Aphophatic Microtonality;
Notatio per Nega-

Aphophatic Microtonality;


Notatio per Negationem

In the study of musicianship, the method most often applied follows in the order of the analysis of a work, the practicing of it, and a subsequent removal of all that is erroneous, unnecessary, or unfitting, with the hope that the pure essence of the music alone might appear in the act of performance. The final result of a musician’s training is not the ability to build up a well practiced interpretation of a piece of music, but to discover the true essence of the musical idiom and axioms that define a piece of music; to be explicit, that the result of one’s training, beyond musical facilities and technique, is that

knowing how to put music together

is not the same as

understanding what it is;

one is a recreation, the other is an actualization; or, that both methods may lead to the same result, but one is merely reading the score, whereas the other is seeking a result that, though requiring greater effort, leads to a greater understanding of truth, beauty, and goodness.

It is not that creating music is inherently an apophatic exercise, but that the proper way of understanding a piece of music is to treat it

via negativa,

because the contemporary notation it is provided in is uniquely cataphatic, which,

via positiva,

provides everything, especially in a notational context, extraneous to the essence of the music. The cataphatic method might perhaps spawn from both a musical landscape in which we cannot accept flaws or errors, where we must be perfect from the start, and an environment where the law of the composer is of higher value than the intuition of the interpreter, wherein the former somehow knows best despite the environmental conditions and personal experiences that occur during performance; yet, more importantly, it perhaps stems from a determination that we cannot allow anything other than what has been written, no ornamentations or deviations, if only because it is not in ink. Thus, it adds on to a score in a manner that explains attributes that would otherwise be understood through diligent practice and study, such as fingerings, accidentals, barlines, time signatures, tempo, rubato, intonation, and any historically informed knowledge.

Yet, there must be in music a dual understanding of

what it is


what it is not,

as there is in a theological methodology, for the experiencing of music is one in the same as a contemplation of what is not intimately knowable or is immaterial, something beyond our common understanding without abstract validation, yet is equally knowable in the truth, beauty, and goodness that it provides. The kind of knowledge that one can know might be defined by what is provided by the composer, but what is more important is that sort of knowledge that is not intimately knowable through notation, that which is not defined, being those things found and expressed in performance. They are perhaps like those being as in the example I had once read somewhere of the ineffable experience of hearing Froberger play, which was beyond the ink that he himself notated with; that is, each time one performs music there is always something beyond what is granted through the notation, some magic element that might only be sought through the elimination of everything other than the core essence; yet, this essence is momentary, for, in the performance of

Méditation sur ma mort future,

that which is from Froberger is that which can only be from Froberger, and that which is from me is that which can only be from me; thus, it must be said the primary goal of music is not simply performance, but investigation: the development of the mind, of the ear, and of the heart. To do otherwise is to fail the basic humanistic qualities of music.

Of course, these truths might be labeled as musings or as broad philosophical statements, not of value in discussing the apparent subject of the technical aspects of microtonal notation, yet they are the starting point for the expansion of this cataphatic/apophatic dichotomy in music notation to the question of microtonality; for, a scientific approach to music and performance is the primary goal prior to the development of technical facility, but a philosophical approach to music and performance becomes the primary goal following the development of said technical facility, and once one knows the notes, one must then possess the ability to remove that conscious knowledge of technique to develop the music itself, for to possess technique can no longer be the bare minimum in a world such as ours today, one with easily programmable, mechanistic music; indeed, music is becoming more and more like that of the traditional craft world, in which it must no longer be about the perfection of the object itself, which can be fulfilled in mass production, but the way in which the object can provide intangible value beyond its utilitarian use; a cup is a vessel for water, but in the right hands it is also an object of beauty, one which changes the manner in which we handle and view it, so that it becomes a vessel for the spirit. An object is charged by the dignity that it is given in creation, if this was not so then there would be no potters; likewise, a piece of music is given purpose through the manner it is intended to be used. If it were so that we were simply interested in defining the purpose of music as a series of perfectly performed pitches, then we would certainly be satisfied with machines, and then there would be no use for musicians or any further development of a sense of musicality.

