Chapters

6.1.Fifth-repeating modes, fourth-repeating modes (tetraphonia, triphonia)

in the Third Percussion Concerto and A Seasong

An aspect which is particular to this concerto is the application of the fifth-repeating modes of the Byzantine medieval modal system, as described by Mechkova.^{146 (click)}  (See also Chapter 4.1.) Although the reform of Chrysanthos introduced a general octave-based theoretical thinking in the Post-Byzantine tradition^{147 (click)}  (and such thinking does prevail both in the theory and the practice of this tradition today), he does nevertheless mention the fifth-repeating and fourth-repeating modes in his treatise ^{148 (click)} (albeit somewhat unclearly). Despite that imposition of a newer octave-based theoretical framework, the fifth-repeating modes do exist in the practice today, and a standard singers’ manual would give you the scale of the Sixth Tone as in the following example:

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Figure 29: The scale of the 6th Tone in contemporary Eastern Chant, as to be found in contemporary singers’ manuals. (e.g.: Metodi Grigorov, 2005; Petar Dinev, etc.).

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This however is not explained today with the principle of fifth-repeating modes (Chapter 4.1), as reconstructed uniquely in Mechkova’s research. Instead an octave-based description is given, in which ‘certain degrees are altered differently in the different octaves’. Although Mechkova’s description, which is based on an extensive research of primary sources, makes much more sense, I have been curious about the perceptual and cognitive basis for such modes, as octave similarity and respectively octave cyclicity in scalar constructions is claimed by the majority of music psychologists as ubiquitous.^{149 (click)    150 (click)} Sethares posits, however, that there are world cultures that use scales/modes that are not octave-repeating in their scalar structure and furthermore he establishes a connection between that fact and the nature of the spectrum of the instruments these cultures use.^{151 (click)}  In his opinion the scalar structures used by a culture is a function of the spectral structure of the timbres of the instruments in use in that culture.^{152 (click)}  That is because scales and tunings are constructed in such a way that the optimum perceptual consonance is sought, which itself is determined by the partials of the timbre of the instruments.^{153 (click)}  Therefore the optimum scales for the Western classical tradition are determined by the harmonic spectrum of the human voice and the instruments used in our tradition.^{154 (click)}  (See also Chapter 2.1.) It is true that in Eastern Chant the only timbre used is the human voice and it has a harmonic spectrum. Therefore the octave cyclicity of modes should be just as ubiquitous as it is in the Western tradition. However, research by Födermayr and Deutsch on the psychoacoustic significance of the Ison in Bulgarian Chant^{155 (click)}  has shown that the particular strength of the sixth partial, the physical absence of the fundamental and a particular kind of masking in the process of movement of the chant melody contour, create a very strong psychoacoustic ‘framing’ through the interval of perfect fifth. In their opinion this shapes and ‘anchors’ the harmonic content of the chant^156(click)  which in my view determines the structure and cyclicity of the mode in this case. Because I would add that in the living practice of singing the chants at church, when the chant develops above the fifth degree of the mode, the Ison will be repositioned to that fifth degree, as it will then become the first degree of the next cycle of the fifth-repeating mode. Thus the new Ison would frame with its overtones the next fifth up, forming the next – upper cycle of the fifth-repeating mode. That might be one of the perceptual reasons for the existence of these fifth-repeating modes in Eastern Chant, from a psychoacoustic/psychological/perceptual/cognitive perspective.

Another reason might be the fact, that with the establishment of modal centre through linear means (Chapter 4.2), any kind of disposition of centres, and respectively – cyclicity of modes could be established within this monophonic context (Chapter 4.2). This could account also for the fourth-repeating modes in Eastern Chant (triphonia), and the diphonia etc.. ^{157 (click)}

Nevertheless, these modes are attributes of the monophonic nature of this tradition, and I have puzzled for a long time whether these could be applied to a non-monophonic, multi-voiced (polyphonic, heterophonic etc.) context in my music, having in mind also that the harmonic timbre of the instruments of the Symphony Orchestra makes the octave very important perceptually, and I use octave doublings extensively, which both have implications for the possibilities for cyclicity of modes employed.

I have attempted to use fifth-repeating modes for the first time in the last movement of the 3rd Percussion Concerto, bars 359-383 (Example 15), which is an extended passage. It is quite an important passage, as it is positioned by the very end of the concerto. The background morphomodal network for that passage of 24 bars could be summarized to its briefest as follows:

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Figure 30: Percussion Concerto No.3, b. 359-383 – the morphomodal network (very brief summary). Full Score and recording in Example 15.

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The passage is supported by multiple Isons (drones), situated at the modal centre in each of the cycles of the mode, in this case – a fifth apart, and designated by white noteheads in Figure 30. A significant number of scale degrees are fluctuated continuously, as designated by black noteheads and wavy lines. (The reader is refered to Chapter 1.2 for description of fluctuation.) There are two scale degrees, different from the modal centres, which are not fluctuated, given in diamond noteheads. The fluctuation of so many scale degrees perhaps obscures the percept of fifth-repeating mode to some extent, but these fluctuations are important musically for such an extended passage in a single mode, and altogether this musical passage is not intended as a laboratory experiment. Therefore I followed the needs of the musical development. Despite that, and the fact that the fifth-repeating mode might be therefore less distinct from an octave-repeating mode in this particular context, the harmony in this passage does sound unique to some extent. Also, when the fifth-repeating mode is transformed into an octave-repeating mode in bar 383, an audible transformation of the character of harmony is evident, although the texture does not alter significantly, which appears to me as significant in the line of the present discussion.

Furthermore, I have also used fifth-repeating, as well as fourth-repeating modes in the symphonic piece A Seasong which I composed soon after the 3rd Concerto. From letter F onwards in that work (Example 4) an octave-repeating mode is morphed into a fifth-repeating mode, which is then morphed into a fourth-repeating mode, contracting further into a stack of thirds and then into a single modal cluster, spanning a major third (as summarized in Figure 31)(Full Score excerpt and Sound Recording in Example 4 (excerpt starts earlier than bar 58).)

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Figure 31: A Seasong, bars 58-79 – morphomodal network. )(Full Score and Sound Recording in Example 4).

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I have also used fifth-repeating modes in the form of vertical modal clusters in both the Third Percussion Concerto (e.g. bb.110-117) (Example 3) and A Seasong (e.g. bb. 44-48) (Example 4).

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7.Apocalyptic Passacaglia on a Theme by John Cage

‘rhythm box rhythm’, Fibonacci, Fontana, visuals, silence, cuts, war

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