Kaleidoscopic Music

A Study Of Musical Materials

Towards the establishment of a re-integrated
diatonic / chromatic system

(Fall 1985) By Richard Byron Strunk BA

In the 20th century the once universal language of Western Art music has been fragmented into a number of distinct languages, schools and musical systems. There are few, if any, translators who bridge the differences between these apparently distinct musical systems. Each composer has their own tongue and the result is babel.

The significant composers of the past often achieved their greatness by distinguishing themselves from their contemporaries. I firmly believe that the significant composers of our own time will acheive their greatness by assimilating in one vision the chaotic distinctiveness of the present. This fusion of chaos can not be a simple eclecticism, but must be a recognition of an underlying logic which without exceptions or inconsistencies reconciles all apparent incongruities between seemingly separate musical systems. This paper is my first small step forward toward this goal. Within this paper I shall demonstrate that certain musical materials which serve as the basis for defining and distinguishing several major 20th century musical systems are intrinsically and inseparably connected.There are two types of musical materials which the composer utilizes in the process of composing. There is musical material which the composer generates from a particular musical idea (motive) for use in a specific composition. This kind of musical material is derived by such musical operations as transposition, retrogradation and inversion. Then there is the kind of musical material which exists independently of specific musical ideas or compositions. It is to these musical materials I will be referring throughout this paper. Examples of musical materials of this second type would include the traditional diatonic scale, synthetic scales, and 12-tone rows.In this paper I shall demonstrate that these apparently different musical materials can be shown to be potentially indistinuishable. What composers have tended to think of as different materials are but differences in focus and perspective on the same musical material. These different materials can be viewed like the traditional modes Ioian and Aeolian, not as different materials, but as differences in focus on one musical material (the diatonic scale). One does not think of Ionian-based music as being fundamentally distinct from Aeolian-based music, but rather as intrinsically linked. One thinks of modal-based music which allows a choice in focus, Ioian or Aeolian. In choosing an Ionian focus (within the diatonic scale) one has not severed oneself from the options and lines of emphasis particular to Aeolian for one can easily and naturally shift in focus without loss of organic integrity. Since the supposed different materials I have mentioned have been used as the basis to establish and develop several different musical systems, it follows that if these materials can be shown to be potentially indistinguishable, these musical systems can also be potentially united with any surface incongruities and contradictions reconciled and resolved.

These musical materials have been used by composers of this century as a basis for developing several new musical systems. While retaining the traditional tonal-modal system, composers have epanded their resources to include:The 12-tone based system (resulting in 12-tone based music);The synthetic scale-based system (resulting in synthetic scale based music);The polytonal-modal based system (resulting in polytonal-modal based music).Although various aspects of these different musical systems may be touched upon when appropriate in the course of this paper, my primary concern in this study has to do with the musical materials employed in each of these musical systems and not with the musical systems themselves. The specific musical materials that are included in the scope of this study are:Cyclic 12-tone rows;
Synthetic scales derived from such rows;
The traditional diatonic scale
The polytonal or modal use of the traditional diatonic scale

A composer's choice of musical system and musical material are mutually effecting. A composer's choice of musical material determines his/her choice of which musical system to employ (or vice versa). The kind of musical idea that the composer intends to develop and to express will often predispose or influence his/her choice of musical material and musical system. A composer's choice of musical material, within which he/she intends to generate his/hermusical ideas, predisposes him/her to develop his/her musical ideas along lines of emphasis particular to that musical material. This effects how his/her musical ideas are generated, developed and finally embodied into larger forms. His/her choice excludes the development of musical ideas along lines of emphasis particular to other musical materials and their musical systems.The four musical systems already mentioned:

• 12-tone based systemsynthetic scale based systempolytonal-modal based system
• the traditional tonal-modal based system

are distinct primarily because different musical materials are used as the basis for each system. These basic musical materials are:

• 12-tone rowssynthetic scalesthe traditional diatonic scale (and the 'circle of perfect 5ths')
• the simultanous use of diatonic scales or synthetic scales (polytonal-modal)

