music theory anyway), there were only sporadic attempts to
introduce the new techniques of minimalism to an educated musical public
prior to Michael Nyman's chapter on the subject in "Experimental Music:
Cage and Beyond".(2) Quite simply, there would have been no point -
it was a characteristic of early minimal compositions that their overall
form and moment-to-moment content were one and the same thing: the process.
Only with the introduction of established harmonic procedures (chord
sequences, cadential progressions) in the mid-1970s did it become possible
to make such distinctions once more. By that time, though, Glass had
already signed with Virgin Records to record "Music in Twelve Parts",
and the ever-voracious rock press had "discovered" minimal music. The
handful of academics who had shown interest beat a hasty retreat - paradoxically,
at the moment it became more open to conventional analysis, the more
the music was ignored.
Recently, however, there has been a resurgence of interest in the subject,
which seems to be the result of a number of factors. Firstly, minimal
music has become more openly conventional, i.e. it has actively sought
to reclaim harmonic and contrapuntal procedures more commonly associated
with Western music. To this end, it seems to have attracted the attention
of composers as diverse in aesthetic as Ligeti, Andriessen, Pärt and
Tavener, who have each brought more "classical" (or classically avant-garde)
concepts of organization into the minimalist field. Secondly, the kind
of analysis of mainstream twentieth-century music that was fashionable
some ten or so years ago now seems rather primitive in the light of
the formalized refinement and somewhat forbidding elegance of recent
set theory. Accordingly, some students may have turned to minimal music
thinking that it presents less of a problem in terms of terminology
- this however is not the case. The aim of this paper is to explain
the confusion that has arisen within the vocabulary of minimal music,
and hopefully to dispel it by presenting a more precise terminology
suitable to the analytical requirements of future students. Before embarking
on this, however, certain questions have to be asked regarding the nature
of their proposed analyses.
Music analysis, especially in America, where Schenkerian and set-theoretical
disciplines have become integral components of university curricula,
is generally predicated on the concept that a composition can be analysed
to reveal various hierarchical levels of structure, and that events
on the surface of music can be deemed to be more or less valuable
in terms of their relationships to the structural hierarchy. To this
end, a Schenker graph and a Forte K/Kh lattice diagram serve the same
purpose (admittedly this is a drastic oversimplification of the issues
involved), both providing an out-of-time representational model
of the music's structure. With minimalism, such an approach is of little
value, as it fails to take into account the in-time listening
experience, i.e. the specific location of events and the durations of
the sections in relation to the musical material they contain, or to
the proportions of the work as a whole. This is not to say that an analysis
of a minimalist composition should resemble a recipe book (ingredients
and cooking times) but rather that the process by which events are taken
from the musical surface and presented out of context should be less
oriented towards an underlying deep structure and more concerned with
how the selected material unfolds during the course of a performance.
With Schenkerian or set theory it is quite possible - though hardly
desirable, one would think - to produce a successful analysis of a work
without having heard it; in an analysis of a minimalist composition,
events are deemed to be significant because they are heard to
be significant, and not the other way round. Given a music as
consciously "self-explanatory" as minimalism, it is up to the student
to determine to what extent his/her observations will remain merely
descriptions - it is hoped that the following will be of use and will
be adapted to their particular demands. Reference is made in the text
to the author's article on Reich's "Sextet" (3) , and musical examples
are taken from that work with the kind permission of the composer.
a composer and writer working in this general area one is constantly
frustrated at having the preface the term "minimalism" with "so-called"
- it seems to be a name-tag that has no existence outside of quotation
marks, and all minimalist composers are acutely conscious of its potentially
misleading and even pejorative implications (4). Minimal music (for
the time being we shall continue to use the term as fearlessly as possible)
has been variously described as "trance music" (5), "systems music"
(6), "process music", "solid state music" (7), "repetitive music" and
"structuralist music" (8). Before discussing more systematic and specific
terms, these generic labels need to be dealt with. Both "systems music"
and "process music" are generally quite useful as descriptions; we propose
to differentiate between the two, preferring the "process" term as being
more applicable to the early works of the genre, where the compositions
are structurally nothing more than single processes. Terry Riley described
"In C" as a "people process" (9), and in terms of the general descriptions
proposed by Reich in his "Music as a Gradual Process" (10), both his
(Reich's) and Glass's works of the late 1960s and early 70s are justifiably
described as processes in their own right. (The list also includes the
works of Frederic Rzewski from about this time: "Les Moutons de Panurge";
"Attica"; and "Coming Together".) "Systems music" we take to encompass
more than one single linear process, and under this label we propose
to include Reich's works from 1973 on, Glass's entire oeuvre after "Music
in Twelve Parts", most of the recent music of John Adams, and the work
of the European minimalists including Michael Nyman, Wim Mertens and
Diderik Wagenaar, to name a few. The distinguishing feature about these
pieces as opposed to the earlier process works is their concern with
multiple process: the rigid polemic laid down by Reich in 1968
is no longer applicable (11).
