My music emerges from the following axioms and techniques.




Possible musical forms are as limitless as the exterior forms of crystals.

- Varèse, The Liberation of Sound


As have many musicians before me, I compose as a way of conducting experimental research. In my case not uniquely, such research constitutes exploration of the following realms:


  1. The epistemology of musical time, with dual emphases on temporal perception via musical aesthesis and the apprehension of musical form through temporal unfurling;

  2. The phenomenology of musical form, with particular emphases on formal principles and compositional techniques concatenated with the practice of modular counterpoint; and

  3. A dialectic between compositional technique and material technology by means of which processes and structures are developed immanently from concrete affordances of sound-making devices.




For me, the process of composing begins with the intentional act of listening for yet-to-be- actualized potential in pre-given sound. As a matter of principle, I take each and every such sound to be possessed a priori of two qualities - those are, morphological integrity and structural momentum. Having thus conceived of its materials, the craft of composition becomes the task of educing such qualities as they inhere in pre-given sound through recombinant juxtaposition with analogously-conceived aesthetic phenomena.

An illuminative precedent for this approach to composition is the 20th-century French tradition of musique concrète. Distinctive of it is a compositional worldview in which sounds are conceived of first and foremost as concrete phenomena to be worked on directly by the composer. To throw its distinctness into the starkest possible relief, a comparison of this musical worldview with that of the contemporaneous German tradition of elektronische Musik is useful. Unlike composers of elektronische Musik, who focused largely on the synthesis of electronic sounds de novo, those of musique concrète adapted audio recordings indexing a pre-given world of sound as the points of departure for their works.




To continue with this historical heuristic: Whereas makers of elektronische Musik may be said to have prioritized the abstract over the concrete, insofar as they focused on synthesizing artificial sounds, they also, to their credit, emphasized the unique constructive possibilities afforded by the technologies constitutive of electronic music as fundamental to compositional practice. By contrast, composers of musique concrète largely conceived of such technologies solely as a means to the end of fixing sound onto a workable medium. In so doing, one could argue that they gave inadequate consideration to the aforementioned possibilities afforded by concrete audio technologies constitutive of the compositional process.

Heeding the lessons of these forebears, I ground my music directly in the morphological qualities immanent to sounds I adapt as the bases for new compositions as well as in concrete features of the technological devices I employ in the construction thereof. Rather than naturalize the audio technologies that condition the practice of electro-acoustic music, then, I foreground them by developing both techniques of composition and principles of form directly from their unique affordances.

A historically-informed dialectic between compositional technique and material technology thus animates my approach to composition at its core. In characterizing this dialectic, etymology is a useful tool. The Greek equivalent of the Latin term ars from which latter we get our words "art" and "artifice" - that is, techne - emblematizes, by serving as a common etymon, the type of relationship between "technique" and "technology" here intended. Mindful of the original conceptual unity of these two terms, then, I place the two ostensibly distinct realms of the compositional process they are conventionally held to demarcate in dialogue with one another to reveal their true nature as dual extensions of one and the same activity.




That said, most fundamental to my approach to composition is a particular understanding of the ontology of musical sound, one correlative to an equally fundamental aesthetic axiom. To formulate these briefly: Music is not, contrary to the music theorist, information arranged statically, but rather, pace the physicist, energy moving dynamically. The aesthetic axiom that follows from this ontological fact runs as follows: To grasp the true nature of music, we must, as makers of and listeners to it, transcend our habitual modes of aesthetic perception, modes that have, over time, come to present themselves as prerequisite to experiencing music as such.

Consider, for example, the paradoxical identity of pitch and pulse - elemental substrates, respectively, of harmony and rhythm. Although perceived as distinct by the mind’s ear, it is evident from an ontological perspective that there is no essential difference between a single pitch, resulting from the regular oscillation of a sound wave, and discrete pulses, resulting from the relatively slower oscillation of exactly the same type of sound wave. Thus the categorization of sound waves as discrete pulses as opposed to a discrete pitch depends not on the objective properties of the phenomenon perceived but rather on the faculties of the perceiving subject.