Paradoxically, the newer notational methods are defined by a composer as if one is composing for a machine, yet given to human performers to sort out. This is exasperated by the development of non-temperamental microtonality—that being those tunings that are defined by divisions of the octave into more than 29 tones (diatonic with enharmonic accidentals and quarter tones, including the tone between B-C and E-F) often compounded by the increasing specification of tiny, nearly unplayable intervals, and these tunings not being interchangeable at a base level, otherwise a primary trait seen in the ancient methods of shade and renaissance temperament—in which the individual views developing new symbols for the current standardized notation as the solution to the problem of defining intonation other than equal temperament. This decision, undertaken by a vast strain of individuals who cannot agree on any standard, but continually cheer one another on in defining more and more physically unplayable, and ultimately useless, divisions of the octave, often for the sake of science or study alone, has been facilitated by the fact that notation in the late 20th and early 21st century has developed in such a way that the cataphatic model of contemporary notation is primary, thus there can be no “errors” in the oft chance one wishes to attempt a performance. The primary nature of the initial development of cataphatic notation as being beneficial to musical performance has been extended for the project of the recording of new music—after which it should be noted that everyone might wash their hands of the music and forget about it, knowing that the only necessary performance is on file—as a properly defined notation allows for easier sight reading, thus less time and expenses wasted on an unfamiliar piece of music; yet, this is not beneficial for anything beyond reading music, and does nothing for musicality and the good of the individual, which requires more study, practice, and reflection than the music industry allows. Rather, it is precisely because the notation is a window to the composer’s initial experience, who puts into down on ink as to guide others to that same experience, that the development of it was of value, but one should not take that precedent as an excuse for hyper specificity, because the further one moves along that path, the less likely the performer is to have an authentic, organic experience, and more likely are they to have one manufactured for easy consumption, to be discarded at a later time.

Beyond the ridiculous reasons for cataphatic notation, there is also the belief that everything that the performer is capable of should be designated in symbols as opposed to them finding it naturally, that there is a way of expressing something that only exists because the composer believes that they should exist, not that they truly do. As in its counterparts in tonal notation, where one has more than three dozen distinct symbols and text instructions for a harp player, there is a great wealth of cataphatic microtonal symbols that supposedly define something that is difficult to even imagine in the inner ear; in fact, all prior microtonal theory, as a development or reimagination of tonal theory, is in some sense an argument for what the music is believed to be, just as the developments in tonal notation are an adding on of more ideas of what music is believed to be or express.

However, the beliefs that microtonal systems develop to an unimaginable extent is the exactitude of the frequencies of a set of pitches on a piece of paper themselves. Whereas in the past one would work somewhat indeterminately—an example being in the case of the split key keyboard or the archicembalo, where the idea of that pitch occurs to the composer when he performs the music that he would define as a sharp or a flat accordingly in his notation; however, after this there is no true indication whether the meantone was 2/7 comma or otherwise, and the performer would define their tuning, something as personal as their instrument—much microtonal notation functions in the opposite manner: one defines initially what the pitch is in notation by impossibly exact specifications, whether it be raised sharps and lowered flats in Helmholtz-Ellis to the complete revision of common notation in Sagittal, both of which require the performer to learn a swath of esoteric knowledge to perform even a single passage of music. What this does is limit the actual value of the music, for it is not inherently portable or universal because it is already hampered by a specificity that defines how the composer sees the essence of the music, whereas Couperin, whose unmeasured preludes are essentially undefined in all parameters aside from the notes themselves, provides a fascinatingly coherent specimen of music in which the differences in performance develop according to the stylistic qualities of the performer and his chosen tuning.

Thus, as it might be construed, the primary problem with microtonality’s festishization of precise intonation and the development of symbols for that cause is the same as the problem with the cataphatic argument in standard notation: it defines the musical language in a way that assumes it can be known, without doubt, as uniquely true for that piece; moreover, that truth can be defined immediately, that it does not take the efforts of learning and self-development to reveal it, so that it might be read on the spot. Cataphatic notational systems, and the microtonality that they give rise to, cannot implore the individual to put an effort into understanding what is, but only put in the effort to realize what a third party believes what is; that is, it is merely a method of actualizing the “composer's vision,” as if it is some eternal truth that cannot be disobeyed, as opposed to generating an environment where the interpreter, and hopefully the listener, might find something of value through performance. A fully realized cataphatic notation is wholly quantitative, more fitting for the computer than it is for humans, more interested in efficiency and results than the common good; indeed, it is a trashing of the ethical necessity of music as a humanizing force, one that has the possibility of bettering the individual, in exchange for a post-industrial machine that is capable of filling the required amounts of work to satisfy a cultural agenda, which judges prestige and skill not by the ability to conjure a unique, communal experience from the proper study and understanding of a piece of music, but by how few rehearsals it takes to complete the task, by how many new works are commissioned and executed within a season, and by its subsequent international reputation.

