Robert Willey- Conlon Nancarrow’s Study No. 37 for Player Piano

Conlon Nancarrow (1912 – 1997) was one of the most original composers of the twentieth century, devoting most of his composing to a series of dazzling Studies for player piano. About three quarters of the work employed canonic procedures in which lines of the music proceed independently in different simultaneous tempi. A series of electronic realizations were made for his Study No. 37 in order to add timbral variety and expose the work’s temporal dissonance.

Study No. 37

I first heard Nancarrow’s music on KPFA radio one day in the car. I had joined the program in the middle of one of his Studies and, not knowing that it was player piano music, had to pull over to the side of the road, imagining the physical effort necessary to play such a piece. The glissandi that were being played would turn a player’s hands into bloody stumps, sweeping up and down the keyboard at astonishing speed. Afterwards they announced that it was a piece by Conlon Nancarrow, a composer I had not heard of, so I started doing some research. One of things that caught my attention was the composer’s comment in an interview that he had been frustrated by the impossibility to synchronize two player pianos. I wrote to him and said that with MIDI (new at the time) it was possible to synchronize up to sixteen synthesizers, and that it would be possible to use a variety of timbres, instead of being limited to the sound of the Ampico reproducing piano. He wrote back and said that he was aware of advances in technology and were he younger he would use computers, but he was at a point in life where he knew very well how his system worked, and had more work planned out than he had time to complete as it was. He sent me a couple of volumes of his work and said I was welcome to try an electronic realization.

The short Study No. 14 from the volume Nancarrow sent as a test of software environment and musical value. The piece is one of the early studies, there are two voices separated by register playing the same material in different keys producing a bitonal effect. The tempi of the two voices is in the ratio of 4:5. A tape was made with two synthesizers and sent to him, to see if he was curious to hear any of the Studies with different timbres.  Nancarrow answered that when he had been composing Study No. 37 (in the late 1960’s) he’d wondered about timbral extensions. He described the piece as “long and complex” and enclosed a copy for me to consider. The work is a twelve-voice canon in twelve tempi, an idea Nancarrow got twenty years before while reading Henry Cowell’s New Musical Resources. Cowell described his idea of a scale of tempi derived from simplified overtone ratios approximating pitch intervals, and suggested that a player piano would be a good vehicle to realize such a method:

“Since our appreciation has been limited, for the most part, to the simplest rhythms, and since it is difficult to play accurately more complex ones, it is necessary to form rhythmic scales of the simplest possible ratios…we employ the simplest overtone ratios which can be found to approximate each interval…It would be interesting…to hear such rhythms cut on a player piano roll.” [1]

The twelve tempi are proportional to the frequencies of a chromatic scale. Nancarrow chose the tempo for the slowest member in the scale (150MM), and then worked the others out based on their relationship to the “fundamental”:
















187 ½


















262 ½



281 ¼

The two columns on the left are from Cowell,
the one on the right Nancarrow’s choice of scale.

Description of the canons in Study No. 37

Tempo and rhythm are by far the most important elements in Nancarrow’s works. Melody is simply a vehicle to fill out the time structures, as are chords formed out of simultaneous-sounding voices. “I use blocks of notes, but they’re usually not chords in the functional harmonic sense of the nineteenth century harmony.  For me, chords are just blocks of notes I can use to make a rhythm.”[2]  Study No. 37 is a series of twelve canons. Each of the twelve canons in the Study has a different combinations of characteristics. Some, like canon IV, diverge (start together and spread out). Some, like canon V, converge (start spread out and end together). The entrances for these two types are included in the table below, which shows the tempo number (from slowest to fastest following the scale of tempos suggested by Cowell) and line of the score (numbered from bottom to top in Nancarrow’s score). The score consists of twelve staves, with the lowest notes on the bottom, the highest on the top. Sometimes (i.e. canon IV) the fastest tempo is on the lowest line of the score, or it could be on the highest line (i.e. canon V). Nancarrow developed the idea of the voices entering at different tempi by arranging them in three groups of four speeding up or slowing down. For example, canon VIII has three sets of slowing down tempi: the first set of tempi numbers 12/9/6/3, followed by second set 11/8/5/2, and last 10/7/4/1. These are highlighed in the table with different colors. The listener then experiences three waves of entrances. This happens again in canon IX, except this time the first two sets (indicated in blue and red) 1/4/7/10 overlap with the second set 2/5/8/11.

canon IV

canon V
(p. 19)

canon VIII
(p. 48)
canon IX
(p. 57)
tempo line
1 12
2 11
3 10
4 9
5 8
6 7
7 6
8 5
9 4
10 3
11 2
12 1
tempo line
1 1
2 2
3 3
4 4
5 5
6 6
7 7
8 8
9 9
10 10
11 11
12 12
tempo line
12 6
9 2
6 8
3 4
11 10
8 12
5 7
2 9
10 3
7 11
4 7
1 1
tempo line
1 1
4 4
7 7
2 2
10 10
5 5
8 8
11 11
3 3
6 6
9 9
12 12

Four canons with variety of relationship of tempo to score line, and pattern in tempo of entrances.

