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[October, 2011: Rhythmicon pages archived, no longer updated or maintained.]

The Rhythmicon The Rhythmicon: Harmonic Analysis

The inherent conflict in using the harmonic series as the basis for a compositional system is that the tones of the system are the same as the constituent tones that constitute the sounds themselves. Sounds are a composite of a fundamental and its harmonic partials. The timbre of a sound is determined by the relative volume levels of its partials which usually change at varying rates. There are also, of course, inharmonic partials which are not whole number multiples of the fundamental. These have a great effect on timbre and are evident in many of the sounds used in Rhythmiconic Sections. However this harmonic analysis of the rhythmicon is confined to harmonic, whole number partials.

It is not my intention to create a system of scales or tonalities -- I generally think of pitch in lose "high-middle-low" terms -- but an understanding of the relationships inherent in the harmonic series is important background information and can make a difference in immediate compositional decisions. For example, while the ratios of some common scale degrees are present (for example: 3/2, "perfect fifth"; 5/4, "major third"; and 9/8, ""major second"), others do not appear in the harmonic series (for example: 4/3, "perfect fourth"; 6/5. "minor third").

In addition to the sounds used for the harmonics, which range through simple sounds relatively free of harmonic content to complex harmonically rich samples, the tempo of the rhythmicon is highly relevant. The basic rhythmicon sounding at four seconds to the measure is the maximum speed at which I can hear all 24 harmonics as discrete sounds, and thus the setting of the four second measure as the basic tempo in many of the Rhythmiconic Sections. At faster tempos the harmonics begin to blend. At high speeds, the rhythmicon becomes an exercise in additive synthesis -- a single complex sound that can be varied by changing the volume levels of selected harmonics. At extreme speeds, the rhythmicon crosses the boundary between rhythm and tone and whole new sound qualities emerge. At slower tempos the rhythmical melodic attributes of the rhythmicon begin to reveal themselves. As the tempo continues to slow there comes a point -- about 20 seconds per measure to my ears -- when the harmonics become separate notes, and the rhythmicon begins to lose coherence as a unified entity.

A chart of the intervals (ratios) of the harmonics relative to the fundamental shows that as the harmonics rise in pitch, the ratio of dissonant to consonant tones increases.

I use the terms consonance and dissonance in the psychoacoustical sense -- smaller ratios are consonant, larger ones dissonant -- not in a judgmental sense. The ratios act simply as a guide to desired sound quality though in reality I determine this more by ear than by consulting a chart.

<Structural Analysis----------Multiple Rhythmicons>

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