Superparticular


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Related to Superparticular: Superparticular number

Su`per`par`tic´u`lar


a.1.(Math.) Of or pertaining to a ratio when the excess of the greater term over the less is a unit, as the ratio of 1 to 2, or of 3 to 4.
References in periodicals archive ?
In some cases, such as Lou Harrison's Cinna and Symfony in Free Style and many works by Ezra Sims (who doesn't even consider his method to be strict just intonation), such as his Quintet for clarinet and strings, Elegie nach Rilke and Flight, they have emphasized those higher partials (or superparticular ratios, in Harrison's case) which sound the most unusual to our twelve-note, equal-tempered ears, such as the seventh, eleventh and thirteenth partials (or Harrison's 7/6 minor third, 16/15 minor second and 10/9 major second), and often have de-emphas ized the first through the sixth partials, which sound very unremarkable.
As for those frequent claims which cite no evidence other than merely to assert simple numbers, superparticular ratios, or derivation from the harmonic series (no matter how high up), as guarantors in and of themselves of sonoric superiority, these really just fall into the realm of numerology, and should simply identify themselves as such, rather than as science.
I do not here include the simple image of the scale as a forty-three-step stairway superimposed on a twelve-step stairway, nor the graph of Perpetual Tonal Descent and Ascent, which is drawn to chart the wider field of superparticular ratios from which certain elements are chosen as "secondary ratios" in the formation of his scale.