Like the rest of Nancarrow’s work, there is a rich variety of effects obtained from the simple methods of strict imitation, and each canon contrasts with the one that comes before and after. Canons I and II are divergent–they start out together and spread out since some voices proceed slower than others. Nancarrow’s choice of slowly moving melodic material disguises the technique of canon. In canon I a series of descending fifths is produced and the listener perceives the opening as a series of downward rolled chords rather than a canon with twelve voices.

page 1 score


1st page of  Study No. 37.  The canon I starts with a rest.

This first page of the score is approximately the first quarter of the piano roll representation below, in which time goes along the horizontal axis and pitch rises along the vertical axis:

Canon I displayed graphically

The way the notes are perceived can be explained by Gestalt psychology principles of perception, which propose that we group things by proximity and similarity. When displayed graphically, the notes of the first canon can be seen two ways: as a series of five descending vertical patterns of twelve notes, or twelve horizontal layers of five notes.

The opening of Canon I
A descending vertical pattern resulting
from the first note in each of the voices
One of twelve
horizontal voices

While it is possible to see the twelve horizontal voices, each in a different tempo on its own staff, what we are drawn to perceptually are groups of descending notes created by the temporal proximity of notes. The opening descending group is the easiest to hear, and highlighted below with a red arrow. It gets the listener’s attention since the first note of the top voice (marked “1”) is closer in time/space to the second note (“2”) below it than it is to the next note of its own voice (which will be the twelfth note played). The proximity of the successive entrances vertically overwhelms the perception of the horizontal continuity of each voice of the canon.

The notes at the beginning are heard as descending arpeggiated chords (the red path)
rather than as horizontal lines (the blue path)

The clarity of the groups gradually disolves as their entrances overlap more. Order evolving to disorder, and the reverse condition of disorder moving towards order were used by Nancarrow to achieve the same variety and development as others have done with melodic and harmonic tension and release. Nancarrow’s music takes such a non-traditional approach to composition as to require new methods of analysis, for example, looking at time and tempo as organizing principles of greater importance than pitch.

It is not until the Study is experienced in a polytimbral arrangement that it becomes possible to hear the continuity of lines in the opening canon. Keying the voices with contrasting timbres or colors makes it possible to recognize the continuity of voices. With this treatment it becomes possible to pay attention to the top voice, with the notes now shown in red (played by a flute, for example).  The second line in blue would be played by a different instrument (i.e. clarinet). The similarity of color between the notes of each voice of the canon weakens the perceptual grouping of notes resulting from proximity. When played on the player piano all canonic voices are realized with the same timbre, and when graphed appear all in black. In the synthesizer realization each line is played with a different timbre, and graphed with a different color:

Canon I with voices keyed by color, increasing perception of horizontal lines.
Now the horizontal lines stand out.

In canon V (pp. 19-33) it is easier to hear the imitation, since the note values are shorter relative to the tempo and the entrances further apart. The first voice (at MM 150) has time to establish itself on the bottom before the second voice (at MM 160 5/7) enters on the voice above it. Besides proximity and similarity, Gestalt psychology suggests that grouping can also occur based on common direction or comon destiny, and these attributes would seem to apply to the intervals and rhythm of a melody played by a canon’s melodic voice. If the theme is recognizable (i.e. “catchy”) and given a chance to establish itself before the next voice enters, the the listener may understand that imitation is being used.

Beginning of canon V
The first voice has time to establish itself before the second voice enters.

When played on the player piano this eventually becomes a jumbled sound mass as the later voices make stretto entrances. Electronic realization provides opportunities for a range of possible clarities. Adding either a spatial or timbral identity to a voice increases the listener’s ability to follow it over the course of the canon; doing both provides the greatest clarity. In the following four examples, we hear the twelve voices of the canon becoming increasingly clear.

