Hey folks, wondering if anyone’s come across a musical structure like this before: It’s based on arithmetic puns, specifically of interesting near-equalities of sums of fractions. The best example I’ve discovered so far is that 1 ~= 1/3 + 1/5 + 1/7 + 1/11 + 1/13 + 1/17 + 1/19 + 1/23. In other words, the unit fractions with the second through ninth primes as their denominators sum to within about a musically imperceptible thousandth of 1. What can be done musically with this? I’ve been focusing mostly on rhythm myself so far, a special polyrhythm — in this case an octorhythm of whole triplets against whole quintuplets against whole septuplets ... against whole vigintitriplets — where initial onsets are offset from each other so that when considered together they produce an additional ninth repeating structure: an ostinato built out of one accented note from each rhythm set end-to-end. It’s a continuous contour, but erratic: each of its notes have a different duration, and none of them are multiples of another’s duration. To be clear, this emergent ostinato is possible because one member from each of the eight steady pulse streams sums to the same metrical duration of which each of the eight steady pulse streams are different integer divisions. (And in the background as side-effect, the offsetting of the polyrhythms avoids the distinctive massively-polyrhythmic texture from Ivess Universe Symphony, and avoids the case of all eight rhythms striking simultaneously.) However I am looking at implementing an analogous tuning on this beast. Meter : octave :: duration : pitch, I mean. The eight-note tuning would have eight different intervals: 1/3 of the octave, 1/5 of the octave, … 1/23 of the octave. One could bind either pitch or interval to the note durations, i.e. either every note of duration 1/3 of a meter would always have the same pitch, or maybe every note of duration 1/3 of a meter would increment the pitch up or down by 1/3 of an octave (latter case would obviously lead to more chaotic/chromatic harmonics). Anyway, I haven’t been able to find any examples of folks trying a technique like this out — feedback very welcome!
Posted on: Sun, 21 Sep 2014 18:17:50 +0000
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