For our purposes, the point is this: Induced movement between such ontological modes may be leveraged in the compositional process to enable the apprehension of a distinctly temporal type of "phase transition" - itself characterized by a sudden supersession of structural accretions by a singular morphological transformation - that serves as the hallmark of all process-based music.




The following rule may be set up as a primary law in the evolution of music: From a certain form A, one arrives at a new form B, by varying A gradually until finally it is so far varied that it becomes the new form B. From this viewpoint, one may, with a certain justification, regard all music […] as an unending chain of variations, all naturally standing in more or less obvious relation to the theme, but all having one thing in common, namely, the visible or invisible, actual or ideal cantus firmus, to which they are linked and upon which they continue to build.

- Jeppesen, Counterpoint: The Polyphonic Vocal Style of the Sixteenth Century


The Latin phrase "cantus firmus" that figures in the quotation above may be translated as "fixed voice-part." Here a question arises: What is the distinctive feature of a cantus firmus? It is not, as might be imagined in light of its fundamental importance to European polyphony composed from 1200 to 1700, the type of "voice-part" in question, nor the manner by which it is fixed. It is, rather simply, hierarchical conceptual fundamentality - i.e. "fixedness" - that makes a cantus firmus a cantus firmus. Otherwise put, a cantus firmus is what it is insofar as it serves as architectonic structural foundation for subsequent elaboration. The molar edifice of contrapuntal music built piecemeal by European musicians of the Medieval, Renaissance and Baroque eras may thus be, as it is above, most fittingly thought of as the accretion of elaborative structures, all of which may be construed in turn as transformations of - and thus derivable from - a single originary source.




Western musicians habitually distinguish between two principal textures - the first, polyphony, conceived as the result of weaving together independent musical entities themselves typically understood as “linear” successions of pitched sonorities known as "melodies;" and the second, homophony, in which an abstract schematized system governing simultaneous relationships of pitch serves as the structural framework for a melody of hierarchical focus. In homophonically organized music, structural coherence derives from melodic participation in, and fulfillment of, patterns of pitch simultaneities known as "harmonic progressions." By contrast, in polyphonic music, such coherence is achieved via a process called "counterpoint," in which multiple voice-parts are integrated into an aesthetic whole through the coordination of momentum immanent to their modular components all while at once maintaining said voice-parts’ morphological integrity.

Thus, the essence of polyphony resides not, as Western musicians would have it, in the degree of autonomy exhibited by individual pitched sonorities from some schematized harmonic logic. Rather, it resides solely in an intentional attitude adopted by the composer toward the nature of the musical material at hand. On the one hand, such an attitude is exemplified by processes that adapt pre-given sonic structures - be they of abstractly notated melodies or concretely recorded sounds - as the bases for subsequent elaboration. On the other hand, it is further epitomized by a correlative preservation of each voice-part as the index of a unique sonic source.



To rephrase the preceding point: The two principal textures of Western music have been traditionally defined according to the ways in which pitch-based ratios and proportions are coordinated among their elemental components, postulated a priori as voice-parts. By contrast, it is not the differentiability of compositional structures perceived through the analytic parameter of pitch that I take as prerequisite to the distinctness of voice-parts, but rather timbre. That is to say, rather than construe "voice-parthood" as an abstract quality emergent a posteriori from evaluation of differences inherent in pitch-based structures instantiated by entities merely asserted as distinct, I take it to be determined first, foremost and always by its concrete sonic origins.

In my music, then, timbre functions an index of haecceity. What is haecceity? In short, haecceity is a heuristic device devised by Medieval Scottish philosopher Duns Scotus (c1266-1308) to refute the then-influential doctrine of nominalism, which holds universals not to exist apart from their particular instantiations. Haecceity was accordingly intended by Scotus to serve as a bridge mediating between two extremes - i.e. the particular and the universal - and to demonstrate them as compatible rather than mutually exclusive. Specifically, rather than to claim, for instance, that universals are only ex post facto abstractions from the world of phenomena, or, by contrast, that only universals are truly real and particulars only imperfect instantiations thereof, Scotus devised haecceity in order to validate the participation of universals in particular phenomena while at the same time appreciating that which makes any given phenomenon uniquely and particularly itself.

