

[October, 2011: Rhythmicon pages archived, no longer updated or maintained.] 



There is no reason to limit the music of the rhythmicon to a fixed fundamental sounding at a fixed tempo. In "Positions of Effective Proximity", for example, I used rhythmicon sounds in which both the tempo and internal pitch relationships vary through time. For Rhythmiconic Sections I thought initially to vary the fundamental and tempo of a single rhythmicon, as was possible with Theremin's instrument, but a more elegant and musically satisfying solution was to posit multiple rhythmicons. Taking Cowell's idea of "polyharmony" as a cue  that each harmonic of a given harmonic series is itself the fundamental of a new series  I devised a set of 24 theoretical rhythmicons. Each harmonic of the basic rhythmicon (R1) is the fundamental of a new rhythmicon. Thus the second harmonic of R1 becomes the fundamental of the second rhythmicon: R1/H2 = R2/H1; the third harmonic of R1 becomes the fundamental of the third rhythmicon: R1/H3 = R3/H1; and so on through R1/H24 = R24/H1. Using 65.406 hz as the fundamental of R1 in this ever rising scenario, the limits of human hearing are reached (about 20k hz) long before the higher rhythmicons reach their 24th harmonic. For example, R21/H14 is 19229.364 hz and R24/H12 is 18836.928 hz. I added R0, the "bass rhythmicon", with a fundamental one octave below R1 at 32.703 hz. R0 adds weight to the system and helps close the rather large frequency gaps at the low end of R1. This completed the set of 25 rhythmicons. Since, as mentioned before, I am not creating a scale or a system of tonalities, I accepted the still comparatively wide gaps among the lower tones as an inherent quality of the rhythmicon and composed Rhythmiconic Sections accordingly. It would, of course, be possible to start the whole thing at some very low frequency  say one Hz  and build the system from there, thus filling these gaps. This has been done for some works completed after Rhythmiconic Sections. Many observations about patterns and relationships among the harmonics, ratios and cents can be made upon examining a chart of all the humanly discernible harmonics of R0 through R24.
I will leave these observations to you. Playing with the numbers soon becomes a game of obsessive numerology of questionable musical value. To me, this chart is a reference, a generator of ideas, a resource for solving tonal problems, etc., not a prescriptive system. Rhythmically, the basic rhythmiconic idea of whole number multiples of basic units applies nicely to multiple rhythmicons, in this case inversely so with each R lasting a fraction of the length of R1. If an R1 measure lasts four seconds, an R2 measure lasts two seconds: R1 * 1/2; an R3 measure lasts 1.333... seconds: R1 * 1/3; and so on through R24 at 0.1666... seconds per measure: R1 * 1/24. R0 is twice as slow at eight seconds: R1 * 2. The length of the measure of each R is thus equivalent to the length of the beat of the harmonic of R1 that is the fundamental of that R. For example, an entire measure of R8 would complete between successive beats of R1/H8. R1/H8 = R8/H1 both in frequency and time.
Any subset of the 25 rhythmicons, and any subsets of their harmonics, can be treated according to the methods described under Structural Analysis. The multiple rhythmicons provide a rich, challenging and delightful playground for musical composition. <Harmonic AnalysisCompositional Methods>  