a further clarification (hopefully), we propose to use the term "solid
state music" to refer to works whose surface activity and texture is
repetitive in nature when considered in self-contained blocks,
but whose overall form no longer presents a definable progression from
one point to another. For example, under this definition, "Spaceship"
from Glass's "Einstein on the Beach" is systemic but not solid state,
while for "Trial/Prison" from the same opera the converse is true.
As for the three other terms, they are either redundant or misleading,
or both. "Repetitive music" is clearly as facile as it is vague - it
imparts as much information as describing all post-War serialism as
"twelve-tone music". "Structuralist music" suffers from the same problems
as "minimalism" (which we shall discuss in due course): to imply a connection
between the European intellectual movement (itself exemplified by such
diverse figures as Claude Lévi-Strauss, Roland Barthes, Jacques Lacan
and Jacques Derrida) and minimal music is superficially attractive (as
in the case of Nyman's soundtracks for Peter Greenaway's movies), but
the term "structuralist" could apply equally well to the music of such
resolute anti-minimalists as Babbitt, Berio and Stockhausen. Finally,
"trance music" is a downright harmful description for the majority of
minimalists. True, Riley said that the ultimate goal of music is "to
get far out", but for composers in the field as diverse in orientation
as Glass and Andriessen the prospect of the audience just switching
off - not actively concentrating - is quite abhorrent. The fact that
even the most rigorous process pieces are often worshipped by those
who have ascended to a higher state of (chemically induced?) consciousness
is a problematic aspect of the genre, which has been ably if not totally
convincingly addressed by Mertens (12).
And so to "minimalism" itself: despite persistent attempts to find out,
it is still unclear who first coined the term. A BBC interview with
Nyman (13) proudly proclaimed him as the originator, though he has since
refused to commit himself on the matter (understandably not wishing
to be the target of the pent-up wrath of many of his fellow composers).
If Nyman did first use the term, it was probably during his time as
music critic of "The Spectator", prior to the publication of "Experimental
Music" in 1974. Perhaps we shall never find out who was responsible
- already the history books are being rewritten in the mouths of the
composers, Reich and Glass included - but insofar as there was much
direct contact between these composers and the minimalist/conceptual
artists in New York City in the early 1970s (including Serra, Flavin
and LeWitt), there is some historical value in the term. However, its
possible pejorative implications are immediately apparent - hence Milton
Babbitt's description of himself as a "maximalist" (14) - and hence
Reich's opinion of the nametag: "It's unfortunate - but it's better
than 'trance music'..." (15) Therefore we shall continue to use it as
an all-purpose umbrella term, in the hope that we shall not be misunderstood.