In ascertaining the nature of haecceity as it pertains to the musical relationship between timbre and the voice-part just articulated, it is useful to consider differences obtaining between analog and digital sound production, differences which may be aligned with ontological poles of discrete and continuous value. That is to say - the continuous transduction of molecular fluctuations in air pressure into electromagnetic waves, such as takes place, for example, during the recording of a sound to magnetic tape, is a process qualitatively distinct from the translation of such fluctuations into discrete units of binary code. One consequence, among many, of this distinction is that every piece of analog technology imparts a unique timbral quality to the sounds passed therethrough. By contrast, all digital devices impart one and the same timbre to all sounds so processed - i.e., they impart no timbre at all.




Further axiomatic principles govern my approach to composition. For instance, the desideratum traditionally characteristic of counterpoint - i.e. that no one voice-part gain undue emphasis over another - necessitates that certain compositional measurements be made according to the serial arrangement of structural events. When taken in conjunction with the aforementioned stipulation that the modular components of individual voice-parts must be at all times integrally maintained, this desideratum further stipulates that all transformations brought about by such measurements assume the more specific forms of permutational techniques of iterative variation - i.e. diminution, augmentation, and retrograde.

First implemented in Europe by composers of polyphonic vocal music during the Middle Ages, these three techniques were eventually to migrate across performance contexts to become of particular value to Baroque composers of keyboard music. Following an extended period of desuetude thereafter, these techniques became once again vital to the music of twelve-tone composers of the 20th century. The vast timespans separating their heydays recommends these techniques to the composer uniquely, though not more so than the security of their foundation in the nature of musical material. To understand the fundamental importance of these techniques to my music, then, it is useful to consider their conceptual relationship to that of melodic inversion.

Melodic inversion is implemented around an axis of frequency effectuated by a factor of transformation - e.g. A440 : A880 :: A440 : A220. We ask: Is there a qualitative difference between the solutions to the equations 440(x) = 880 and 220(x) = 440? No - there could only ever be a quantitative one. Pursuing this a bit further, we might next ask: To the mind's ear, is there a qualitative difference between the perception of a "low" pitch as opposed to a "high" one? Indeed: The "higher" the frequency, the more "tension" perceived - i.e. the greater the sonic energy conveyed. Considered in this manner, it is clear that the logic of melodic inversion relies on a reduction of pitch to number, one that essentializes pitch to its quantitative dimension.

Inversion is thus exemplary of a type of compositional transformation that proceeds from the insight that the ultimate distinctive feature of musical sound qua sound is its rootedness in ratios and periodicities reducible to abstract numerical relationships. This sets inversion subtly apart from the aforementioned techniques of augmentation, diminution, and retrograde, all of which proceed from a dimension immanent to the perception of sound as such. In conceiving of such difference, a heuristic developed from the compositional affordances of material technologies is useful. Compare to inversion the technique of retrograde, or the sounding of a series of entities in its backward permutation. What makes the technique of retrograde more immanent to sound as such than inversion? Retrograde also happens around an axis; however, in this case crucially, such an axis is a qualitatively experiential moment in time, rather than a quantitative abstraction therefrom. There remains a paradox: Time as we perceive it cannot run backwards. And yet, if a sequence of sonic events is recorded to, for instance, magnetic tape, it may then be retrograded (i.e. by flipping the cassette) with the identity of said sequence remaining intact. Thus, in this case not uniquely, material technology informs compositional technique.

Lest the foregoing seem to elevate the analog at the expense of the digital, consider the fact that augmentation and diminution - techniques of transformation equally immanent to sound as such - are not implementable in their most essentially abstract forms by virtue of analog technology. This is because the perceptual qualities of pitch and tempo as inherent in any given sound recorded to a physical medium remain inextricably intertwined. Both of the aforementioned techniques, then, are only possible with the digital transformation of sound, by virtue of which proportional relationships of rhythm and pitch can be preserved while the entirety of the sample is either slowed down or sped up.

Finally, it remains to be observed (in a manner disproportionate to the significance of the observation) that to proceed on principle from the self-sameness of musical entities across permutations further courts serial logic, insofar as both modes of musical thinking are predicated on the ontological foundation of musical form and structure as a sequence of events qualitatively experienced in durational time.




