content of one form of media, i.e., television, as consisting of another medium, i.e., movies), illustrates this. But a fundamental problem of music notation may be shown by a clearer example: verbal language translated into algebra, a lower order symbolic extension system to a higher one. A typical situation may be stated in English:

A composer produces 360 copies of a sound recording. He can sell each record for $5.00. His total production costs are $3.50 per copy. What is his total net profit?

For greater efficiency and ease this is converted to the abstract algebraic equivalent, where: x = net profit
y = total gross return
z = total costs

and so, x = y - z

This totally abstract formula is the highest order of extension. Note the ease of the potential for symbolic manipulation as well as the complete separation of symbol from that which is symbolized. But lost in the translation between initial problem and final highest order extension are all of the specifics and nuances of the problem. Some of these are reinstated when the equation is completed:

x = (360 x $5) - (360 x $3.50)

Still, few of the specifics are explicit in the latter equation. And furthermore, even when the initial problem was expressed in English, only those elements that could be translated or extended directly into mathematical language were mentioned. We do not know the style of the composer, his motivation for choosing that particular work, etc. None of these important items will translate into the higher order efficient impersonal algebraic language. Thus, they were subconsciously eliminated from consideration even before the problem was converted. In the case of traditional Western music notation, not only is the notation itself restrictive in its inability to express (for example) gesture and to define an unbroken continuum between events, but also it acts as a subliminal "filtering" device to the incipient creative idea, allowing only those impulses to get through which can be scribed according to its dictates. And I find it interesting that, just as the composer cited previously needed first to formulate his problem verbally in a severely restricted mode lending itself to the algebraic syntax, many composers and theorists even today conceive and formulate musical ideas entirely within and in accord with the dictates of the old Western pitch-rhythm system without realizing that, however useful this may be in ensemble playing and for developing theoretical concepts, it is in truth a censoring device, an artificial creation of the Western cultural inclination to model all of its institutions after, as McLuhan would put it, the modularized phonetic alphabet. And in music this is particularly dangerous, since this art is perhaps the clearest example of one which transcends verbal or other extensions and "plugs in" directly to the receptor's holistic, emotional, intellectual and physical senses. Wishart lends a historical context to the situation:

Undoubtedly, musical notation like 'speech notation,' originated first as a mnemonic device for already well-established musical practice, but, like writing, it quickly grew to dominate that musical practice.

Just as the original form of writing, the ideogram, did not attempt to convey the sounds of words (as with alphabetic writing) but the ideas which were expressed through the word-sounds and hence demanded a familiar[ity] with, and an adherence to, the sphere of those ideas, so the neume did not attempt to mark out what we now have come to regard as individual pitches and units of rhythm, but only shapes and contours of melodic lines customary in current practice, and hence also requiring a complete familiarity with current melodic practice, and an adherence to it, before becoming usable. In this way, these first notation procedures tended to stabilize, if not to atrophy, the pre-existing ideological and musical praxes.

The effect of analytic notation on music, in the context of a writing-dominated world was much more fundamental.

However, even pitch and rhythm could only be captured in a very particular way, determined by the exigencies of analytic notation itself. Thus, where aural rhythm, enabling the aural musician to indulge in the most intricate articulations of time, notated rhythm is limited by the problems of notational economy. . . . Hence, analytically notated music is bound within the limitations of summative rhythms.19

So much for the translation from a lower to a higher-order symbolic extension system as observed in algebra and traditional music notation. And what about the reverse? To what degree can the highly abstract symbolic extension system, without any supporting data, be translated back into a less-extended system with more variety, richness, and specificity than the higher system can contain? In algebra the answer is simple: it cannot. Without knowing what x, y, or z are, they remain abstract. In traditional music notation the answer is disguised by the superimposition of performance gesture and nuance enabling the performer to reach beyond the abstract symbol, to circumvent it as it were, attempting to establish a direct communication with the listener. In fact it is precisely this quality, the treatment of our modular, analytical musical language ideogrammatically, that performers will cite in their attempt to refute my basic point of the severe limitations imposed by the notation system. They will say that it is flexible enough to allow the real flesh of the music to penetrate the abstract symbology in the hands of a skilled performer (and will further state that this is what characterizes a real artist). As Charles Wuorinen says:

Notes and other noises are the things in music, but can never be said to exist; it has either just happened, or is about to. And at that instant when music is sounding, it is merely intervals of time and pitch, intervals that are themselves only 'empty space.' This is why one may say that music is the 'nothing between the notes.'20

I have no quarrel with the implication of the power of Western notation and of its performers to flesh out skeletal abstract symbols. Traditional notation's limitations do not lie so much in translation from symbol to something approximating human esthetic responses in a given composition, but rather in the ways that initial holistic, continuous creative ideas must be crammed into the Procrustean bed of a discrete, modular system. Thus our traditional system, through long training of performers, succeeds in dealing with the y s and z s of the symbolic problem as our math example could not; but the system fails because of its initial constraints on the creator to formulate ideas only in discrete, modular and combinatorial modes. And even then, to the extent that the system succeeds, to that extent it needs to be treated ideogrammatically in performance in order to be fleshed out.


