Porcupine family: Difference between revisions
Cmloegcmluin (talk | contribs) "optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence |
Mousemambo (talk | contribs) modified first line to indicate this is a temperament family |
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The [[5-limit]] parent [[comma]] | The porcupine family is the [[rank]]-2 [[Temperament_families_and_clans|family of temperaments]] whose [[5-limit]] parent [[comma]] is [[250/243]], also called the maximal diesis or porcupine comma. | ||
Its [[monzo]] is {{monzo| 1 -5 3 }}, and flipping that yields {{multival| 3 5 1 }} for the [[wedgie]]. This tells us the [[generator]] is a minor whole tone, the [[10/9]] interval, and that three of these add up to a perfect fourth ([[4/3]]), with two more giving the minor sixth ([[8/5]]). In fact, (10/9)<sup>3</sup> = 4/3 × 250/243, and (10/9)<sup>5</sup> = 8/5 × (250/243)<sup>2</sup>. [[22edo|3\22]] is a very recommendable generator, and [[mos scale]]s of 7, 8 and 15 notes make for some nice scale possibilities. | |||
Notice 250/243 = ([[55/54]])([[100/99]]), the temperament thus extends naturally to the 2.3.5.11 [[subgroup]], sometimes known as ''porkypine''. | Notice 250/243 = ([[55/54]])([[100/99]]), the temperament thus extends naturally to the 2.3.5.11 [[subgroup]], sometimes known as ''porkypine''. | ||