1. INTRODUCTIONcontext.fm/mills/thesis/HORVITZ_THESIS-FINAL_PRINT.docx · Web viewMaster of Fine...
Transcript of 1. INTRODUCTIONcontext.fm/mills/thesis/HORVITZ_THESIS-FINAL_PRINT.docx · Web viewMaster of Fine...
AUTOMATION IS MY SALVATION:
EIGHT STUDIES FOR AUTOMATIC PIANO
Thesis
Submitted in partial fulfillment of the
requirements for the
Degree of
Master of Fine Arts in
Electronic Music and Recording Media
Mills College, 2010
By
Seth Horvitz
Approved by:
_______________________________James FeiDirector of Thesis
_______________________________Chris BrownHead, Music Department
__________________________Sandra C. GreerProvost and Dean of the Faculty
Reading Committee:
______________________________Chris Brown
_______________________________Fred Frith
Table of Contents
1. INTRODUCTION................................................................................................................... 6
2. HISTORY................................................................................................................................. 62.1 Prehistory..................................................................................................................................... 62.2 Rise and Fall................................................................................................................................. 82.3 Rediscovery............................................................................................................................... 102.4 Nancarrow Considered.......................................................................................................... 11
3. INFLUENCES........................................................................................................................ 133.1 Tenney......................................................................................................................................... 133.2 Ligeti............................................................................................................................................. 14
4. REFLECTIONS..................................................................................................................... 174.1 Disklavier vs. Player Piano...................................................................................................174.2 The Sound of the Piano.......................................................................................................... 174.3 The Basic Shape........................................................................................................................ 184.4 The Harmonic Series...............................................................................................................184.5 Hand-made Algorithms..........................................................................................................194.6 Time.............................................................................................................................................. 194.7 Emergence.................................................................................................................................. 204.8a Human Music, Living Music................................................................................................214.8b Living Music, Live Music......................................................................................................224.9 Electronic Music....................................................................................................................... 224.10 Immersion............................................................................................................................... 234.11 The Visual................................................................................................................................ 234.12 The Concert............................................................................................................................. 24
5. DESCRIPTIONS................................................................................................................... 25CLASS A: IDEALIZED SYMMETRICAL FORM [14, 4]......................................................................26CLASS B: CONSTRUCTED BINARY FORM [1, 2]...............................................................................26CLASS C: INTUITIVE LINEAR FORM [21, 99]....................................................................................26CLASS D: INTUITIVE TRANSFORMATIONAL FORM [13, 29].....................................................26Note on order and numbering:................................................................................................................27
5.1 Study No. 14: Arch Study for the Highest Eight Notes..................................................275.2 Study No. 4: Sixteen Diatonic Glissandi Moving at Harmonic Rates.......................295.3 Study No. 2 : An Approximate Series of Approximate Harmonic Series................325.4 Study No. 13 : Echoes.............................................................................................................. 365.5 Study No. 21 : Bells.................................................................................................................. 395.6 Study No. 1 : Octaves, Systematically Filled and Folded.............................................395.7 Study No. 29 : Tentacles......................................................................................................... 425.8 Study No. 99 : Strumming Machine....................................................................................45
6. CONCLUSION...................................................................................................................... 47
APPENDIX A : OVERVIEWS................................................................................................. 49
APPENDIX B : PHOTOGRAPHS.......................................................................................... 54
BIBLIOGRAPHY...................................................................................................................... 56
EVERYONE SHOULD BE AWARE:THE BEST TRADEMARK IN THE WORLD – IS ‘LIFE’
Beware of Forgeries!
-Sergei Yutkevich, The Eccentric Manifesto, 1922
1. INTRODUCTIONThe main purpose of this thesis is to illuminate the methods, processes,
philosophy, and influences at work in Eight Studies for Automatic Piano, composed for
the Yamaha C7 Disklavier® Mark III. Given the unique historical role of this instrument,
the discussion will be preceded by a brief overview of the history of mechanical music,
up to and including its earlier cousin, the pneumatic roll-operated player piano. This
history will highlight the aims of composers, especially those who saw the "potential to
create rather than recreate music"1 with mechanical instruments, culminating in a brief
consideration of Conlon Nancarrow's work. The second part of the thesis will discuss two
works that have been pivotal in my approach to the "automatic" piano: James Tenney's
Spectral Canon for Conlon Nancarrow (1974), and György Ligeti's Continuum for
Cembalo (1968). This section also considers the influence of Ligeti’s dynamic,
interactive approach to generating form, specifically in regard to his Études for piano. A
third section provides a series of personal reflections and mini-essays regarding my
working process, considering both the pragmatic and philosophical implications of the
ideas at hand. Finally, a detailed description of each work will be provided.
2. HISTORY2.1 Prehistory
As Arthur W. J. G. Ord-Hume, scholar of mechanical music, notes: "The
production of music without attendant performing skills is no recent phenomenon. From
the earliest times, the creation of a musical instrument went hand-in-hand with the
creation of a non-participant means of playing."2 Throughout their history – a history 1 Henry Wong Doe, “Musician or Machine: The Player Piano and Composers of the Twentieth Century,” (Ph.D. Diss., The Juilliard School, 2006), 2.2 Arthur W. J. G. Ord-Hume "Cogs and Crotchets: A View of Mechanical Music," Early Music, 11.2 (Apr., 1983): 168.
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longer than popular knowledge might lead us to believe – automated musical instruments
have rarely provided creative inspiration for composers. Prior to the 20th century, with
few exceptions, these musical machines served either as a method of documentation and
reproduction, or as a novel way to "perform" existing musical compositions. Indeed, the
magic of seeing a machine play "by itself" was often a large part of the attraction.
Secondary sources refer to the existence of an entire mechanical orchestra in the
third century B.C., built for the emperor of China during the Han Dynasty,3 though few
details are known. Later inventions commonly made use of a revolving barrel or cylinder
that could be "programmed" by manually arranging a set of wood or metal pins on its
surface. The earliest documented instrument of this type was a water-powered barrel
organ named "Banu Musa," dating from about 875 AD,4 while the oldest functioning
instrument to survive dates from 1502, and is currently on display at the Burgmuseum in
Salzburg. Over the centuries, artisans and engineers developed countless variations of
this basic cylindrical device, providing instruments for street performers as well as fine
collectibles for royalty.
In the 18th century, mechanical organ and musical clock builders worked closely
with composers such as Haydn, Mozart, and Beethoven, "although it is difficult to say
whether they were personally interested or rather obliged by their patrons to write for
these instruments."5 Haydn clearly considered the creative potential of these instruments,
writing at least thirty original works exclusively for mechanical organ, yet his
3 See Roy Porter, “automata,” <http://www.answers.com/topic/automata-theory> (6 December 2010) and press release from “Automata: Contemporary Mechanical Sculpture,” Chazen Museum of Art <http://www.isthmus.com/theguide/details.php?event=233789> (6 December 2010), among many others.4 Charles B. Fowler, “The Museum of Music: A History of Mechanical Instruments,” Music Educators Journal, 54.2 (Oct., 1967): 45.5 Wong Doe, 9.
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compositions do not vary greatly from his other work apart from the use of larger leaps
and faster embellishments6.
While much of the music written for early mechanical instruments has been lost,
we can be fairly certain that composers of the time did not intend to invent new forms or
styles of music around these instruments, but instead made use of instruments’
capabilities to either extend the virtuosity of human performance or to achieve a more
precise document of their work than sheet music could provide. These aims persisted
until the early 20th century, when a handful of composers first began to consider a music
that would derive its creative potential directly from the idiosyncrasies of the machine.
