1-3-9-17 by 19/16 bihexany: Difference between revisions

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1 3 9 17 by 19/16 2-combination Bihexany
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Latest revision as of 19:15, 21 November 2025

Circle diagram.

A 19-odd-limit Bihexany. This creates a scale of 1 17/16 9/8 19/16 323/256 171/128 17/12 3/2 51/32 323/192 57/32 969/512 2/1, with steps of 17/16 18/17 19/18 17/16 18/17 544/513 18/17 17/16 19/18 18/17 17/16 1024/969. Since the base hexany maps closely to a subset of 12edo comprised of two equidistant clusters, offsetting two copies of it by 19/16 turns this into a highly accurate detemper of 12edo, with no note deviating by more than 7 cents. It has 8 perfect fifths, many clusters of the harmonic sequence that make close voicings noticeably more consonant and the closest thing to a wolf fifth is the 690.6 cent one between Ab-Eb. As such it's not particularly useful if you want to explore the more adventurous reaches of xenharmony, but it does demonstrate just how well 12edo approximates this subset of the harmonic sequence, which was a significant contributor to it becoming the dominant system of tuning across the world.

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