Mertens, in "American Minimal Music" (16) offers an analysis of trends
in minimalism posited on developments in earlier twentieth-century music
and philosophy - taking Adorno as a starting point he discusses the
crisis of the concept of "work" in Schoenberg and Webern, the embracing
of aleatoric procedures in both the European and American post-War avant-gardes,
the problem of temporal perception in Stockhausen's "moment form", finally
arriving at a somewhat ambiguous moral stance supported by extracts
from the modern French philosophers Deleuze and Lyotard. The problem
with Mertens' analysis, assuming one concurs with the philosophers,
that it occupies itself with a music governed by the aesthetic position
of Reich in the "Writings", that is, a music where form and content
(17) are inseparable - the process at one and the same time is both
the form and the content. In doing so, Mertens' analysis seems to ignore
the critical change that minimal music underwent about 1973, when for
the first time it began to be occupied with definable chord sequences
as a means of structural articulation. Glass's "Another Look at Harmony"
is a major landmark in this respect - in choosing to use standard cadential
progressions towards a recognizable tonal centre, Glass at once subverts
the concept of a linear, out-of-time listening experience. The listener
is immediately aware of a work consisting of larger units defined by
chord sequences, in a manner similar to the way a jazz or rock track
is heard as a certain number of "choruses". This mode of listening is
now nothing less than a standard feature of our modern Western ear,
where the vast majority of music we hear on a daily basis is determined
precisely by these structural concerns, and no doubt explains to some
extent the crossover phenomenon of minimalism into popular markets,
while at the same time casting doubt on Mertens' rather cloistered philosophical
a chord sequence as a defining unit then prompts us to re-evaluate the
question of structure. Clearly Glass is no longer accurate when he says
"there is no structure at all - the structure defines itself from moment
to moment", for it is precisely the expectation that something different
will happen "next time around" that motivates our perception of the
music. Indeed, one is struck by the sheer predictability of Glass's
recent music, hence again its appeal to audiences who have grown up
with music that follows similar conventional and inevitable structural
guidelines (rock, pop and jazz). Reich, on the other hand, uses chord
sequences more flexibly, usually presenting the whole sequence at the
outset of the work ("Music for 18 Musicians", "Sextet", "Desert Music")
and then basing subsequent sections of the piece on each member chord.
Mertens, who in his book surveys the music of Young and Riley as well
as that of Reich and Glass, does not take advantage of the opportunity
to present a clear terminology to describe the techniques used by these
composers. Accordingly, we propose to use the following terms, not only
with reference to compositional (theoretical) details, but also to the
(musicological) development of minimalism as a whole.
Phasing in its most rigorous manifestation is found in
Reich's music from "It's Gonna Rain" up to and including "Drumming"
- two identical patterns, x and y for our purposes (speech fragments
in the tape pieces, melodic or rhythmic units in the instrumental works),
start together but with one at a fractionally faster tempo, moving
increments of a beat ahead until, over the course of a composition or
part of a composition, the two are in synchronization once more. In
the tape compositions "It's Gonna Rain" (1965), "Come Out" (1966) and
"Melodica" (1966) this can happen at a very slow and regular rate of
change (a pure phasing, where the tempo of pattern y (tempo Y)
is consistently slightly faster than that of x); in the live
instrumental phase pieces "Piano Phase", "Reed Phase", "Violin Phase",
"Phase Patterns" and "Drumming" the process is more stepped, reaching
sections of temporary rhythmic stability as each rhythmic unison is
attained. Thus in live instrumental phasing, tempo Y does not
In Ex. 1, the first phase shift occurs over a period of between four
and sixteen times the duration of the original unit (i.e. over a duration
of between 48 and 192 sixteenth-notes in the original tempo X).
If we assume for the sake of convenience an original tempo X
of dotted quarter-note = 60 (each sixteenth-note lasting therefore one
sixth of a second), we can calculate tempo Y, the tempo at which
y drifts out of phase, as being somewhere between dotted quarter-note
= 61.25 (for the faster phase shift where y plays 49 sixteenth-notes
in the time of x's 48) and dotted quarter-note = 60.31 (for the
more gradual phase shift - as preferred by the composer - where y
plays 193 sixteenth-notes in the time of x's 192).
Reich was exploring the possibilities of both pure and live phasing,
Philip Glass's first minimalist works were preoccupied with another
technique that became a standard feature of minimalism, that of linear
additive process. Example 2, "Les Moutons de Panurge", an experimental
composition for variable forces by Frederic Rzewski, explains the technique
in detail (and its logical counterpart, linear subtractive process).
Though the instructions for Rzewski's score make allowances for the
performers' mistakes ("if you get lost, stay lost"), it is perhaps worth
noting that in recent years Rzewski has preferred using a completely
notated version of the piece to prevent this from happening.
*see footnotes for this text
In Glass's music, linear additive process is somewhat more flexible:
only rarely in his works do the melodic units grow by the addition of
only one note at a time. Moreover, unlike in the Rzewski example, after
each addition is made the new unit is repeated a certain number of times
before the additive process continues (one could therefore speak of
"pure" or continuous as opposed to "gradual" or stepped additive process
if a distinction needed to be made). The distinctive feature of Glass's
compositions of this period ("Two Pages", "Music in Fifths", "Music
in Similar Motion", "Music in Contrary Motion") is their preoccupation
with regular running eighth-notes that eschew any possibility of being
heard as measures written in a regular time signature. It soon becomes
impossible for the listener to remember exactly where he/she is in the
linear additive process (bar lines function only to coordinate performers).
contrast, block additive process (which Reich refers to as "replacing
rests by beats") consists of the gradual assembly of a unit within a
predetermined and unchanging time frame (a measure of 4/4 or 3/4, for
example). (See Example 3.)