2.2 Rise and Fall
First introduced in the late 19th century, the pneumatic roll-operated player piano
ushered in a new era for the mechanical instrument, but its rapid rise and fall, in addition
to heavy resistance from detractors, preempted composers from fully exploring its
creative potential. The player piano possessed expressive and technical capabilities far
surpassing anything that came before. Yet, perhaps even more than some instruments of
the 18th century, it was not invented with creative use in mind. Instead, its role in popular
culture can be more accurately described as a precursor to the phonograph, and by
extension, the entire recording industry. The instrument marks the first effort to mass
market existing musical compositions for playback within the home, and for this purpose,
it achieved an astounding level of commercial success. By 1925, sales of player pianos
had overtaken those of standard pianos.7
6 Ibid., 8.7 Arthur Ord-Hume, “Player Piano,” In The New Grove Dictionary of Music and Musicians, 2d ed. Edited by Stanley Sadie, Vol. 25 (London: Macmillan Publishers Ltd., 2000).
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The popularity of the instrument piqued the interest of several prominent
composers of the time, including Paul Hindemith, Igor Stravinsky, Ernst Toch, and
George Antheil. For the first time, composers began to think seriously and deeply about
the machine’s idiosyncratic qualities, and how to exploit them for aesthetic purposes. The
excitement (and confusion) surrounding the player piano's new creative potential is
captured well in this review of a festival organized by Hindemith in 1926:
A brilliant Welte-Mignon played. IT played. The hall was bathed in light from some invisible source, and you could have heard a pin drop as Hindemith adjusted the levers of the instruments, which was to replay three worthy pieces by Ernst Toch. The piano begins to play: musical studies for the instrument, toccatas with row upon row of unplayable chords, with a velocity that the most accomplished virtuoso could never even approach, with a precision far beyond the capability of a human being, with a superhuman power of sound, with a geometrical clarity of rhythm, tempo, dynamics and phrasing, which only a machine can really bring out. What a wonderful box of tricks! The piano reaches the end of the composition and the audience hesitates. Should one applaud? There is, after all, no-one sitting there. It is only a machine. At last just a little applause, which becomes ever more enthusiastic. Cries of “Encore!” And indeed, the piano repeats faultlessly, with the same precision as the first time through.8
The excitement was high, but short-lived. Concerts of this kind were still
relatively rare, and reactions were often hostile, placing outspoken supporters like
Hindemith on the defensive9. Throughout the 1920s, Stravinsky expressed profound
interest in the creative potential of the instrument, yet he only managed to compose one
short and rather underwhelming solo piece for it, the Etude pour Pianola (1921). Antheil
called for the use of sixteen synchronized pianolas in his grand spectacle, Ballet
Mechanique (1924), but technical difficulties later forced him to re-orchestrate. With the
onset of the Great Depression coinciding with the growing popularity of smaller and
cheaper devices such as the phonograph and radio, the player piano experienced a sudden
8 Paul Hindemith quoted in Rex Lawson, “Hindemith: Toccata for mechanical piano.” Pianola Journal 9 (1996): 19-20.9 Wong Doe, 46.
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and rapid commercial decline, and the instrument’s ardent supporters quickly lost
interest.
2.3 Rediscovery
Nearly two decades after the player piano's commercial demise, an American
composer by the name of Conlon Nancarrow, while living in Mexico as a political
refugee, decided to devote the better part of his life to developing a radically new
compositional framework around the instrument. Inspired by Henry Cowell and
Stravinsky's rhythmic ideas, Baroque counterpoint, canon form, and jazz, Nancarrow's
work covers an astonishing range, yet by sheer originality of approach (not to mention
the unique sound of his modified player pianos) his oeuvre carries an instantly
recognizable signature. While most of his work was composed in relative isolation, a
surge of interest in the 1980s has produced a wealth of scholarship, and today, he is
commonly cited as one of the most important composers of the 20th century.
Until he discovered the player piano, Nancarrow struggled to realize his ideas. His
earliest compositions for human performers were met with almost unanimous frustration.
The rhythmic and temporal relationships involved were too complex for humans of the
time to deal with, both mentally and physically10. After several disappointing rehearsals
and cancelled performances, Nancarrow discovered Henry Cowell's highly prescient
treatise New Musical Resources, which contained this offhand recommendation:
Some of the rhythms developed through the present acoustical investigation could not be played by any living performer; but these highly engrossing rhythmical complexities could easily be cut on a player-piano roll. This would give a real reason for writing music specially for player-piano, such as music written for it at present does not seem to have, because almost any of it could be played instead by
10 Roger Reynolds, “Conlon Nancarrow: Interviews in Mexico City and San Francisco", American Music 2.2 (Summer 1984): 1-24.
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two good pianists at the keyboard.11
In 1947, with the help of a small family inheritance, Nancarrow traveled to New
York from Mexico to acquire a player piano and a punching machine12 then proceeded to
spend the next several decades bringing the potential of Cowell's statement to life. While
living in relative isolation from the greater musical world, Nancarrow developed a
massive body of work, making exclusive use of the piano's mechanical properties to
realize complex temporal relationships. In doing so, he completely overshadowed the
relatively limited experiments of previous composers.
2.4 Nancarrow Considered
Although a full analysis of Nancarrow's work is beyond the scope of this thesis,13
his compositional techniques—explained here—serve as a reference point for Eight
Studies for Automatic Piano.
Rather than compose with melody, harmony, or even sound per se, Nancarrow
used time itself, in fact multiple times, as the structural building blocks for his
compositions. The paradox here is that time, in order to be experienced musically, must
be realized as sound—in this case, the sound of a piano. And in this regard, Nancarrow
was never entirely satisfied:
Actually, at the beginning what I would have liked to have had would have been a harpsichord, a mechanical harpsichord 'cos that's the sound I like because of the clear divisions. A nineteenth-century grand piano is not built for contrapuntal music. It's built for rich, harmonic sounds.14
In an effort to create a sharper, more discrete sound from his piano, Nancarrow
11 Henry Cowell, New Musical Resources. (New York: Cambridge University Press, 1996), 64.12 Wong Doe, 61.13 For in-depth analysis, the reader is directed to Kyle Gann's nearly definitive 1995 volume The Music of Conlon Nancarrow.14 Conlon Nancarrow, interview by Natalie Wheen, In The Pianola Journal: Journal of the Pianola Institute. West Wickenham, Kent, England: Vol. 3 (1990): 6.
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experimented with various modifications, eventually settling on a solution that involved
attaching steel and leather straps to the hammers. While his experiments with timbre were
fairly extensive, they were less about exploiting the sonic potential of the piano and more
about the composer's "desire for clarity and precise definition of notes within the
texture."15 Without such clarity, the distinct temporal entities in Nancarrow's work would
meld together, a result he definitely wished to avoid.
Seeking to explore "temporal dissonance" from the start,16 Nancarrow's first study
was a two-part canon setting tempos of 210 and 120 against each other (a ratio equal to
7:4, or a purely tuned minor seventh in the realm of pitch). Over the years, he explored
increasingly complex ratios and rhythmic relationships, culminating in the use of the
irrational numbers e and pi in Studies 40 and 4117. Nancarrow sometimes spent a year or
more punching a single piano roll before he was able to hear the results of his
calculations. As he himself noted, the element of surprise was an exciting part of the
process.18
While respecting the tremendous scope and influence of Nancarrow’s creative
vision, the player piano works discussed here do not emulate his compositional style. In
contrast to Nancarrow’s work, the material in Eight Studies for Automatic Piano
originates from extremely simple temporal building blocks and a minimum of advance
planning. Rather than seeking absolute clarity of articulation, Eight Studies embraces the
piano’s built-in palette and attempts to craft new sonorities from the perceptual fusing of
15 Wong Doe, 64.16 Ibid., 68.17 Ibid., 70.18 “As a matter of fact, after I finish punching a piece and before I put it on, you have no idea how excited I am. What is going to happen? The first time I listen, it's just a matter of how well I did what I thought I was doing. Naturally, the more it comes out the way I thought I did it, the better I feel. It's as simple as that.” (Reynolds, 16).
