commissioned by Chamber Music America, for the Mivos Quartet  (Josh Modney, Olivia de Prato, Victor Lowrie, Mariel Roberts)
first performance of the complete version: November 2, 2015, Roulette, Brooklyn, NY

string quartet and electronic sound

duration: 55'-65'

About the Piece

"Music is time made audible." - Klaus Lang

"The view of time in Buddhism is always very realistic. Specifically, time is always related with existence and existence is always related with momentary time. So in reality, the past and the future are not existent time; the present moment is the only existent time – the point at which existence and time come together. And also, time is always related with action here and now. Action can only be realized in time, yet it is also true that time can only be realized through action." - Gudo Nishijima

And then time is no longer an obstacle, but the means by which the possible is realized.” - Eliane Radigue



PANEL I ("Pure Duration")
PANEL II ("Harmony")
PANEL III ("Tempo")
PANEL IV ("Beating")
PANEL V ("Presence")


At its simplest, this piece is the exposition of a tuning. The quartet retunes to an elaborate scordatura derived from four very low fundamentals,
and the harmonic field generated from the intersection of these four fundamentals, their 16 open-string "partials," and the harmonic series ascending from each of these 16 strings ("partials of partials") serves as the sonic fabric, the "skin" of the piece.

Due to the choice of fundamentals [32.7Hz C, 36.7Hz D, 40Hz E quarter-flat, 60Hz B quarter-flat] several interesting things follow:


The pitch space derived from this tuning contains an abundance of intervals separated by less than 20Hz. Further, due to the scordatura these are idiomatically achievable (as combinations of open strings and harmonics, e.g.) and acoustically stable. In other words, I can write an interval for two of the players in this tuning that sustains a continuous and reliable 14Hz beating (as the interval between two open strings).

This allows for the deployment of precise beating speeds as musical structures (used as rhythms or to set tempi), and also for a more fluid conception of consonance and dissonance – as a spectrum of speeds and intensities of acoustic beating.

beating glyphs

"Schisma" Intervals

While "schisma" does have a precise technical sense in tuning theory, I use it hear in a more metaphorical way, as a kind of tectonic fissure between tuning grids.

In the "Schisma" sections that precede each of the first three panels, the players pass dyads back and forth. Each dyad is just-tuned and in-and-of-itself extemely consonant, but the interval between the two dyads is extremely narrow, generating dissonant friction and fast beating when they overlap and "touch."
[For example, the open D-strings are the Viola and two Violins are tuned to 280Hz, 294.3Hz, and 300Hz, respectively, offering available intervals/beatings of 6.7Hz (moderate and wobbly), 14.3Hz (fast and harsh), and 20Hz (buzzing, almost itself a difference tone).]


The use of 40 and 60Hz as fundamentals offers access to several acoustic and perceptual "formants" (unarbitrary frequencies of special resonance in a space). 

The cellist tunes the C-string down to B quarter-flat, sounding 60Hz. Playing a 60Hz pitch in any room with electrical lighting or idling appliances can produce an acoustic reinforcement akin to the "singing in the shower" effect, as 60Hz is the frequency at which voltage travels in the continental U.S.
It's also a pitch, though– the fundamental pitch of your refrigerator or flourescent lightbulbs or the power lines outside or LaMonte Young's music...

40Hz even more so aligns with the grain of the human auditory and perceptual system. It's an octave multiple of 20Hz, the threshold frequency which both divides the perception of pitch from that of rhythm, and, non-coincidentally, sets a hard limit for the speed of motor/muscular functions in the human body. It has also been proposed as a resonant frequency of certain brain structures, and the rate at which some electrical signals travel in the brain, particularly ones associated with "temporal binding." To put it bluntly, it's possible that 40Hz is the speed at which time moves in the brain
(see the nerdy "Bibliography" below), and that half of a 40Hz period is the smallest grain-size of neural time, a "quantum of consciousness." 


Another conceit of the piece is that the self-similarity of the material allows for it to be either extended in time (i.e. the movements follow each other sequentially, as a traditional concert piece) or remain more or less un-extended, in which case all of the material can be presented simultaneously as a "time-object."

The form again:


PANEL I ("Pure Duration")
PANEL II ("Harmony")
PANEL III ("Tempo")
PANEL IV ("Beating")
PANEL V ("Presence")

Within this form, three versions of the piece co-exist (separated by the asterisks). The sequential, linear, concert version of the piece begins with the first Schisma and proceeds through the end of Panel IV. At this point, the piece is functionally complete, and in the concert version must be shocked back to life by
a "Schreckensfanfare," a series of noise bursts that compress all of the previous 50 minutes of music into 400 milliseconds. This Beethovinian reboot supplants the sequential presentation of the first four panels with the simultaneous "time-object" of Panel V.

Panel V, one its own, is thus a competing and self-standing version of the piece. In Panel V, the material from the first four panels is collaged into two versions of a 45" ritornello/buffer, repeated in alternation against a gradually enveloping electronic drone composed of layers of time-stretched recordings of Panels I-IV, live processing of the quartet with an "infinite reverb" patch, and live improvisation by the electronics performers with up to 16 channels of granulated recordings of the piece.