Subtending these more elaborate instances of motivic transformation is one far more basic to my music - that is, repetition. Indeed, at an architectonic level, my compositions are founded on the coordinated interaction of loops describing proportionally related periodicities. The historical prototype for such an approach to composition is the technique of isorhythm - a method of coordinating voice-parts according to periodic processes that was pioneered by Medieval European composers. A truly speculative pursuit, isorhythm traces its origins to Pythagorean doctrines concerning the mystical qualities of numbers and the orbital harmonies that bind the cosmos. Reverent of the provenance of its fundamental principles, Medieval composers dutifully cultivated isorhythmic relationships, undeterred by the fact that they are not always immediately perceivable by the earthbound listener.

It is worth noting how, perceptibility of the structures it gives rise to notwithstanding, isorhythm necessarily entails a modular conception of motivicity that is itself preconditioned in turn on an atomistic conception of the nature of musical material.




The process of sculpting motivic material from pre-given sound to the end of transforming it into recombinant parts to be reconfigured anew may be termed "modular counterpoint." In my music, such modular components function as the constitutive elements of voice-parts, each themselves of singular, determinate origin. These elements, in conjunction with the irreducibly unique entities that instantiate them, lay the constructional foundation from which aesthetic coherence emerges.




If you study the logistics and heuristics of the mystics you will find that their minds rarely move in a line.

- Eno, Before and After Science


To reformulate the foregoing conception of motivicity: The integrity of the pre-given sounds that I adapt as the bases for subsequent elaboration is of paramount importance to my compositional process. In working with and on sound in such a way, certain principles guide my music - principles that may be illustrated by heuristics adapted from the realm of philosophy and aesthetics.

Practically, in attending to the qualities immanent to sounds I adapt via processes of recombinant transformation, I am guided by the methods of phenomenological reduction and eidetic variation pioneered by the German philosopher Edmund Husserl (1859-1939). Theoretically, in working out from individual samples the form of any given composition in toto I am guided by the relationship between time and identity attendant to the idea of "duration" that figures centrally in the work of the French philosopher Henri Bergson (1859-1941). And subtending the compositional approach exemplified in equal measure by these heuristics is a conscious awareness of musical sound as the physical ornamentation of metaphysical order most notably operative in the teachings of the Greek philosopher, mathematician, and musician Pythagoras (c570-495).




As a composer, I aim to reveal, through their fundamental qualities, how certain sounds might be recombinatorily compatible with ostensibly disparate sonic phenomena. Put another way: I make music in order to illuminate the habitually unheard connections obtaining between the pre-given sounds I adapt as the bases of new works and the world of sound at large. Husserl would attribute this "habitual unheardness" (as it might be termed) to what he terms our "natural attitude," by which he means the unreflective manner in which we navigate day-to-day reality. Conceived along these lines, each sound I adapt as the basis for a new work might be said to "naturally exist" in its original context as part of a matrix of structural and semantic relationships.

Distinguishing it among other approaches to the task, Husserl’s way of unveiling the essence of a phenomenon laden with such "conventional" relationships and associations is subject-based and processual rather than object-centric and definitional. The difference between these two approaches gets at the central theme of Husserl’s work, which goes back to that of Descartes. Briefly put: Both these philosophers sought to determine the precise nature of the relationship between thinker and thought. Proceeding from the hallmark insight of Cartesian epistemology, the goal of Husserlian phenomenology is the apodeictic experience of truth.

The term "phenomenon," in both my work and in Husserl's, then, is therefore to be understood in its etymological sense as an "appearance" of some object of perception to an experiencing mind. Consequently, phenomenological inquiry, in contrast to not a few competing schools of thought, establishes as ineradicably constitutive the role of the observing subject to whom the object of perception is disclosed. What is more, it adopts not part but whole as point of departure, and presupposes not the isolation of objects and subjects from one another but their mutual and radical interdependence.