  1. monotimbral (piano) with all the notes positioned together in the center of the stereo field
  2. monotimbral with the twelve pianos spread across the stereo field
  3. multitimbral with all voices in the center
  4. multitimbral with voices spread out

Later voices do not have the same space in which to enter and overlap each other.  There are a couple of dynamic shifts in this canon when all the voices change level simultaneously.  For example, when the next to last voice enters on the top there is a sudden jump in all the parts to a ff dynamic:

 p. 28 score
The last two voices enter in a jumbled sound mass, with a jump to ff in all voices.


Timbral considerations

Nancarrow had the hammers of his reproducing piano hardened in order to emphasize the attack of each note, making the counterpoint more apparent. His explorations with a wide range of novel techniques were all sounded with the same brittle tone. The goal of the multitimbral synthesizer realizations was to make the individual voices as distinct as possible, but in the process it was possible to experiment with orchestration and hear the piece played with a richer sound. Velocity-sensitive Yamaha FM synthesizers (DX7 family) of the day were used for the top eleven voices, and a Sequential Circuits samplers piano patch was used for the bottom voice.  Pairs of timbrally-similar instruments (i.e. “honky piano” and piano, xylophone and cowbell) were separated in the stereo field. Those that sustained well (i.e. “synthetic brass” and “brass chime”) were separated the most in order to avoid muddying the texture. It was assumed that the multitimbral and spatial treatment would make it easier to perceive the canons. The question was to find out if the effect would be desirable.


Spatial considerations

Nancarrow wrote most of his works for a single reproducing piano, so in addition to the realizations of his canons being monotimbral, they were also sounded from a single, fixed position.  Spatial distribution of the individual lines was used in the synthesizer realization to heighten the perception of individual voices. This, combined with the multitimbral treatment, made the individual lines quite apparent. The synthesizers used in the first realizations were recorded and played back in two- and four-channel versions, allowing the different tempi and their associated timbres to be spread out in front of, or around, the listener. Two versions were made of each: one with the first and last canons played by all synthesizers (by switching MIDI omni on for them) and the remaining ten canons with one synthesizer per line of the score (switching omni off), and a second version was made with all synthesizers playing all voices throughout the entire piece (leavning omni on). The contrast of the first version accentuated the arch structure of the piece and heightened the spatial effect. The second version created a fat composite sound that enveloped the listener.

In the stereo versions the synthesizers were panned from left to right based on how the score was laid out: the lowest line of the score on the left, ranging to the highest on the right, as if the listener is in front of the piano with the bass on the left and treble on the right. This created an wider stereo spread than what is hear with either live or recorded acoustic performances.

In the stereo version the lowest voice is on the left, the highest on the right.  

In the four-channel version the tempos are arranged clockwise around the listener. As fewer channels shared the same position between each pair of speakers, more discrete positioning of voices occurred.

In the quad version the voices are equally spaced,
the listener can face any direction.


Synthesizer realization

The synthesizer realizations were done in 1986 while working as a research assistant at the Computer Audio Research Laboratory at the University of California, San Diego, where Gareth Loy had developed Player, a convenient software language for specifying music data representations, controlling hardware, and developing compositional algorithms. Using a computer to control twelve synthesizer modules not only allowed for independence of voices caused by timbral variety and spatial separation, but also simplified the specification of the pitches. Nancarrow used strips of paper scaled to different tempi in order to locate the position of holes to be punched on his player piano rolls, which were then done one at a time, using a device he had built in order to allow for temporal experimentation. Some of his studies took months to punch. It tooks months for Nancarrow to measuring and punch out the notes of complex studies by hand, and his punching arm was as a result more muscular than the other. Because Nancarrow used strict imitation in the canons the conversion of the score to MIDI data went much quicker. Using computer programs to read the first voice in each canon and then generate the other eleven voices went very quickly. Durations and pitch values were for each of the twelve canons were entered into text files which were then read by a Player program in order to generate MIDI data. A second file told Player the tempo, MIDI channel, and transposition for each voice. The amount of data input to the system was quite small, and subsequent automatic generation of the parts was instantaneous. The following script generated the first canon:

study 281.25 1  canonI  0
study 262.50 2  canonI -7
study 250.00 3  canonI -14
study 240.00 4  canonI -21
study 225.00 5  canonI -28
study 210.00 6  canonI -35
study 200.00 7  canonI -42
study 187.50 8  canonI -49
study 180.00 9  canonI -56
study 168.80 10 canonI -63
study 160.71 11 canonI -70
study 150.00 12 canonI -77
Script for Canon I
There are only a few points where the voices deviate from strict imitation and the notes are modified or the dynamics change. For example, the last whole note of canon I is doubled, allowing it to hang over for the beginning of canon II. While Nancarrow’s reproducing pianos were capable of more sophisticated pedaling and dynamic gradations than regular player pianos, he did not seem interested in taking advantage of effects they would make possible. With the exception of a few accents, each voice usually plays with the same dynamic throughout. Only Canon V departs from the consistency of dynamics: as shown before there are several points at which all voices jump up or down to a new dynamic level together.