A danger in Western music composition and theory lies in the confusion between the primary source, which is aural, and the secondary notational image. "Note composing," prevalent as it still is today, fails to take into consideration the proposition that, in a period of intense discovery of new sounds and techniques as we are now experiencing, it behooves artists to consider returning to primary extension systems, to probe ever deeper into basic primordial human artistic responses (gesture) while building creative concepts from the ground up. This, of course, is being and has been accomplished in every conceivable manner as we move into the '80s. Electronic music is perhaps the most direct means with which the creator can imprint the idea while subverting the extension barriers. Music utilizing the various ingenious ideogrammatic (graphic and indeterminate) notation systems, often in combination with traditional notation, has become commonplace. Various means of incorporating improvisation have surfaced. Process-oriented (phase) music has flourished. These and many other quasi-systems, styles, and genres have provided many creators with every possible avenue to explore.

It can be said that the history of Western music from the early troubadors and chant through the full flowering of the common practice period is one of increasing sophistication and abstraction. As composers we have many times experienced the deep chasm between the initial internal idea and its final external realization in performable abstract notation. In essence, the process is one of conceiving first from (as Jack Fincher would put it) the right brain intuitive side, with its basic emotional and primordial qualities, then to the left brain, which is verbal-intellectual-abstract, the side which has to reduce the first sound impressions with all of their excitement, uniqueness, and personal qualities to the common denominator of a standard (or semi-standard in much of today's music) notation quantifiable in practical terms. It was precisely this need to quantify pitch and rhythm, the two parameters necessary for scribing ensemble music with several vertical parts sung together, that produced our unique Western notational system. But in the process we are beginning to discover that Western notation is a double-edged sword, at once serving the necessity of coordination in performance but also dictating to the composer the final mode the ideas must be couched in. It is fascinating that many composers (as well as theorists, musicologists, concert-goers, and other consumers of abstract classical music) still essentially fail to conceive beyond what can be conventionally notated, thereby increasing the danger of falling into the extension transference trap, not realizing that the farther the basic sound material is extended intellectually, symbolically, or verbally, the farther one may be from the basic creative truth.

In conclusion, I would like to stress that the main point of the article lies not so much in the various terrible ways we composers and theorists can go "astray" (although that is part of the larger idea). My main point--that the human intellect's inexorable tendency toward higher and higher orders of extension is often in direct conflict with the holistic art of music--is far broader than that, attempting as it does to help lay a theoretical foundation describing the potential and the limitations of, as well as defining the differences between, sound and its symbolic extension.

1 John Vinton, Essays After a Dictionary (Lewisburg, PA: Bucknell University Press, 1977). 2 Edward T. Hall, Beyond Culture, 1st ed. (Garden City, N.Y.: Anchor Press, 1976), p. 25.

2 Edward T. Hall, Beyond Culture, 1st ed. (Garden City, N.Y.: Anchor Press, 1976), p. 25.

3 Ibid., p. 25.

4 Marshall McLuhan, Understanding Media, 1st Ed. (New York: McGraw-Hill, 1964), p. 132.

5 Ibid., p. 25.

6 Rollo May, Love and Will (New York: Dell, 1969), p. 302.

7 Hall, Beyond Culture, p. 24.

8 McLuhan, Understanding Media, p. 42.

9 Robert C. Ehle, "From Sound to Silence: The Classical Tradition and the Avant-Garde," Music Educators Journal 65, no. 7 (1979): 36-41.

10 Hall, Beyond Culture, p. 34.
11 Ibid., p. 45.
12 John Shepherd (with P. Virden and T. Wishart), Whose Music? (London: Latimer, 1977), p. 132. 13 Ibid., p. 31.

14 I use the term 'meaning' loosely. Since one of the points of this section is the limitation of the verbal symbol (let alone the musical symbol, which is even more limited) in its ability to convey meaning, I agree with Wishart when he states that ultimately the symbol can 'mean' only itself, and that we should not confuse 'signification' with 'meaning.' 'Meaning,' a characteristic residing not in some abstract quality but rather in each individual beholder, is a function of that individual's consciousness, together with the context of the moment. In music it could further be described as the recognition or relationships together with emotional stimulation.

15 McLuhan, Understanding Media, p. 79.
16 Hall, Beyond Culture, p. 24.
17 Ibid., p. 24-5.
18 McLuhan, Understanding Media, p. 178.
19 Wishart, Whose Music?, pp. 131-133.
20 Elliott Schwartz, Electronic Music (New York: Praeger, 1975), p. 259.

21 Actually, the real substance of the aural rendition manifests itself beyond the notes in two ways: first, the listener fills in what is missing according to his own cultural vocabulary, and second the performer reinterprets far beyond the notes to help fill the gap. In the case of electronic tape music, the second option is denied the listener but in its place is the capability of making the aural impression infinitely more explicit, since the notational system can be completely circumvented. The great excitement and the promise of electronic music is that it has this potential for creativity on a very basic primary extension level.

C 1981 Barton McLean
Permission for copying and use in normal university class work granted.