Thus, the problem of the solution is that the solution is more complicated than the problem. Cataphatic systems imply that greater specialization can remove error, can create precision, can better execute the “composer’s vision," as if an ever growing specificity correlates to an ever developing quality of work. Moreover, and more egregiously, it is an incomplete vision of truth; that is, it can be assumed that the truth IS 13 limit and that 7 limit is incorrect merely because the composer defined it as such, assuming that their opinions about what is possible is of greater value than what actually may be possible. One who specifies something even as simple as temperament as fact must do so by judging the alternatives and questioning one’s own beliefs; yet, even if one does so rigorously, the results that appear as truth to the individual might appear as speculation, or even as thoroughly incorrect, to another, because truth cannot be understood even through the most attuned of senses, for it is so that one cannot strip away one’s perception, one’s subjectivity, because it is undoubtedly so that unless one extinguishes all preconceptions, all taste, all factors of judgement, all investigative desires, and becomes an empty body, with no personality, no love, no hatred, to the point of self-annihilation, then one cannot begin to understand even the slightest bit of truth,

nam sensus deficit.

Even if one assumes purity in just ratios and attempts to escape the senses in favor of mathematical justification, they are making the mistake of assuming that one sound is primary simply because it is not complex; thus, the assumption is that other sounds are wholly worthless, despite their appearance in the natural world, due to abstractions and logic, fully driven by matters of taste and subjectivity, for the role of mathematics in music is subservient to one’s desires. Therefore it is imperative to admit the truth: a cataphatic microtonality is a straitjacket, for it does not open the cage door, it affixes a second lock. To even demand another to perform one degree of any pitch’s intonation over any other is to out oneself as one who cannot listen, or perhaps even worse, one who is unwilling to listen, for the truth is in all things, not only those we prefer. All these notational systems that define anything of specificity, be it Sagittal or Helmholtz-Ellis, are false because they promulgate a dangerous world of inelasticity, and the perplexing result of attempting to shatter the artificially imposed universality and portability of equal temperament is to create music that is non-universal and non-portable. These very ideas are traps because they continue to develop an unsustainable, unintuitive method of notating music, one that requires knowledge of hundreds of symbols with progressively less musical meaning, and one which is a further step in bastardizing the shorthand initially developed for the good of the performer in favor of the strangely accepted notion that the complicated is beneficial to the composer in conveying ideas, which, in action, shuts out anyone but the most well trained performers. This path is foremost a dead end without any real possible development because it cannot be widely disseminated, but it is also self-destructive, as how can one truly destroy anything other than oneself if they attempt a siege on the most widespread and easily available manner of defining an octave? Yet, aside from this, it has become more important for me to reflect upon the reality that it is against the humanist sources of music—one where any being can participate in the musical experience, privately or publicly, without the necessity of arcane knowledge or divine revelation—and it is unethical because, by creating a barrier to entry through the use of esoteric ciphers, it does the very thing that music must never do: exclude people.

It is thus so that the answer to the philosophical and moral problems raised is an apophatic microtonality, which, through structural, notational, and intonational indeterminacy, is defined not by what it is, whether that be according to the whims of its creator or of the arbitrary nature of its theory, but by what it is not. If only by removing all the superfluous notational configurations that attempt to define truth do we find that the final truth was available in the essence of the line all along, and that our exercises in definition are a waste of energy. To clarify, notation is indeed a means to an end, and a composer's job is to use notation to clear the path as to better express to the musician what might be done, but not to decide how to fulfill it. Rather than being one who creates something for a motive exterior to the musical experience, the composer is akin to a prophet: his “vision” is in that which he experiences in the musical idea, and he must struggle with the feeble work of the hands to form an expression of that which is formless, that is ephemeral, transient; something that comes and goes with the experience itself, that even might be lost before transcribed, though may reside in the memory as if a pale shadow, but not as if made flesh. Through his notation, the composer offers a promise of this ineffable experience through symbols and ciphers, draftsmanship and rhetoric, but the fulfillment of that promise is up to the interpreter's technique, finesse, and heart.

