38edo: Difference between revisions

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Revision as of 10:20, 6 December 2020 view source Xenwolf (talk \| contribs) autopatrolled, Bureaucrats, confirmaccount-notify, Interface administrators, Sysops 8,705 edits m cat fixed ← Older edit		Revision as of 10:34, 6 December 2020 view source Xenwolf (talk \| contribs) autopatrolled, Bureaucrats, confirmaccount-notify, Interface administrators, Sysops 8,705 edits m improved linking, added 3 digits to cent size in the intro to be consistent with the interval table, a better solution would be to reduce all of these phone numbers. Newer edit →
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	'''38edo''' divides the octave into 38 equal parts of 31.~~579~~ [[cent~~\|cents~~]]. Since 38 = 2*19, it can be thought of as two parallel [[19edo~~\|19edos~~]]. It [[~~tempering_out\|~~tempers out]] the same [[5-limit]] commas as [[19edo~~\|19]]~~, namely 81/80, 3125/3072 and 15625/15552. In the [[7-limit]], we can add 50/49, and tempering out 81/80 and 50/49 gives [[~~Meantone_family\|~~injera ~~temperament~~]], for which 38 is the [[~~Optimal_patent_val\|~~optimal patent val]]. In the [[11-limit]], we can add 121/120 and 176/175.		'''38edo''' divides the octave into 38 equal parts of 31.578947 [[cent]]s. Since 38 = 2*19, it can be thought of as two parallel [[19edo]]s. It [[tempers out]] the same [[5-limit]] commas as 19edo, namely [[81/80]], [[3125/3072]] and [[15625/15552]]. In the [[7-limit]], we can add [[50/49]], and tempering out 81/80 and 50/49 gives [[injera]] temperament, for which 38 is the [[optimal patent val]]. In the [[11-limit]], we can add 121/120 and 176/175.

	== Intervals ==		== Intervals ==