Block additive process features prominently in the music of Reich from
1973 to the present day, and is usually used in conjunction with canon
- repeating units, once assembled, are a certain number of beats out
of phase with each other. (See Example 4.)
The end product (Fig. 23 in Example 4) is similar then to those sections
of the live instrumental phase pieces that occur between the phase shifts
(where the tempo X is constant for both performers) and the pattern
is heard as displaced against itself. In "Clapping Music" Reich dispenses
with the phase shifts altogether, and the work consists of a basic rhythm
(lasting a measure of 6/4) heard against the eleven possible displaced
(by eighth-notes) variants of itself (see Examples 6 and 7).
Because the time signature remains constant and is heard to do so (unlike
as was the case with linear additive process), it is possible to notate
the process numerically, assuming that each measure be divided into
x small regular units (eighth-notes here for our purposes), numbered
from 0 to x-1 (this is analogous to the concept of pitch-class
notation where C is represented by 0 and B by 11 (Y or B)): thus a measure
of 6/4 can represent twelve beat-classes (bcs). (See Example 5.)
A rhythmic displacement "d" ("transposition") of a pattern "A"
by x eighth-notes can be unambiguously represented by positive
integers, where x is a positive integer. Thus the opening of
"Clapping Music" can be shown as in Example 6, and the whole work can
be easily represented, as shown in Example 7.
rhythmic pattern of "Clapping Music" is in fact the same as in our earlier
example from the "Sextet" (Ex.4), but in the latter the displaced forms
are assembled by block additive process, not necessarily beginning with
the first note of each unit. Accordingly we must number the notes of
the melodic unit before we can chart its introduction through block
additive process. (See Example 8.)
Thus "d2A" denotes only notes three, four and five
of the pattern displaced by two eighth-notes (see Ex. 4 fig. 18). The
musical development of the passage in Example 4 can be represented by
Because displaced patterns will overlap bar lines, the analyst should
state clearly in the case of the above that the number of repeats is
specified in terms of repetitions of the original pattern A (and
is the actual number of measures as shown in the score). In the "Sextet",
as opposed to Reich's earlier work, the number of repeats is precisely
specified and is therefore of structural importance and not to be ignored.
A method such as the above reveals at a glance many striking formal
cross-connections between the work's five movements.
survey of the music of Terry Riley in the 1960s and 1970s would require
the use of the term overlapping pattern work to denote its fluctuating
and intermediary position between the rhythmic regularity of block additive
and the more expansive linear additive processes; Riley's work, arising
to a certain extent out of his own performance practice, uses the simultaneous
layering of musical ideas of different lengths over each other or over
a basic pattern or pulse (e.g. "In C", "A Rainbow in Curved Air", "Dorian
Reeds" and "Persian Surgery Dervishes"). As much of it is at least partially
improvised, it can present some problems of transcription, and as a
result may not lend itself as readily to the detailed approach outlined
above. (18) Example 10, however, presents a notated version of the technique.
defined above, systems music involves not one but a number of such processes.
These do not necessarily occur simultaneously; in the music of Michael
Nyman ("M-Work", "Think Slow, Act Fast"), one process may abruptly switch
to another, as if two independent pieces had been cut up and spliced
together. Example 11 is taken not from Nyman, but from the author's
composition "Manhattan Systematic" (1986).
contrast to the splicing technique, a smooth transition between
processes can be effected by dovetailing the end of one into
the beginning of the next. This features prominently in the music of
Reich written in the 1970s ("Six Pianos", "Music for 18 Musicians",
"Octet") and is usually achieved by dropping the lower voices of the
texture to have them return with new material underneath the upper voices
of the old texture, as shown in Example 12.