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different “lines.” The following section will discuss works by two composers that have
been more important than Nancarrow in shaping Eight Studies. Both composers praised
Nancarrow, but departed from his compositional techniques in significant ways.
3. INFLUENCES3.1 Tenney
The impetus for composing Eight Studies for Automatic Piano came as a direct
result of hearing James Tenney's Spectral Canon for Conlon Nancarrow (1974). Tenney's
piece sounded completely alien to me, almost unreal, and certainly unlike any other piano
music that came before it, including Nancarrow's. What struck me most was just how
easy it was to forget that I was hearing a piano, or for that matter, a composition at all.
The piece sounded more like a "fact of nature,"19 but one that constantly confused, rather
than confirmed my intuitive sense of time. Despite an obvious and precise pulse, the
piece draws attention to various perceptual entities that emerge from a process, entities
that stretch, multiply, and overlap in several directions at once.20
If the above description sounds suspiciously like Steve Reich's idea of "Music as a
Gradual Process,”21 it comes as no coincidence; Reich even quoted Tenney in his seminal
essay. Reich stated that "whether a musical process is realized through live human
performance or through some electro-mechanical means is not finally the main issue."22
However, after the disappointing 1969 premiere of his “Phase Shifting Pulse Gate” – an
electronic instrument developed over the course of a year in collaboration with engineers
19 Larry Polansky, “The Early Works of James Tenney," Soundings #13 (1983): 225.20 For further discussion of Spectral Canon, see section 5.2 (Study No. 4).21 Steve Reich, “Music as a Gradual Process,” in Writings on Music 1965-2000 (New York: Oxford University Press, 2002), 34.22 Ibid., 34.
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from New Jersey Bell Laboratories23 – Reich abandoned automated music altogether. He
declared: "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."24 By contrast, Tenney's piece depends absolutely on
the precision of the machine for its "life." As noble as the challenge to "play" it might be,
any variations introduced by a human performer would simply muddy the experience.
Inspired by Tenney, I set out to make piano music that depends entirely on the
precision of the machine—music that deliberately avoids the micro-variations introduced
by human performers, yet is nonetheless full of "life." Rather than relying on human
hands for "micro-variation," Eight Studies exploits those micro-variations that exist in
acoustic sound itself, and in human perception, in a way that requires machine precision
to be realized. The machine, working hand in hand with various compositional processes,
becomes an equalizer; if we know that the music is being reproduced with exact,
superhuman precision, we are free to focus our perception on other aspects of the
resulting sound. In deference to Reich's original essay, this music shifts the listener's
attention "away from he and she and you and me outwards towards it."25
3.2 Ligeti
Remarkably, the second work to directly influence Eight Studies for Automatic
Piano was written for a human harpsichordist. Hungarian composer György Ligeti's
Continuum for Cembalo (1968) embodies his lifelong fascination with malfunctioning
machines, yet it was composed more than a decade before his own revelatory discovery
23 K. Robert Schwarz, “Music as a Gradual Process Part II", Perspectives of New Music, 20.1-2 (Autumn, 1981 - Summer, 1982): 227.24 Ibid., 22825 Reich, 34.
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of Nancarrow.26 While Nancarrow went to great lengths to make his mechanical piano
sound more like a harpsichord in an effort to achieve clearer divisions between notes,
Ligeti sought to create a continuous, gradually shifting texture from the harpsichord, and
to use a human performer to bring out the instrument’s machine-like qualities:
It had never occurred to me to write for harpsichord, but… it suddenly came to me that the harpsichord was really like some strange machine… I also remembered that a harpsichord was most typically an instrument with a non-continuous sound, the twang of the string is of short duration, followed by silence. I thought to myself, what about composing a piece that would be a paradoxically continuous sound...but that would have to consist of innumerable thin slices of salami? A harpsichord has an easy touch; it can be played very fast, almost fast enough to reach the level of continuum, but not quite (it takes about eighteen separate sounds per second to reach the threshold where you can no longer make out individual notes and the limit set by the mechanism of the harpsichord is about fifteen to sixteen notes a second). As the string is plucked by the plectrum, apart from the tone you also hear quite a loud noise. The entire process is a series of sound impulses in rapid succession which create the impression of continuous sound.27
Eight Studies for Automatic Piano reflects a similar child-like fascination with machines,
human perception and the sonic characteristics of instruments, including those aspects
that are normally thought of as superfluous or undesirable.
In Continuum, along with other pieces in his so-called "pattern-meccanico"
style,28 Ligeti creates slowly evolving textures from rapidly repeating rhythmic figures—
as he describes them, periods of "mistiness" contrasted with periods of "clearing up."29
The listener's perception of the passing of time is shaped by the rate of change of the
rhythmic figures rather than tempo or meter. Similar, though not identical techniques are
employed in two of my Eight Studies, Nos. 13 and 29.
26 “After the few player piano studies of Nancarrow I listened to, I affirm with all my serious judgement that Conlon Nancarrow is the absolutely greatest living composer.” (György Ligeti to Mario di Bonaventura, letter from 28 June 1980, quoted in Jürgen Hocker, “My soul is in the machine: Conlon Nancarrow” In I sing the body electric: Music and technology in the 20th century (Hofheim: Wolke, 2000), 94.)27 György Ligeti, Ligeti in Conversation (London: Ernst Eulenburg Ltd., 1983), 31.28 Jane Piper Clendinning, “The Pattern-Meccanico Compositions of Györgi Ligeti,” Perspectives of New Music, 31.1 (1993): 192.29 Ligeti, 1983.
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Ligeti’s dynamic, interactive approach to generating form has provided additional
inspiration for Eight Studies for Automatic Piano. Even when there is a strict conception
guiding Ligeti’s work, the material goes through extensive testing and modification
before reaching its final state30. The role of the composer, then, is to act as a dynamic
intermediary between form and content. The best way to describe this working method is
that of a continuous feedback loop between the composer, the material, and the
instrument. My relationship to the piano is strikingly similar to Ligeti’s, with the vital
insertion of a computer added to the loop:31
I lay my ten fingers on the keyboard and imagine music. My fingers copy this mental image as I press the keys, but this copy is very inexact: a feedback emerges between idea and tactile/motor execution. This feedback loop repeats itself many times, enriched by provisional sketches: a mill wheel turns between my inner ear, my fingers and the marks on the paper. The result sounds completely different from my initial conceptions: the anatomical reality of my hands and the configuration of the piano keyboard have transformed my imaginary constructs. In addition, all the details of the resulting music must fit together coherently, the gears must mesh. The criteria are only partly determined in my imagination; to some extent they also lie in the nature of the piano – I have to feel them out with my hand.32
4. REFLECTIONS4.1 Disklavier vs. Player Piano
Eight Studies for Automatic Piano was composed specifically for the Yamaha C7
Disklavier Mark III, a modern-day player piano. An important difference between the
Disklavier and its earlier cousin is that it can be controlled directly and immediately by a
computer using the MIDI (Musical Instrument Digital Interface) protocol, rather than
requiring the composer to punch a paper roll in advance. This affords the opportunity to
30 One notable exception is Poeme Symphonique (1962), a Fluxus-inspired "happening" for 100 metronomes.31 Ironically, the description refers to Ligeti's Études pour Piano, a series of works for human performer, inspired directly by Nancarrow's machine music.32 György Ligeti, CD liner notes, Gyorgy Ligeti Edition 3: Works for Piano, SK 62308, 1996.
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engage in an intimate, dynamic relationship with the instrument, instantly hearing and
evaluating even the smallest modifications to a work.