For these musical systems to be united in one underlying and comprehensive sense, the musical materials in each of these systems must first be seen as equally applicable to them all.The traditional tonal-modal system is neither exclusively diatonic nor exclusively chromatic in its tonal organization. In the traditional tonal-modal system the composer has two basic frames-of-reference for defining and preceiving tonal organization. The traditional diatonic scale serves the composer as a frame-ofreference for organizing the twelve chromatic tones (the total chromatic) into twelve distinct, yet like tone-groups with each group containing seven tones. In the diatonic spectrum the composer is primarily concerned with how these seven tones within the domain of a single scale may interrelate. The composer may be equally interested in the different kinds of chords (aggregates) that can be formed from these seven tones and how these chords may interrelate. The 'circle of perfect 5ths' serves the composer as a frame-ofreference for organizing the twelve transpositions of the traditional diatonic scale. In the chromatic spectrum the composer focuses primarily upon the various tonal interrelationships that can occur between the twelve diatonic scales and their aggreates (chords). Both the operation of modulation and the establushment of secondary chordal relationships (such as V/V exemplify this chromatic level of tonal organization).In the traditional tonal-modal system the 'circle of perfect 5ths' (a cyclic 12-tone row) embodies and subsumes the diatonic spectrum of tone-relationships (the twelve transpostions of the diatonic scale). These two frames-of -reference which are used by the composer for establishing tonal organization within a musical composition are mutually interdependent and interpenetrating. The 'circle of perfect 5ths' may be inferred from a chromatic overview of the tonal-interrelationships that exist between the twelve transpositions of the diatonic scale. Likewise, the twelve transpositions of the diatonic scale can be derived from the 'circle of perfect 5ths' by partitioning this cyclic 12-tone row into twelve overlapping segments of seven adjacent tones. Taken togather these two frames-of-reference provide the composer with two extreme perspectives for defining and perceiving tonal organization within a single integrated tonal environment (continuum). The 'circle of perfect 5ths' provides the composer with a macroscopic frame-of-reference, while each of the twelve transpositions of the diatonic scale provide the composer with a microscopic frame-of-reference.

Just as the 'circle of perfect 5ths' (a cyclic 12-tone row) embodies and subsumes the twelve transpositions of the traditional diatonic scale so other cyclic 12-tone rows may be viewed as embodying and subsuming synthetic scales. I am suggesting that using a cyclic 12-tone row as a macroscopic frame-of-reference does not invalidate using a diatonic frame-of-reference, traditional or synthetic, as an equal partner in defining and preceiving tonal organization.

The fundamental difference that exists between the 'cicle of perfect 5ths' and the '414' cyclic 12-tone row is that all transpostions of the 'circle of perfect 5ths' end up being rotations of the 'cicle of perfect 5ths.' With the '414' cyclic 12-tone row in Example 1b only three of its twelve possible transpositions end up being rotations of itself. This occurs because the repeating '414' intervallic pattern which defines this 12-tone row's ordered-interval-succession can manifest in three possible rotations:

• '414''144'
• '441'

This means in the diatonic spectrum that rather than having, as in Example 1a, one cyclic 12-tone row (the cicle of perfect 5ths) which embodies twelve trnaspositions of one diatonic scale, in Example 1b one cyclic 12-tone row ('414') embodies four transpositions of three intrinsically related synthetic scales. These three synthetic scales are intrinsically related (as delineated in Example 1b), because each of them is generated and determined by the three possible rotations of the same intervallic pattern ('414', '144' and '441').

While the '414' ordered-interval-succession, in Example 1b, both defines and binds this '414' cyclic 12-tone row with its diatonic scales (segments), it also manifests as the primary organizer of harmonies and harmonic relations within those diatonic scales (as illustrated in Example 2b).