Graphic overview

The organization of the piece into a series of canons becomes apparent when seen in the graphic overview, with some canons more easily perceived than others. Notes in red are at the fastest tempo and are usually at the top. Sometimes the relationship is inverted, as in the fourth canon, where the notes in fastest notes are on the bottom.  Usually the layout is continuous, with each strata one tempo faster or slower than its neighbor, so the order remains the same: red, light blue, green, blues, black, grey, etc.


Meeting the master

Conlon Nancarrow, John Cage, and Roger Reynolds
Photo by Marc L. Lieberman

Nancarrow made one of his first visits from Mexico back to the United States to participate in the University of California, San Diego’s Pacific Rim Festival.  I played my two versions for him, Gareth Loy, and Roger Reynolds at the Center for Music Experiment. After hearing the first version Nancarrow said that it was the first time that his music had been improved upon over the original. The second version kept all the synthesizers playing all twelve parts throughout the whole piece (leaving omni on mode throughout). He said he preferred it over the first version. Maybe it was just a bigger sound, and more like what he was used to, with the play between clarity and confusion of voices that he was after when he composed it. The second version is that it had a very full sound, with notes having a strong attack, caused by those synthesizer channels with percussive onsets. At the same time it also has more power than the reproducing pianos he is used to, thanks to the synthesizer channels with high sustain levels such as the brass patches.  Having the twelve synthesizers arranged quadraphonically also surrounds the listener in a way that a single piano does not. James Tenney referes to the “resultant” in parts of Nancarrow’s work, an important textural phenomenon created by a fusion of two or more rhythmically independent layers or voices. Kyle Gann puts this Study in a group with what he describes as “sound-mass” canons, in which canonic imitation is not the point, but rather a way to produce a multidimensional texture. While the first, more defined synthesizer version made it easier to follow the lines, it seems that it is not always necessary, or perhaps, even desirable. I decided to play the first version in concerts since it is the most different from the player piano version. Rick Bidlack, another graduate student at UC San Diego, played his synthesizer version of Nancarrow’s Study No. 21 (Canon X) on the same programs.

Nancarrow wrote the music in a monotimbral environment and at times the individual lines in different tempo proportions can be followed, when he meant them to be clear. The listener’s emerging and submerging of awareness of his technique of a multi-tempi canon seems to be part of the mystery and allure this and other of his works. Over the course of centuries composers have held listeners’ attention by the finding the right balance between dissonance and consonance, tension and release, unpredictability and predictability. Nancarrow has developed another dimension in which to work. He used canons in order to help focus attention on temporal aspects. Depending on the how long canons are, how fast the tempi are, how much overlap there are in voices, how close together they are in register, and what sort of melodic material is used (length of notes, number of rests, range within which the voice exists), the canonic technique can be exposed or disguised.

I asked him if he liked the variety of timbres, the stereo/quad fields in which the synthesizers were placed, and the reverb that was added. He said that was fine. When asked how he realizes legato when he punches, whether he makes the notes longer to create an overla, he said “only when the music calls for it.” I asked how he composes canons, hoping there was some trick he could share. He said that one simply starts writing the first voice and then sees how it combines with the second, and then so on.


Change of environment

Over time the synthezer patches used have become dated and surround sound distribution more standardized. In 2005, eighteen years after the original work, the MIDI stream had to be recreated since its software and hardware environment was no longer available. In order to take advantage of new hardware (more powerful personal computers, standardized DVD surround sound delivery), software (recording and software synthesizers), and to allow for video display, a new version was begun, using a similar approach using pairs of text files but without the help of Player. The audio examples in this paper are GM MIDI clips for web delivery, not the synthesizer voices that would be played for the entire piece in a recording or concert.