These principles have methodological ramifications. Specifically, rather than break an object down into constituent parts in analytic fashion, a phenomenologist seeks to apprehend it as a synthetic whole by systematically exploring its many aspects. This is why Husserl terms his dual processes "eidetic variation" and "phenomenological reduction" - the latter involves "reduction" insofar as in such investigations a phenomenon undergoes a process of estrangement from its original context that results in the shedding of non-essential properties, and the former entails "variation" insofar as one must continually alter one’s perspective on the object considered in order to open oneself up to the possibility of apprehending its essence.




In my music, then, eidetic variation and phenomenological reduction correlate to the distillation of a given compositional idea to its essence through processes of recombinant variation applied to its modular components. As a means employed toward an end of uncovering such an essence, Husserl's methods find a complement in Bergson’s concept of "duration," which holds, inter alia, no two experiences of the "same" phenomenon to be in any significant way "the same." In other words, we, as perceiving subjects, bring the sum total of our experiences, which is ever growing, to each and every new situation. Although commonsensical, such a basic truth, Bergson reminds us, is often obfuscated, such as when, for example, we conflate spatialized modes of existence with temporal ones. Such a habitual conflation is at the heart of Bergson’s distinction between "clock time," which is discrete, quantitative, and divisible, and "durational time," which is, at its core, a qualitatively indivisible unity of experience.

In fact, "clock time" is a misnomer, seeing as what goes by that name is not really "time" strictu sensu but rather an atemporal consequence of the misapplication of spatial logic to "real time" - i.e. durational time. Only in spatialized modes of perception, in other words, do we number things as quantitative multiplicities. Moreover, were we never to apply a spatial lens to the indivisible flow of time, we would never be able to conceive of lived experience as made up of discrete moments separable one from the other. In durational time, then, multiplicity is by necessity qualitative, and each entity inhabiting durational time is constituted a priori by its radical uniqueness.

Another consequence of Bergson’s distinction between "clock" and "durational” time is that the existence of any such thing as repetition held as distinct from variation is precluded. Otherwise put, repetition as enacted in durational time (as is done paradigmatically in music) ought not to be conceived of as the reproduction of so many copies of some ideal essence. Rather, the accretion of experience by the perceiving subject transforms the phenomenon repeated. Otherwise put, no two experiences of the "same" phenomenon are themselves ever in fact "the same," as we bring the sum total of our experiences, which are ever growing, to each and every new perceptual situation.




In my music, then, Bergson’s notion of duration, coupled with Husserl’s methods of eidetic variation and phenomenological reduction, serve as lodestars guiding the implementation of compositional techniques aimed at revealing the essence of both its constituent and synthetic perceptual entities as dynamically emergent, not categorically asserted.

Freedom from categorical imperatives imposed from without is a goal traditionally shared by artistic and philosophical enterprises alike. To wit: Of the philosophical issues that were of importance to Bergson, the most vital was this type of freedom - that is, freedom from the unreflective subsumption of particular phenomena under generalized categories. To forge a conceptual framework for the experience of such freedom, Bergson sought the aforementioned a priori separation of the realms of space and time, which, when conflated, give rise to a situation in which absolutized categories of thought metamorphose into barriers barring the appreciation of phenomenal particularity.

Aesthetic unity - in our case not uniquely, the perception of the compositional idea - thus occurs as a synthesis of consciousness emerging in durational time - that is, as a moment of cumulative insight by virtue of which the essence of the totality comes into perceptibility while its individual components simultaneously stand out in all morphological uniqueness. As it happens, Medieval European thinkers conceived of and experienced this mode of aesthesis as anagoge. For them, the locus classicus of music as conduit for the anagogic apprehension of metaphysical truth was Plato’s Pythagorean vision of the universe, wherein sounding harmony metaphorizes the primacy of cosmos - a Greek term translatable as both "order" and "ornament" - that imbues all creation. For Plato as for every Pythagorean, such cosmos may be expressed most potently in numerical terms. Indeed, a central tenet of Pythagoreanism is that the ratios governing, for example, the division of a monochord into consonant intervals also govern the disposition of the physical universe. Such logic forms the basis of the fabled doctrine of the music of the spheres, which holds the proportional motions of celestial bodies to produce real, actual harmonies - the sounds, to a Pythagorean, of cosmos cosmetos, or "order adorned."