In the album version, the first Schisma is preceded by a 1-minute hyper-compressed "pill" version of the piece, a seed in which it is possible to hear the entirety of the material that will unfold over the course of the subsequent hour. This, again, represents a functional and self-contained "version" of the piece that challenges the full concert-version for primacy (... kind of, anyway).

A final, yet-to-be-presented version of the piece exists as a multi-channel installation, diffusing the granulated recordings from Panel V throughout a concert/gallery space over an indefinite duration in a continuous, non-repeating fabric. (And again again, I consider this version more-or-less "equal" in some meaningful sense to the concert version of the piece.)


The theoretical underpinning for this piece was informed by a long period of research. While my pursuit of this "research" was more poetic, intuitive, and cherry-pick-y than rigorously scientific (and e.g. often done with bottle or joint in hand...), I imagine that many of the articles/ideas/ways of thinking that I came across in the course of it could be interesting for similarly minded musicians.

So, to that end:

Amacher, M. “Psychoacoustic Phenomena in Musical Composition: Some Features of a ‘Perceptual Geography’,” in Arcana III, New York, NY: Hips Road, 2008.

Castanet, P.A. (2000). Gérard Grisey and the Foliation of Time. Contemporary Music Review, Vol. 19, Part 3, p.29-40.

Castro-Alamancos, M. (2013). The motor cortex: a network tuned to 7-14 Hz. Frontiers in Neural Circuits, 7(21).

Clarke, E. (1987). Levels of structure in the organization of musical time. Contemporary Music Review, Vol. 2, p.211-238.

Edmonds, E.D.M. et al. (1981) The estimation of time as a function of positive, neutral or negative expectancies. Bull. Psychonomic Soc. 17, 41 259–260

Eihei Dogen (trans. Rev. Hubert Nearman, O.B.C.). Shobogenzo. Shasta Abbey Press, Mount Shasta, CA.

Droit-Volet, S. and Meck, W. (2007). How emotions colour our perception of time. TRENDS in Cognitive Sciences, Vol. 11 No. 12.

Farb N., Segal Z., Mayberg H., Bean J., McKeon D., Fatima Z., Anderson A. (2007). Attending to the present: mindfulness meditation reveals distinct neural modes of self-reference. SCAN 2, 313-322.

Grisey, G. (1987). Tempus ex Machina: A composer's reflections of musical time. Contemporary Music Review, Vol. 2, p. 239-275.

Harrison, Bryn (2007). Cyclical Structures and the Organisation of Time. University of Huddersfield.

Katagiri, D. Each Moment is the Universe. Boston: Shambala, 2008. 

D. T. Kemp, “Stimulated acoustic emissions from within the human auditory system,” J. Acoust. Soc. Am., vol. 64, no. 5, pp. 1386–1391, Nov. 1978.

G. Kendall, C. Haworth, and R. F. Cadiz, “Sound Synthesis with Auditory Distortion Products,” Computer Music Journal, vol. 38, no. 4, Winter 2014.

Kirk, J. (2010). Otoacoustic Emissions as a Compositional Tool. ICMC 2010, p.316-318.

Llinás R. and Ribary U. (1993). Coherent 40-Hz oscillation characterizes dream state in humans. Proc. Natl. Acad. Sci. USA, Vol. 90, pp. 2078-2081.

Llinás R. and Ribary U. (1994). Human oscillatory brain activity near 40 Hz coexists with cognitive temporal binding. Proc. Natl. Acad. Sci. USA, Vol. 91, pp. 11748-11751.

McAdams, S. (1989). Psychological constraints on form-bearing dimensions in music. Contemporary Music Review, Vol. 4, p. 181-198.

Oster G. (1973). Auditory Beats in the Brain. Scientific American, 1973, 229(4), 94-103.

Salt, A. and Kaltenbach, J. (2011). Infrasound from Wind Turbines Could Affect Humans. Bulletin of Science, Technology, and Society, 31(4) p.296-302.

Stockhausen, K. (1955). Structure and Experiential Time. Die Reihe, Vol. 2, p. 64-74.

Wittmann M., van Wassenhove V., Craig A.D., Paulus M. (2010). The neural substrates of subjective time dilation. Frontiers in Human Neuroscience, Vol. 4.

Wittmann M. (2009). The inner experience of time. Phil. Trans. R. Soc. B, 364, 1955-1967.

... and music by Peter Ablinger (in particular Weiss/Weisslich 22: Haydn, Mozart, Beethoven, Schubert, Bruckner, Mahler), Maryanne Amacher, Anthony Braxton,
Aldo Clementi (Madrigale), James Fei (Horizontal / Vertical), Morton Feldman, Gérard Grisey, Bryn Harrison (Surface Forms Repeating), Klaus Lang, Alvin Lucier, Giorgio Netti, Chris Otto (Violin Octet), Eliane Radigue, Wolfgang von Schweinitz, Karlheinz Stockhausen, and LaMonte Young.

... and film/TV by David Lynch and Eric Andre (esp. The Eric Andre Show Season Two Finale, which was the key that opened up a way to realize Panel V...).