In Example 2a the triads outer interval is the interval of a perfect 5th which is, of course, the interval which constitutes the ordered-interval-succession of the scale's cyclic 12-tone row (the circle of perfect 5ths). The diminished triad is the lone exception because its outer interval is the tritone. In Example 2b we can see that the synthetic scale manifests trichords whose outer intervals (major 4ths and minor2nds) affirm the ordered-interval-succession of this scale's cyclic 12-tone row. Again, as in Example 2a, we find in Example 2b the lone exception of a diminished triad whose outer interval is a tritone.In Example 2a the triads traditional harmonic functions:

• tonicdominant
• subdominant.

in major Ionian or minor Aeolian have been labeled beneath the chords. The tonic (T) F# major chord and the tonic (t) e-flat minor chord are both seperated from their respective dominant and subdominant chords by the interval of a perfect 5th. This is the interval which constitutes the ordered-interval-succession of this scale's cyclic 12-tone row (the 'circle of perfect 5ths'). Although I have not indicated specific harmonic functions beneath the trichords in Example 2b, one can easily surmise that, as in Example 2a, in which the interval of a perfect 5th defines and determines the primary harmonic functions between the chords within that scale, so also in Example 2b, the intervals which make up the ordered-interval-succession of that scale's cyclic 12-tone row (major 3rds and minor 2nds) play a key role in defining that scale's inner harmonic tonal hierarchy and in determining the primary harmonic functions between the chords within that scale.

So writes Charles Wuorinen in his book 'Simple Composition' (PP 155-6).

The 'circle of perfect 5ths' ordered-interval-succession, is, of course, the repeating interval of a perfect 5th. This interval not only defines the macroscopic (chromatic) frame-of-reference, but, in addition, it pervades the diatonic level of tonal organization. In the traditional tonal-modal system this single interval defines harmonies, harmonic relationships, key and mode relationships, and much more. What is vitally important to realize here is that the interval or intervals which constitute the ordered-interval-succession of a cyclic 12-tone row are not only 'real determinants' underlying the formation of those 12-tone rows, but are also simultaneously the real determinants underlying the formation of harmonies and harmonic relationships within those cyclic 12-tone rows diatonic scales.Although in traditional 12-tone musical practice, composers have used only a single macroscopic (chromatic) frame-of-reference (the row) for creating music, Arnold Schoenberg, himself, described the 12-tone row as 'pantonal.' Does this not mean that a 12-tone row may be viewed as embodying and subsuming a diatonic (scale based) speectrum of tonal organization? It seems obvious that the vast majority of 12-tone composers through the years have severely limited themselves and their music by not recognizing that the 7-tone segments embedded in a 12-tone row can be considered in their own right as synthetic scales and that neither frame-of-reference, row or scale, is more or less important than the other for defining and perceiving tonal organization. On the other hand, those composers working mainly with synthetic scales have had equal, if opposite, short-sightedness. They have tended to either ignor the chromatic domain or arbitratily attempt to establish chromatic interrelationships between scales without first recognizing the natural chromatic implications (ordered-interval-successions) which are intrinsic to the scales themselves.Until now, composers have been employing the 12-tone row as immediate foreground musical material, to be articulated and defined in its entirety, and used as the only structural unifier for generating pitches within a musical piece. I would like to move the 12-tone row into a background structural role (much like the 'circle of perfect 5ths' role in the traditional tonal-modal system) and then use the synthetic scales which are embedded in the row for the generation of musical ideas which can then be developed into musical compositions. Musical ideas generated within a synthetic scale could modulate or mutate by common tones smoothly into adjacent scales or more abruptly into distant scales, and the harmonies and harmonic relationships within and between these synthetic scales all would be mutually consistent with the one 12-tone row and its ordered-interval-succession.This is not a violation of orthodox 12-tone principles, for the rules which govern the making of music with a 12-tone row are still valid when the composer limits himself/herself to using a 12-tone row as the only frame-of-reference for structuring a musical piece. However, if the composer chooses to use both a 12-tone row and its embedded synthetic scales as co-existent equal frames-of-reference for establishing tonal organization within a musical piece, then the orthodox 12-tone principles and rules are no longer directly relevant, and, in short, are transcended. By looking at a 12-tone row as a network of interlocking (synthetic) diatonic scales the orthodox 12-tone principles and rules no longer directly apply to the ordering of tones, but serve to delineate the natural tonal interrelationships that occur between the 12-tone row's twelve (synthetic) diatonic scales.

Will Be done In late 2005

White Crow Poetry Banner Exchange

Provided By CGISpy.com