12 also provides us with an illustration of textural additive process,
which is quite simply the bringing in of one voice at a time until the
whole texture is complete. It is found in much minimal music, from Reich
("Drumming", "Music for Pieces of Wood" and all subsequent works) to
Glass (the music from "North Star" onwards) and especially in the music
of Michael Nyman, whose soundtrack for Peter Greenaway's "The Draughtsman's
Contract" emphasizes the connection between the technique and earlier
polyphonic models (in this case, the chaconnes of Purcell). Textural
additive process is therefore ideally suited to systems music in which
different processes are superimposed (especially overlapping patterns
- see Example 10).
Having presented the above, it is obviously for the individual to decide
to what extent it can be used effectively in a theoretical or musicological
context. Inevitably an analysis of a minimalist composition to a certain
extent must involve simply describing what happens; it should be stressed
though that this alone does not constitute analysis - although minimalist
composers may be generally sceptical of the pre-compositional artifice
of their uptown cousins, the terminology outlined here can and should
be used to reveal not, as is commonly assumed, the paucity of their
imagination, but rather the enormous sophistication and elegance of
their music. The advantages of such an approach would be mutual - not
only would minimal music be assimilated into the canon of Western art
music (a goal to which it undoubtedly aspires, if the recent statements
of Reich and Glass are to be believed), but the comparatively recent
descriptions of pitch-class and time-point theory would be seen to be
relevant, if not indefensible, to a meaningful analysis of a composition
written in a style not usually associated with it. In the light of these
remarks, it is hoped that the forthcoming study of Reich's "Sextet"
will satisfy many of the conditions outlined above.
(1) "Writings About Music" (London: Universal Edition, 1975): 9-11
(2) "Experimental Music: Cage and Beyond" (London: Studio Vista, 1974).
(3) Presented as the author's PhD thesis at Eastman School Of Music,
Rochester NY in 1987. Originally intended for publication in 1988 (hence
the references above).
Apart from the many published interviews with these composers, my personal
encounters with four minimalists confirm their unease with the label.
Michael Nyman continues to use the "so-called"; Louis Andriessen described
his "Hoketus" (1977) most emphatically as "MAXIMAL music - I am a maximalist!";
Glass was uneasy at the mention of the word after "Akhnaten" received
its world premiere in 1984; Reich's own comment appears in the text
This is still popular in Europe, though more recently records of minimal
music are also appearing in "New Age" bins in major record stores.
Originally used in connection with Nyman's music, this is currently
in vogue with the British rock press.
This seems to appear first in the "Village Voice" shortly after the
U.S. premiere of "Einstein on the Beach".
Nyman has collaborated extensively with self-styled "structuralist"
filmmaker Peter Greenaway; the term appears with reference to minimal
music after the widespread success of "The Draughtsman's Contract" in
Riley, as cited by Nyman in "Experimental Music" (note 2, above).
"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 all the note-to-note (sound-to-sound)
details and the overall form simultaneously. (Think of a round or infinite
canon.)" From "Music as a Gradual Process" (1968) in "Writings" (see
note 1, above).
(12) "American Minimal Music" (New York: Alexander Broude, 1983). The
ideological observations are found in Part Three.
From an interview with Nyman on BBC Radio Three's "Music In Our Time"
series, recorded in the autumn of 1983.
From the composer's sleeve notes to Robert Taub's recording of the piano
(15) Reich speaking at the Eastman School of Music, Rochester, New York,
Mertens, op.cit., pp. 95-109.
(17) By content Mertens is referring to what Reich describes as "note-to-note"
details; it is another example of Mertens' somewhat loose use of terminology.
Overlapping also features in the work of rock guitarist Robert Fripp,
and examples can be found on his "Exposure" album of 1977, as well as
on the King Crimson albums "Discipline" (1981), "Beat" (1982) and "Three
of a Perfect Pair" (1984).
* notes to Ex. 2
in strict unison; octave doubling allowed if at least two instruments
are in each octave. Read from left to right, playing the notes as follows:
1, 1-2, 1-2-3, 1-2-3-4, etc. When you have reached note 65, play the
whole melody once again and then begin subtracting notes from the beginning:
2-3-4...65, 3-4-5...65, ... , 62-63-64-65, 63-64-65, 64-65, 65. Hold
that note until everybody has reached it, then begin an improvisation
using any instruments. In the melody above, never stop or falter, always
play loud. Stay together as long as you can, but if you get lost, stay
lost. Do not try to find your way back into the fold. Continue to follow
the rules strictly.