This being paramount, the questions that must be posed are: how can we write music in a manner that expresses itself in the most perfect form as to best find truth? Why is it that standardized notation has failed us in the late 20th century so that we have had to overcomplicate it or turn to other notational forms to express these experiences? Is it perhaps that there can be no standardized manner for the composer, and can we even truly standardize something which has no physicality, or are we to simply do the best we can to write, in ink, on paper, as if blood on flesh?

Thus, for me,

via negativa

is the only way to clear the path on the search for the purest form, and one which I believe is of the greatest value in ultrachromatic or microtonal or xenharmonic music—whatever one wishes to define their non-equal tempered path—for it might be legitimized by past forms, the development of personal adiastematic and Solesmes derived neumes in my own practice, but also accepted as a form of graphic notation in its contemporaneous nature. These forms of notation are simplistic in their readability, but I do not believe that I am ignorantly seeking the past, and I certainly do not believe that they are not inferior to modern notation, for they can express contemporary musical ideas despite their appearance, just as figured bass and chord symbols can express contemporary harmonic figuration without any extra, unnecessary notation.

Therefore, it is in the conception and execution of the pieces that stirred my need to write this essay,



Sicut in Prologo Evangelium Ioannis,

that I have made my first attempts to sever my reliance on the paradoxical nature of modern notation's ability to define everything, yet only one thing, and attach myself to an apophatic form of notation in which I define only one thing, yet everything; that is, I give a point, but the value of that point is not determined by me; conversely, in that one point exists a universe beyond anything I might ever comprehend, though it appears small, limited, and crude. It is because what I seek as a composer is to express what I have experienced, those things that spurred on the composition, in such a way that the interpreter might also easily experience those things, but also convey that we cannot know any other experience other than our own, and it is up to us to decrypt what our musical experience might be through our study and execution of the score. Whether the pitches have some equivalent value or are entirely relative, the primary attempt in my notation is to facilitate the indeterminacy of the direct musical experience so that one can only express what they experience, not my experience that I am forcing them to recreate.

To explain this subject of my own experience of the musical idea, in composing something as daunting as the prologue to the Gospel according to John, one might simply rely on recitation formula, word painting, or vocal inflection, but these approaches will lead one to eventually reproduce what another has already done, for there are only so many ways one can approach the written word in these manners; instead, what I have found is the necessity of expressing the experience I myself found while reciting the text, from which a completely unique moment arises as I begin to stress certain attributes that are important to my own reading of the Word. When I read “In principio erat Verbum” my response is immediate, and that response is not inflective, but expressive; that is, how I have already expressed this phrase is defined by my experience of the text at that point in time, influenced by how often I had read, studied, and grown through my experience of such a text, and my musical line derives from this experience, so much so that I might, at a later time, come upon the same text and find something different. Thus, we find contrasts in different sections of the text, where I have read quickly without any inflective differentiation, to those that express melisma or undulating lines, in which I might have found something of value that I wished to stress, whether it be a physical utterance or a symbolic expression.

Likewise, in the notation and the written word one finds that they cannot strictly sight read, but carefully and purposefully pour over so that the reading of the manuscript is as part of the musical experience as the writing of it. The reasoning for this is because the conception of the musical act is personally experiential, thus it is necessary to express in notation that experience I myself had found, down to it being handmade as an integral part of it. It can be said that engraving has its time and place, but for the composer, and perhaps even the performer, it creates a distancing effect in which the experience expressed in the actual writing of the music has no place in the notational procedure. Considering the practical defenses for engraving, it should be noted that the development of mass production has allowed for the printing of facsimile scores, such as those of Harry Partch’s tablature, which defeats the purpose, both in time and cost, of spending time engraving scores, for which only an engraver would argue otherwise.