The Disklavier cannot exceed sixteen simultaneous notes, but I found this
limitation to be more of a blessing than a curse. It provided a nice round number to guide
the compositions, a number that is handily divisible into four groups of four, or two
groups of eight. I also came to realize that from the listener's perspective, the difference
between sixteen simultaneous notes and eighty-eight simultaneous notes is not as great as
it might seem on paper.
4.2 The Sound of the Piano
Conlon Nancarrow never really liked the sound of the piano that much. He felt it
was, in some ways, inappropriate for his work and tried hard to make his instrument
sound more like a harpsichord. James Fei, after a few meetings discussing my piano
music, revealed that he did not actually like the sound of the piano either, mainly for its
weighty historical associations. I happen to like the sound of the Yamaha C7 Grand Piano
Disklavier very much, although I am also interested in finding ways to make it sound
unlike a piano, without resorting to the use of leather strips, metal screws, or ping pong
balls.
4.3 The Basic Shape
I prefer to start with something simple: a set of octaves, a repeating note, a steady
glissando, occasionally a very short melody, maybe an interval or two or a rhythmic
shape. I make everything else by repeating this "basic shape," transposing it, copying it,
rhythmically displacing it, and layering it. Every once in a while, I push something in or
out of place so that it sounds better, or different. This is a little bit like Arnold
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Schoenberg's notion of the “grundgestalt,”33 though I doubt he would have liked this
music very much.
4.4 The Harmonic Series
A string, pulled taut (as on a piano), has the natural tendency to vibrate at a rate
proportional to its length. It also has the tendency to vibrate at twice that rate, three times
that rate, and so on. Each successive "harmonic" will sound a little closer in pitch to the
one that preceded it, and will generally be a little quieter, with variations determined by
the physical material of the string, the material it is connected to, and the surrounding
acoustic space.
While I am interested in the acoustic principles of the harmonic series and often
take them into account when arranging notes, I tend to apply the idea in the way a toddler
might, one number at a time, counting in order. Perhaps even more important to my work
than any specific scientific or acoustic implication is the revelation that the series, at its
core, is nothing more than the natural numbers: 1, 2, 3, and so on. And yet, from the
simplest applications of this series to musical data (adding, subtracting, multiplying or
dividing), one can easily derive both astonishingly elegant complexity and
incomprehensible garbage.
4.5 Hand-made Algorithms
I have been told that my music is algorithmic, although I don't really think of it
that way. I don't use any math other than simple addition, subtraction, multiplication and
division. I copy something (often a repeating figure), paste it next to itself, and then
33 "Whatever happens in a piece of music is the endless reshaping of the basic shape... There is nothing in a piece of music but what comes from the theme, springs from it and can be traced back to it; to put it still more severely, nothing but the theme itself’ (Arnold Schoenberg, quoted in Michael J. Schiano, “Grundgestalt,” in New Grove Dictionary of Music and Musicians (Vol. 25), 2nd ed., Stanley Sadie, Vol. 25, (London: Macmillan Publishers Ltd., 2000).
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change it a little. Then I do it again and again, changing it by the same amount each time,
and listening all the while. If it doesn't sound good, I might just start over. Or I might
copy half of all the copies and put them somewhere else, then change that a little. Then
do that again and again (listening all the while). I might make something go backwards or
turn upside-down, each time listening to how it sounds. Sometimes, when I am away
from the piano, I get an idea for how to make a very interesting composition by doing a
slightly more complicated thing over and over, but only occasionally do these ideas turn
out to sound interesting. I avoid using equations, because I never want the music to get
too far away from my ear.
4.6 Time
I prefer to focus on simple temporal relationships, or at least closely related ones.
In other words, I don't want things to drift too far apart. I like to create tension between
the feeling of speeding up and the feeling of slowing down. For example, a single phrase
might consist of progressively longer notes (giving the impression of slowing down), and
that phrase could be repeated a number of times. Meanwhile, the overall tempo could
speed up. In cases like these, it is difficult for a listener to tell what is speeding up and
what is slowing down, but both directions can be sensed simultaneously from the same
material. Another example to try: start with a steady pulse, gradually allowing it to slow
down. When the pulse has slowed to half its original speed, start another pulse at double
the speed (equaling the speed of the first pulse at the beginning). This process could
continue for quite a while, making for an interesting effect. Similar processes occur in the
traditional music of Indonesia and James Tenney's Spectral Canon for Conlon
Nancarrow.
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4.7 Emergence
I don't so much want the listener to hear my compositions as I want them to hear
the sounds, patterns, textures, and forms that emerge from them, as a result of the
interactions between elements. If it is unclear whether these entities are forming in the
music itself or the mind of the listener, all the better.
The concept of emergence can be applied to simple ideas in tonal music, such as a
chord arising from multiple notes, or to aural phenomena such as acoustic beating and
difference tones. An example in the visual realm is the moiré pattern, exploited at length
in the Op Art of the 1960s and countless "psychedelic" videos. Moiré patterns can also be
observed in daily life, for example when light passes through folds in silk fabric, or in
nature, when the feathers of a parrot overlap. We tend to understand the world by making
connections between closely related things, but sometimes these attempts just makes us
more confused.
Often, as a result of the application of strict processes in my music, the visual
view of the notes resembles a moiré. I am especially excited if listening to the music
inspires a similar feeling. While I have no scientific explanation to prove it, I can be
fairly certain that other human beings, outfitted with similar perceptual apparati, will
experience something similar to what I experience when listening, depending on the type
and amount of cultural baggage that goes along with it.
4.8a Human Music, Living Music
Music composed by humans or listened to by humans is always, by definition,
human, but the "life" of music need not resemble human form, nor must it be "warm."
Cold-blooded animals are alive, as are trees. One might also say the planet itself is alive,
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even the cosmos. Why stop at a scientific definition of life when evaluating something as
non-scientific as music? The life of music depends on human life; nonetheless, it cannot
be sufficiently described in terms of its resemblance to humans or other known creatures.
With this statement, I do not mean to invalidate any resemblances (which can surely aid
in our appreciation and understanding of music), but to argue that the emergent life of the
work itself, the life that we can never adequately describe in words, is what paradoxically
confirms its identity as a "living" work of art.
Many people have argued that the "human element" is missing in automated
and/or electronic music not involving human performance, and that this is a bad thing.
Milton Babbitt had this to say in defense of electronic music without human performers:
Never has music been more human. It begins with a human composer who tries to realize his conception of the musical work in every sense. Except for the intervention of the speakers, the only limitations on the other side are those of the human perceptor.34
Babbitt is right in one sense, music without human performers provides a more direct
(but not necessarily better) way for a single composer to communicate with an audience
(that is, unless s/he assumes the dual role of composer and performer). With regard to the
human performer, I would argue that certain compositional approaches lend themselves
to interpretations by a sentient performer while other types simply do not. Both are
equally valid, and both are equally "human."
4.8b Living Music, Live Music
It is all too common that musicians attempt to bestow "life" upon their music by
finding a way to make it "live." We live in an age where most popular music is many
times removed from the classic, caveman's notion of live music, generated in real-time by
34 Milton Babbitt, live interview by Charles Amirkhanian, 1984, transcribed by the author. Original audio available at <http://archive.org/details/SOM_1984_11_15> (6 December 2010).
21
musicians. Perhaps it is time to admit that most of these efforts are just for show (and
there's nothing wrong with a good show).
Steve Reich has said that the life of his music originates in the "micro-variations"
introduced by human performers. While performers have certainly added life to his
music, I disagree that its life originates there. Admittedly, there are many cases where the
performance of music by humans causes a composer to rethink his or her approach —
indeed, reshaping the life of the music. There are also many cases where the life of music
is inexorably linked to human performance—for example, the African music that inspired
Steve Reich. In all cases, music “comes to life” when it is experienced by a human
listener, but the performer of the music need not be alive.