In the new version the line of the score determines the output’s position. In a DVD surround sound setup, the top line (12) with the highest pitches of the score is heard from the side right speaker, with the rest of the eleven score lines spaced around an arc, ending with the bass of the bottom line (1) from the side left speaker. The distribution is less evenly spaced because of the suggested arrangement of home theatre systems, with the front speakers theoretically positioned closer together, and on the sides (where there is less awarness of position) further apart. As described before, at times (like the canon I) voices’ entrances proceed consecutively in order of tempo around the listener resulting in a smooth progression from one side of the space to the other. In other canons (i.e. the eighth) the voices skip members of the series and the entrances jump from one side to the other.  This spatial treatment results from the organization of the score.

In the 5.1 surround version the listener faces front
and will evenutally have something to watch

In this version the choice of timbre for a voice depends on its tempo. The timbres follow the tempi as they move around the space. Twelve synthesizer timbres (in Reason) were assigned to the twelve tempi according to the speed of the patches’ attacks. Sounds that evolve gradually are used for voices at slower tempi, since there is time for the notes to evolve and be heard; whereas the faster voices were given more percussive sounds that speak quickly. The lines of the score, arranged by register, are fixed in space. When the tempo changes on a score line, the timbre changes accordingly.


It is up to the listener to decide whether a multitimbral is preferable to a monotimbral version. Even if the monotimbral version is decided upon, it is still instructive to listen to the multitimbral version in order to understand the work’s construction, made possible by the perception of the continuity of each line. Nancarrow designed the piece for a monotimbral instrument, and I believe chose when to make the continuity of line clear, when to hide it in a resultant sound mass, and to control the rate of change from one state to another.

The opportunity to witness the performance of the rolls in person and in close proximity, as Nancarrow did, is not available to us. There is no substitute for the drama and acoustic intimacy, where the power of the music could probably be best experienced. We have to depend on recordings since we cannot experience the pieces “live”. It seems that the greatest benefit of elecronic realization is the variety of timbres it makes possible, resulting in sounds that are spectrally richer and better suited to recording and playback than those of the player piano.


[1] Henry Cowell, New Musical Resources (New York: Alfred A. Knopf, 1930), 98-104.

[2] Roger Reynolds, “Conlon Nancarrow: Interviews in Mexico City and San Francisco”, American Music, vol. 2, no. 2, 5.



Thanks to Roger Reynolds (for bringing Nancarrow to San Diego), Gareth Loy (for use of, and help with his Player software), and F. Richard Moore (director of the Center for Music Experiment, University of California San Diego).


Amirkhanian, Charles, “Interview with Composer Conlon Nancarrow”, in Conlon Nancarrow: Selected Studies for Player Piano, ed. Peter Garland. Berkeley: Soundings Press, 1977: 7-24.

Bidlack, Rick, “Canonic Structure in Conlon Nancarrow’s Study No. 37 For Player Piano”, University of California, San Diego, 1988.  Unpublished.

Carlsen, Philip, “The Player-Piano Music of Conlon Nancarrow: An Analysis of Selected Studies”, Brooklyn, Institute for Studies in American Music, Conservatory of Music, Brooklyn College of the City University of New York, 1988.

Cowell, Henry, New Musical Resources, New York, Alfred A. Knopf, 1930.

Gann, Kyle, The Music of Conlon Nancarrow, Cambridge University Press, 1995.

Garland, Peter, Selected Studies for Player Piano, Soundings Press, 1997.

Nancarrow, Conlon: Conlon Nancarrow: Collected Studies for Player Piano, Santa Fe: Soundings Press.  Study No. 37 (1982).

Thomas, Margaret, “Conlon Nancarrow’s ‘Temporal Dissonance”: Rhythmic and Textural Stratification in the Studies for Player Piano”, Ph.D. dissertation, Yale University, 1996.

Thomas, Margaret, “Nancarrow’s Canons: Projections of Temporal and Formal Structures”, Perspectives of New Music, Summer, 2000, 106-133.

Reynolds, Roger, “Conlon Nancarrow: Interviews in Mexico City and San Francisco”, American Music, vol. 2, no. 2 (Summer 1984): 1-24.

Wertheimer, Max, “Untersuchungen zur Lehre von der Gestalt II”, in Psycologische Forschung, 4, 301-350. Translation published in Ellis, W. (1938) in A source book of Gestalt psychology (pp. 71-88). London: Routledge & Kegan Paul.

Categorie:K20.01- Musica e Matematica - Music and Mathematics, S03- Il Novecento musicale degli irregolari e degli isolati, S03- Musica del secolo breve- Avant Garde



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