All of these developments allowed for the one of the greatest importance: in the prologue I finally eschew the necessity of a specific sound. In the Mesonyctycon I stressed the importance of the enharmonic divisions of my personal tuning as how I experienced the work, and thus how I desired the work to be experienced; consequently, I mistakenly implored the interpreter to find their own sound, but then discussed the sound I knew, contradicting my own desires. Instead, I wanted to express in the prologue only the possibilities in the pitches given, so that the pitches that are enharmonic in the work, C# and Db, are different in my own conception of the experience, but have the potential to be anything in any other experience, not because I have no control over how an interpreter will perform the work, but because their experience of reading and studying the work, as well as the sound that is best for them, will define that final result.

What I have come to accept in composition is that notation means nothing if it has no meaning, but that meaning is only granted if the notation allows for it; that is, when one reads the notation they must be able to use it to define something they know, and I must free myself from what I expect to realize that which I do not expect, because what I expect may have no actual meaning if one finds meaning in that which I do not expect. The ultimate goal in music is not in expressing what I want, but giving others the ability to experience what I might have experienced, yet, perhaps more importantly, that they experience their own world through my notation. Unlike any conventional composer, my goal is not to make something that is extra-musically beneficial to me, or to anyone else for that matter, for there is nothing I truly want in the performance of the music I have written, and there is nothing I can truly gain from the performance of the music I have written, because I have already had the experience of it; it is rather that someone else might gain their experience of it through my notation that I chose to commit my experience to paper and distribute it.

Thus, despite my choices of notation being derived from past sources and not contemporary practices, I am not attempting to say that these methods are better for some reason of anti-modernism or it being some farfetched effort to recapture past glory, but that their simplicity allows for anyone to express pure musicality—moreover, because I believe the contour of a line and its shade are the primary factors of a non-tonal music, it is all the more obvious that I might view these ancient methods as superior because their initial use is for delineation of lines—and it is this seemingly paradoxical idea that moving progressively backwards, as I have already done in probing the idea of square neumes on a four line staff, is the logical endpoint to an indeterminate, relative pitch line, for the oldest neumes may reveal any series of pitches that the interpreter deems necessary for their performance, and the open ended nature of the choices cannot destroy the line, but rather it fulfills the line. As in the καθολικότητα of the early Christian church that developed these forms of notation, I do believe the methods that I apply fulfill a promise of true universality; one in which I have provided a method in which all men are equal, despite their skill, in the performance of these sorts of works, and it is because I believe that true musicianship is not about being the best virtuosi, but is about trying to express truth, and that true musicianship is about the search for the right sound, even if one does not possess the greatest of resources, and the fulfillment of it leads to the unique, ineffable experience that occurs in the making of music.

Therefore, this is the humanist value I place in musical performance: in most situations we listen, we are the beneficiaries of powers outside of us, be that as listeners of a performance, live or recorded, or as distant creators through electronics, and we have no true, physical control over the experience itself, thus we ourselves are not the focus of the experience and we are not able to fully participate in its goodness; yet, in a universal music making, as found in chant, we are all participants in the physicality of creating an experience, and no one member is denied this as an audience. However, it should be stressed that a humanistic music is not a childish or didactic music, but one that challenges the performer beyond technical skill and allows for growth and discovery. Just so, a humanist music should not be facile, but complicated in such a manner so that it gives pause, and it must be nuanced enough that it might invite new experiences on each performance.

Consequently, what I wish to tell you is that the answers to the problems raised in the development of microtonality are not you being able to find and define the "notes your piano hides from you" nor are they a radical specificity in response to the radical specificity of equal temperament; it is so that none of the theoretical and intonational developments made in the 20th century are the true solution, but rather that they are a means for you to free yourself from the restrictions imposed upon you by the system of equal temperament; and, instead of the building up of new definitions it is the removal of those definitions, of all these extraneous notations and all their technical barriers, and perhaps even moreso it is the ability to recognize that music is not what we attribute to it through notational symbols, but what we know those symbols to truly be. It is the acceptance that intonation cannot be codified, not on a sheet of paper, and certainly not in sets of silly little symbols. It is the realization that what is true is also what is not true; that there is no truth, yet everywhere there is truth; that what I hear and what I do not hear are different, but equal; that I can believe in what I know, but that the truth is more likely in what I can never know; it is, in all the ways that it might be expressed, that the proper intonation is within you.