4.9 Electronic Music
My background is in electronic music. I started with synthesizers, drum machines,
turntables, and tape recorders, before pianos or even notes. Part of my approach to the
piano involves simulating certain common effects in electronic music such as the
crossfade, the echo, the loop, and the splice. It turns out this is not very difficult when
using a computer-based sequencer to compose.
Where there are aggregates of notes in my work, I treat the piano like a sound
designer might approach a synthesizer, meticulously shaping attacks, sustains, decays,
and velocities in non-real-time, and paying close attention to the resulting acoustic
interactions, so that the boundaries between notes might either dissolve or combine to
create the perception of something new. In the end, it strikes me that the difference
between acoustic and electronic sound may be smaller (and more complicated) than it
seems.
22
4.10 Immersion
Generally speaking, I don't want to create a situation in which the listener must
mentally sift through the notes, apart from his or her direct experience, in order to
appreciate the work (although she or he is welcome to do so). Nor do I want the listener
to relate what they hear to specific emotional events in their life or the life of the
composer (ultimately, this cannot be controlled, but it is worth making an effort). Rather
than spending extra time sifting through the musical information on an intellectual level
or looking for easily recognizable feelings of nostalgia (a type of immersion I prefer to
avoid), the listener should attempt to become immersed in the impressions that the sounds
(and the accompanying visual patterns) make on their senses.
4.11 The Visual
Often, the music I make generates striking visual patterns when viewed as a
"piano roll." I use the computer's piano roll like a canvas, manually moving chunks of
notes around on a two-dimensional plane. Seeing the notes arranged in this way (as
opposed to traditional Western notation) helps me understand the structures that they
combine to create. In some cases, these structures are also clearly visible on the piano
keys—always a pleasant surprise. Sometimes I have an idea that generates a beautiful
visual pattern on the piano roll, but when I send that pattern to the piano, it just sounds
like a bunch of notes. I save those ideas for later, but I don't let other people hear them.
4.12 The Concert
The idea of watching a piano play by itself on stage is still disconcerting to many,
even after all these years. Just a few years ago, Rex Lawson, pianola expert and personal
friend of Conlon Nancarrow, wrote:
23
It was clearly the memory of a lifetime to stand in Nancarrow's studio and marvel at the sounds emanating at high volume from the nearby upright piano, no doubt accompanied by a gleeful expression on the face of the composer. It is quite another matter to sit in serried ranks in a smart concert hall and listen to a piano with no-one sitting at the keyboard. Human audiences need human performers. For five minutes it is quite fun to see the keys going up and down on their own, but the excitement soon fades. Reproducing piano concerts need entertaining and careful presentation. 35
While I agree that careful presentation is essential, I tend to disagree with this general
sentiment.
For the premiere of Eight Studies, I took special care to craft an immersive
concert experience, removing extraneous sensory input in order to draw attention to the
abstract nature of the piano keyboard and its associated sound. By controlling the lighting
with a single spotlight and providing a video projection of the light reflected on the keys,
I was able to display the keyboard as a simple row of lines and dots (see Appendix B for
photo documentation). I organized the program order so that it would be diverse enough
to avoid fatigue, yet clever enough to illustrate a compositional thread. At the beginning
of the performance, I entered the stage to press the “play” button on the Disklavier, but
this was my only intrusion into an otherwise entirely mechanical performance. A “live”
performance of this kind involves plenty of real-time interaction, but the focus of such
interaction shifts from the actions of a human performer to the connection between the
instrument/object/performer and the perceptual faculties of the audience. To some extent,
the audience is forced to confront their own opinions concerning the role of the
composer, performer, and themselves in a concert setting like this.
Mechanical musical instruments are able to repeat their performances ad
infinitum, with very little variation, and without asking questions. This fact makes it easy
35 Rex Lawson, “Compositions for Pianola – Conlon Nancarrow” The Pianola Institute History Page, <http://www.pianola.org/history/history_nancarrow.cfm> (6 December 2010).
24
to adapt such performances to an installation setting, where the audience is allowed to
come and go at will. In some ways, the concert setting is similar; we are also allowed to
come and go at will, but it is generally assumed that we will stay and experience the
whole thing together. In that sense, Eight Studies benefits from a hint of benevolent
subjugation.
5. DESCRIPTIONSIdeally, the listener should be able to enjoy these works without a prior
understanding of the technical processes, technologies, or conceptual framework at play.
I hope the experience of listening will pique the listener's curiosity about these aspects
while creating a pleasurable confusion of the senses. While not a required precursor to
listening, the descriptions included here may enhance the understanding and appreciation
of the work.
The eight works presented here can be divided into four thematic classes, based
on approach and outcome. Regarding the application of transformational processes to the
musical material, the classes proceed from most to least strict. The level of strict process
is also reflected in the amount of technical versus non-technical language used in each
description. These classes do not constitute a pre-ordained strategy, but were formed only
in retrospect.
CLASS A: IDEALIZED SYMMETRICAL FORM [14, 4]
The highest level of symmetry and objective process is maintained, the final result
resembling an idealized mathematical form. Intuitive decisions are limited mainly to
high-level parameters. Gradual global tempo shifts are commonly employed.
25
CLASS B: CONSTRUCTED BINARY FORM [1, 2]
This form consists of two sections: an exposition and a development. In the exposition, a
basic, repeating shape is introduced and systematically layered, transposed, and
rhythmically offset against itself. After all layers have been introduced, the development
begins by incrementally shortening the length of each repeating shape, producing a
rhythmic phasing process. The exposition is generally handled in a strict manner, while
the development may be altered intuitively, eventually determining how the piece will
end. Both shifting and steady global tempos are commonly employed.
CLASS C: INTUITIVE LINEAR FORM [21, 99]
Intuitively generated elements are introduced linearly, above a steady pulse. No
systematic transformations occur with the exception of gradual increases or decreases in
velocity. Works of this type generally proceed at a steady, perceptible tempo.
CLASS D: INTUITIVE TRANSFORMATIONAL FORM [13, 29]
Systematic transformations of a basic, repeating shape are applied intuitively, sometimes
haphazardly. Suggestions of form and structure are led by the outcome of the
transformations. The composer listens to the materials and follows their lead, splitting,
splintering, and chiseling away. This form emphasizes intervals, scales, and rhythmic
development, and generally proceeds at a steady, perceptible tempo.
Note on order and numbering:
The order of works presented here is not chronological, but corresponds to the order in
which they were originally presented in concert and will be presented as an album on the
LINE record label36 in spring of 2011. The numbering system of the studies is 36 See www.12k.com/line/
26
chronological, based on the order in which the idea for the piece was first explored, but
not necessarily completed.
5.1 Study No. 14: Arch Study for the Highest Eight Notes
Tempo range: 5-750 BPMMeter: 1/1Duration: 4:54Class: A
Three simple limitations were imposed in order to generate the material of this
piece. The first was to use only the highest eight notes of the piano, the second was that
each note should pulse at a rate which is related sub-harmonically (whole number
fraction) to a "base" rate, and the third was that each pulse would not remain at a steady
velocity, but would be in a constant state of either "fading in" or "fading out" according
to a set of gradual velocity curves.
The first limitation was imposed in order to make use of the unique sonic qualities
of the highest notes. The short strings of the highest octave are less spectrally complex,
yet more confusing to the ear, than the rest of the strings. In isolation, they take on a
distinctly non-pianistic character, with a much higher ratio of hammer noise to tone.
Because of the relatively pure, almost sine-like character of their tonal components, they
are also more subject to interference from room acoustics.
The use of steady pulses and gradual velocity curves are meant to simultaneously
blur the perception of tempo and tone. The piece begins at the lowest possible velocity,
making hardly any sound but a slight noise from the hammers. The global tempo begins
at a rate so slow that it is nearly impossible to perceive rhythm, and gradually increases
until it nearly becomes a continuous texture. During the first third of the piece, the pulses
fade in and out systematically, overlapping to form perceivable polyrhythms. As the
27
global tempo speeds up, the slower pulses fade away, one by one, creating an interplay
between the global tempo and the relative tempos of the individual pulses. This effect,
also explored in Studies 1 and 4, can be likened to a Shepard tone37 in the realm of tempo.
The piece approaches its crescendo as the global increase in tempo accelerates and takes
over any relative perception of speed. At its peak, only two pulses are left - they are the
highest two notes as well as the slowest two pulses, whose rates are closest to each other
(at a ratio of 7/6). It is at this point that the two pulses briefly coincide, illustrating the
close perceptual connection between polyrhythm and phasing.
After the climax, the piece proceeds in exact retrograde. While the global tempo
ascends in a pseudo-logarithmic fashion during the first half, it descends at a nearly linear
rate. This particular curve was chosen in order to generate the smoothest possible feeling
of motion from beginning to end.
Figure 14-1. mm. 1-16
Seven different pulse rates are present in the piece, as follows:
One pulse every sixteenth note (F6)One pulse every two sixteenth notes (F#6)One pulse every three sixteenth notes (G6)One pulse every four sixteenth notes (G#6)
37 “A Shepard tone, named after Roger Shepard, is a sound consisting of a superposition of sine waves separated by octaves…This creates the auditory illusion of a tone that continually ascends or descends in pitch, yet which ultimately seems to get no higher or lower.” Wikipedia, <http://en.wikipedia.org/wiki/Shepard_tone> (6 December 2010).
28
One pulse every five sixteenth notes (A6)One pulse every six sixteenth notes (A#6)One pulse every seven sixteenth notes (B6)
The highest note, C7, begins pulsing at a rate of one pulse every sixteenth note
and incrementally slows down as it approaches the climax at m. 66, intersecting briefly
with B6 (the second-highest note). The B6 forms the spine of the piece, being the only
voice to follow a single, unbroken, and perfectly symmetrical crescendo and decrescendo,
peaking at the climax.
5.2 Study No. 4: Sixteen Diatonic Glissandi Moving at Harmonic Rates
Tempo range: 5-990 BPMMeter: 1/1Duration: 2:59Class: A
In this piece, sixteen diatonic glissandi (using only white keys) begin
simultaneously, starting at the top-most note (C8) and ending at the bottom-most note
(A0). The first glissando moves down at a rate of one note per measure (52 whole notes,
52 measures total), the second moves at a rate of two notes per measure (52 half notes, 26
measures total), the third at a rate of three notes per measure (52 "third" notes, 17 1/3
measures total), and so on, up to the sixteenth glissando. All glissandi are played legato,
so that each note is held until the following note sounds (important mainly for the visual
accompaniment). The entire process occurs simultaneously in retrograde inversion (and
played staccato), forming an inverted mirror image along the axis of the first glissando.
This axis forms because the first glissando, spanning the entire length of the piece, is its
own retrograde inversion.
The tempo of the piece begins at 5 beats per minute, rising gradually to 990 beats
per minute at the mid-point, then decreasing again to 5 beats per minute according to the
curve shown in Appendix A. The tempo curve was designed to bring attention to the
29
emergent patterns that form at the beginning and end of the piece (see Figure 4-1).
Figure 4-1. Final five measures (chromatic version depicted to enhance clarity)
Unlike the other studies in this series, Study No. 4 was conceived of in a flash and
immediately sketched out as a mathematical shape on paper. The idea was simply to start
sixteen identical processes in motion, moving at successive harmonic rates. Because the
piano keyboard is nothing more than a set of 88 buttons, the simplest process I could
imagine was a glissando, moving from the top of the keyboard down to the bottom.
The first incarnation of the piece used all 88 keys, but was later changed to use
only the white notes. This decision was made due to the fact that this piece, more than
any of the others, depends on the visual display of the keyboard as an accompaniment,
and the white keys allow for the emerging patterns to be displayed in a completely
symmetrical fashion. The downside of this decision is that the 'Shepard tone' effect
created by the overlapping cascades of notes is diminished, since the (Western) ear
naturally hears the notes as members of the major scale (though for some listeners, this
situation may be preferable).
30
The main inspiration for this piece came from the "Rhythmicon" instrument
(conceived of by Henry Cowell in the late 1920s and built by Leon Theremin in 1931)
and James Tenney’s Spectral Canon for Conlon Nancarrow (1974), itself inspired by the
Rhythmicon. Cowell explored the idea of correlating pitches with rhythms extensively in
his writings, and the Rhythmicon marks his first and only attempt to realize this idea in a
mechanical instrument. The Rhythmicon uses a 17-key piano-style interface which
can produce up to sixteen different rhythms—a periodic base rhythm on a selected fundamental pitch and fifteen progressively more rapid rhythms, each associated with one of the ascending notes of the fundamental pitch's overtone series. Like the overtone series itself, the rhythms follow an arithmetic progression, so that for every single beat of the fundamental, the first overtone (if played) beats twice, the second overtone beats three times, and so forth. Using the device's keyboard, each of the sixteen rhythms can be produced individually or in any combination. A seventeenth key permits optional syncopation. The instrument produces its percussion-like sound using a system, proposed by Cowell, that involves light being passed through radially indexed holes in a series of spinning 'cogwheel' discs before arriving at electric photoreceptors.38
In my opinion, James Tenney's 1974 piece constitutes the most sublime realization of
Cowell's original idea to date, making use of 24 pure harmonics on a custom-tuned piano
and adding a brilliant twist: the same ratios that connect pitch and rhythm are also applied
to a logarithmic arc of increasing and decreasing durations.
My own piece throws out the notion of pitch-rhythm correlation altogether,
instead focusing on the narrower application of harmonic ratios to repetitive pulses.
While directly correlating pitches and rhythms may provide worthwhile material for
organizing compositions, I do not believe the connection between them is inherently
perceptible (even if it contributes to a fantastic effect in Tenney's piece). While it is
certainly possible to smoothly transition between these two timescales (demonstrated
famously in Stockhausen's 1960 piece Kontakte), it is only at or near the boundary
38 Wikipedia <http://en.wikipedia.org/w/index.php?title=Rhythmicon&oldid=374970998> (6 December 2010).
31
between them that the perceptual connection is significant39.
5.3 Study No. 2 : An Approximate Series of Approximate Harmonic Series
Tempo range: 55-300 BPMMeter: 9/4Duration: 6:05Class: BNote: Sustain pedal continuously engaged
Figure 2-1. Basic shape (durations drawn for emphasis; continuous use of pedal makes held notes irrelevant)
39 For an in-depth discussion of this issue, the reader is directed to Curtis Roads' book Microsound.
32
Like Study No. 1, the basic shape of this study is a simple procession of
ascending and descending octaves (see Figure 2-1). The difference here is that the
durations increase incrementally throughout the measure, causing each self-contained
measure to feel as if it is slowing down, even as the global tempo speeds up (mm. 1-19).
As in Study No. 1, a systematic process of layering occurs: while the original shape
repeats, a transposed copy of the repeating shape is introduced at measure two, a third at
measure three, and so on, until sixteen overlapping layers have been created. However,
the entry point of each layer never occurs exactly at the beginning of the measure (with
the exception of the first), but is staggered in sixteenth note increments both before and
after the measure line. The increments cause an ascending set of sixteenth notes to
"grow" from each note of the original shape (see Fig 2-2).
33
Figure 2-2. “Sprouts” forming from the basic shape
Since the transpositions of the layers are added in the order of an approximate harmonic
series (octave, octave plus fifth, two octaves, two octaves plus major third, and so on),
each note of the basic shape can be thought of as "sprouting" its own harmonic series.
This process can be contrasted to the exposition section of Study No. 1 in which the
delayed entry points cause a systematic, statistical filling of horizontal space rather than a
"sprouting" from the notes of the basic shape.
As a result of this process of layering, chromatic clusters of notes form in the high
range of the piano. While technically varying from the harmonic series of the lowest note
(E0), these clusters nonetheless add to a natural sense of the overtone spectrum because
of their distance from the base note (since, as overtones get higher, they also get closer).
Put in more universal terms, any note in the highest range of the piano will naturally lie in
close proximity to the overtone series of a note in the lowest range. For this reason, the
piece feels “harmonic” throughout despite extensive chromaticism in the high ranges.
34
At the end of the exposition section, each layer is shortened by exactly the length
its entry was offset, then "looped" again. As a consequence of this process, the notes of
all sixteen layers line up in perfect vertical columns for exactly one repetition (Fig 2-3).
At this point, the global tempo is at its slowest (55 BPM), giving the listener time to
ponder this (quite literal) turn of events. In the measure that follows, the shape of the
exposition is reversed. The tempo ramps back up to a steady 100 BPM as the process
continues, and the shapes move gradually out of phase with one another. The discretely
identifiable cascades in the exposition now fold into slowly evolving, interlocking
patterns. It should be noted that in contrast to the strictness of Study No. 1, this study
utilizes much more intuitive "tinkering." After approximately ten measures of the
development, various pieces of the puzzle are copied, pasted, and carved away to
generate mini-recapitulations of the "turning point" at measure 20 in different ranges. The
piece ends with another subtle intrusion by the composer, hinting at the relative minor
key of c#.
35
Figure 2-3. “Turning point”
5.4 Study No. 13 : Echoes
Tempo: 100 BPM (fixed)Meter: 4/4Duration: 3:54Class: D
Where perfect or ideal symmetry defines Studies No. 4 and 14, this piece embeds
layers of imperfect symmetry. A resemblance may be seen to natural forms whose growth
is guided by ideal principles but whose final shape is inevitably distorted by the
complexity of its surrounding environment. While the rhythm is marked by an incessant
stream of sixteenth notes, the repetition of patterns at times gives the impression of being
suspended or frozen in time, drawing attention to subtle changes in the texture. This
phenomenon is especially noticeable during the middle section of the piece, where the
scalar and rhythmic clarity of the introduction (and conclusion) are intentionally blurred.
36
As in earlier studies, a “basic shape” is used to generate all of the material using
only a few transformational techniques, but the manner in which those techniques are
applied is less strict. Also, the basic shape is not made deliberately sterile, but instead
consists of an intuitively contoured melody in the whole-tone scale (see Figures 13-1 and
13-2). In the opening measures, the original melody is not heard alone, but is
immediately accompanied by seven superimposed copies of itself (see Figure 13-3).
These copies are transposed and offset in a manner similar to Study No. 2, resulting in the
sprouting of clear and regular arpeggios from each note of the original melody.
Figure 13-1. Basic shape (score)
Figure 13-2. Basic shape (piano roll)
37
Figure 13-3. Basic shape (layered)
It is from the material in these first four measures that the rest of the piece is generated,
using the same basic techniques of copying, pasting, transposing, and offsetting.
Additionally, inversions and retrograde inversions are applied on both a small and large
scale. In many cases, the transformations are applied iteratively, causing them to overlap.
For example, an inversion could be applied to a section of material which itself includes
one or more transitions between inverted and non-inverted, transposed and layered
material. As a result of the obsessive application of these processes, I began to hear an
echoing of phrases which I sought to amplify by applying smooth, linear velocity curves.
Using this simple technique, I was able to simulate the classic electronic effects of fading
in, fading out, and crossfading between clusters of repeating and/or related phrases.
Similar to Study No. 4, the overall shape of this piece is one of inverted
symmetry. That is, at the second half of the piece is an approximate retrograde inversion
of the first (see Appendix A). But the symmetry is never quite perfect. With each
transformation, it was necessary to reassess the material and its relationship to what came
before and after. Subtle alterations were made at every step of the way, influencing the
material that would then be used for further transformation
38
5.5 Study No. 21 : Bells
Tempo: 80 BPM (fixed)Meter: 1/1Duration: 5:24Class: CNote: Sustain pedal continuously engaged
A quiet, single, steady pulse at A4 divides this piece with machine precision like a
perforated line. A quiet, unsteady melody appears above, and another below, chiming
together in two-part counterpoint, with just enough space between the chimes to
contemplate each as if it were alone, as if each simultaneity was not a chord but a single
sound. Yet, inevitably, connections are made. Movement is perceived. Lines are drawn.
The notes get a little bit louder as time goes by, the decays overlap a little bit more,
interfering with each other just slightly. An octave is added above the pulse, then a fifth
above that, then another octave. But thanks to the patience and precision of the machine,
we are only able to perceive these changes in retrospect (unless we have our eyes open).
Repetition allows us to focus on details that would otherwise get swept away by the
music.
5.6 Study No. 1 : Octaves, Systematically Filled and Folded
Tempo: 40-990 BPMMeter: 6/8Duration: 5:57Class: B
39
Like Study No. 2, the “basic shape” of this study is a simple procession of
ascending and descending octaves. Here, the notes move at a regular rate of one note per
measure (see Figure 1-1). All additional material is generated by repeating, duplicating,
and layering the basic shape. Each new layer is offset and transposed systematically in
order to fill both the horizontal (rhythmic) and vertical (tonal/chromatic) spaces between
the notes of the first layer.
Figure 1-1. Basic shape
40
Figure 1-2. Basic shape, filled
After the introduction of 12 layers, the rhythmic pulse that began at one note per
measure has "filled in" to become a steady stream of sixteenth notes, and the ascending
and descending octaves become a perfectly filled chromatic scale. An interesting side
effect of this process is that the ascent of the original shape itself becomes a series of
stepped descents, while the descent of the original fills in to form a continuous line (see
Figure 1-2). As new layers are introduced and the rhythmic density increases, the global
tempo decreases. More simply stated: as the rhythm speeds up, the tempo slows down.
A direct correlation is established between the horizontal and vertical offsets, with
each measure (12 notes in 6/8) corresponding to one chromatic octave (12 tones). The
second layer divides the octaves of the basic shape into perfect halves both vertically (as
two tritones) and horizontally (as half notes). As a result, the original octave shape is
transformed into a series of ascending and descending tritones, pulsing at twice the rate
of the original. The third and fourth layers, in turn, divide the tritones in half, producing a
series of ascending and descending minor thirds, pulsing at four times the rate of the
41
original. Here the formula gets slightly trickier, since minor thirds cannot be divided in
half according to the chromatic scale. However, the introduction of layers proceeds in the
most statistically even fashion possible.
At the end of the exposition section, each layer is shortened by exactly the length
its entry was offset, then "looped" again. As a consequence of this process, the notes of
all 12 layers line up in perfect vertical columns for exactly one repetition (Fig 1-3, note
the similarity to Fig 2-3). At this point, the global tempo is at its slowest (40 BPM),
giving the listener time to ponder this (quite literal) turn of events. As the shortened
layers begin to repeat, the tempo ramps back up to 990 BPM, and the direction of the
original shape is reversed. Complex phasing relationships develop as the looping
continues, the lines of notes stretching and folding over each other to form something
akin to a moiré pattern.
42
The phasing process continues unaltered for 672 measures. During this time, the
global tempo drops down to 300 BPM, then back up to 990, but the change is hardly
perceivable by the listener, as the phasing patterns of notes now suggest dozens of
overlapping and ever-changing tempi. After 672 measures, several layers are selectively
removed, leaving behind the notes of a dominant seventh chord. For a moment, the
patterns sound "musical," perhaps even "bluesy," as our brains connect the familiar
harmonic content with the jagged, syncopated rhythms that exist only as a result of the
simplest mathematical combinations. As the tempo slows down further and the notes
begin to sustain, a few more layers are removed to reveal the original octave shape which
was there all along.
Figure 1-3. “Turning point”
5.7 Study No. 29 : Tentacles
Tempo: 110 BPM (fixed)Meter: 3/4Duration: 4:29Class: D
This piece resembles Study No. 13 in approach, using strict processes to start
with, but allowing (and helping) them to bend and fracture in response to their
43
environment. Whereas Study No. 13 is structured symmetrically, this piece follows an
obstructed linear path. One might imagine swirling pools of water forming behind rocks
in a stream, occasionally breaking free, merging with larger pools.
Again, the basic processes of copying, pasting, transposing, and offsetting are
central. However, this study does not utilize any inversion or retrograde transformations.
Instead, the large-scale form takes shape through an intuitively crafted process of
splitting, splintering, and chiseling of the material.
Figure 29-1. Structural overview + opening transformations
44
Figure 29-1 shows the process used to generate the first section of the piece
(which in turn is transformed to generate the remainder). This time, two distinct but
overlapping "seeds" are introduced during the first two measures. The four notes used are
Eb, Gb, Bb, and Db (Figures 29-2, 29-3, 29-4).
Figure 29-2. Seed 1
Figure 29-3. Seed 2
Figure 29-4. Seed 1+2
These notes, in addition to their obvious identity as black keys, are significant for
forming exactly one half of an octatonic scale (defined by a series of alternating half-
steps and whole steps). The exact same configuration of notes, moved a tritone up or
down (to A, C, E, and G), will complete the scale (note that the same rule holds true for
45
other four note combinations within the octatonic scale, as long as the group itself does
not include a tritone). When sounded together as a chord, the sonority of these notes
resembles either a minor seventh chord or a major chord with an added sixth (depending
on the inversion). As the piece progresses, these fairly stable sonorities blur against the
surrounding texture, which itself is formed by shifted copies of the same sonorities. A
struggle ensues between the vertical sonorities and the horizontal/diagonal texture, which
resembles a series of overlapping, ascending scalar patterns, whose frequent use of half
steps and whole steps again recalls the octatonic scale.
In the rhythmic domain, the two seeds alternate between half notes and quarter
notes, mimicking the alternating half steps and whole steps of the octatonic scale. The
second seed (Figure 29-3) contains within it a slight rhythmic irregularity: the high Bb
that begins the second measure is delayed by a sixteenth note. As the seed is layered, this
subtle shift is amplified.
The first section of the piece (mm. 1-60, sections A, A', A'') resembles a
sequential modulation, not moving towards a harmonic goal, but gradually spiraling,
swirling, breaking apart under its own weight. Each cycle of the "A" shape descends a
perfect fifth. At the moment the fourth cycle begins, the shape splits into two. For the rest
of the piece, there is a feeling that the same shape is repeating, yet it never returns in
exactly the same form. Instead, the tentacles that sprung up during the first section
differentiate themselves, occasionally grafting together with other tentacles or breaking
off completely. A contorted skeleton of a classical form appears, just barely, beneath the
bubbling activity, but before it comes into view, the layers melt away, one by one.
5.8 Study No. 99 : Strumming Machine
Tempo: 150 BPM (fixed)
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Meter: 4/4Duration: 12:32Class: C
A 12-note arpeggio, forming an evenly dispersed harmonic series, pulses at a rate
of ten notes per second, 600 notes per minute, overlapping with itself every four notes
(see Figure 99-1). It begins quietly, played staccato. Over the course of the piece, the
velocity increases very gradually, as does the depression of the pedal, transforming the
ultra-precise, grid-like formation into a swarm of sound. Notes are added to both expand
and cloud the harmony. Just as the ear and mind have become fully accustomed to this
state of being, forgetting the notes, forgetting the piano, several layers are peeled away to
reveal hidden formations.
During the performance of this piece, which is the longest and last in the concert
program, the lighting should be gradually reduced to complete darkness following
approximately the curve shown in Figure 99-3.
Figure 99-1. mm. 1-4
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Figure 99-2. mm. 318-324
Figure 99-3. Lighting fade (indicated in red). Complete darkness should be reached at m. 321 (8m30s).
The style of repetitive playing in Strumming Machine is influenced by
Charlemagne Palestine's work (hence the title, a reference to his 1974 piece Strumming
Music), but my approach here differs in two notable respects. First, whereas Palestine's
work is played by alternating between the two hands (starting with one note per hand and
gradually adding notes to create chords), the rhythm of this piece is created by a single,
overlapping arpeggio. Second, Palestine's “strumming” style requires a human performer
to feel the resonance of the piano strings and respond to them dynamically in order to
bring out clouds of overtones. In this piece, the precision of the machine is unflinching
and precise, yet the resulting sound inevitably becomes cloudy and unpredictable, simply
because the state of a vibrating string and its resulting sound can never be predicted with
complete accuracy, as long as it exists in the physical world.
6. CONCLUSIONMechanical musical instruments have existed for almost as long as musical
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instruments themselves. Yet, it is only in the last century that composers have taken
seriously the potential for such instruments to inspire new forms and approaches to music
making. At present, the influence of machines and automated processes on the
composition, performance, and reception of music is vast and undeniable. Long before
the proliferation of electronic and digital instruments, the pneumatic roll-operated player
piano played a seminal role in the complex and evolving relationship between music and
machines.
Eight Studies for Automatic Piano lives in between the colorful past and
unpredictable future of mechanical music, its possibilities and its limitations, its potential
to liberate and to control. Placed in an immersive concert setting, this work advocates for
an expansion of traditional notions of live performance and musical “life.” Each piece
makes use of simple, computer-aided compositional processes to test the limits of human
perception while relying on one of the most recognizable musical sounds in the Western
world: the piano. By adhering to a set of machine-dependent parameters, I hope to raise
questions about the relationship between nature, humanity, and mathematical precision.
As hard as any machine tries, it will never be able to draw a straight line. And if the
precision in this work seems inhuman, it is only to help us scrutinize our own humanity.
Building upon the practical, theoretical, and aesthetic contributions of Conlon
Nancarrow, Steve Reich, James Tenney, György Ligeti, and Charlemagne Palestine,
Eight Studies plants the seeds for an ongoing, focused and innovative approach to
composition and performance for automated piano. To the visionary composers listed
above, this work owes its gratitude: To Nancarrow for unraveling the notion of a single,
linear time into hundreds of jagged, jubilant threads. To Tenney for unraveling it again by
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weaving those very same threads back together in perfect, crystalline order. To Reich for
reassuring us that we are not crazy for fixating on an empty swing as it gradually comes
to rest (and if we are, it is a good kind of crazy). To Ligeti for demonstrating that
"mechanical" is not just about machines, but is a life-giving metaphor with limitless
aesthetic potential. To Palestine for hearing and feeling the piano as an extension of the
body, and for showing that it is possible to invent a new kind of piano music without
writing anything down on paper, or calling oneself a composer.
And finally, to machines and humans everywhere for their enduring,
unpredictable obedience.
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APPENDIX A : OVERVIEWSThe following four pages display visual overviews of each piece, using the computer’s virtual piano roll view. Each overview can be read according to the following key:
NUMBER
TITLE
TEMPO RANGEDURATIONCLASS
TEMPO CURVE (WHERE APPLICABLE)PIANO ROLL VIEW (NOTES)NOTE VELOCITIES
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APPENDIX B : PHOTOGRAPHSThe following photos were taken at the concert premiere of Eight Studies for Automatic Piano at Littlefield Concert Hall, Mills College, April 23rd, 2010.
Camera: Barton McGuire (contrast enhanced digitally)
Camera: Carson Whitley
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