31edo: Difference between revisions
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== Basic theory == | == Basic theory == | ||
{{Harmonics in equal|31|prec=2}} | {{Harmonics in equal|31|prec=2||columns=16}} | ||
31edo's perfect fifth is flat of the just interval 3/2 (over five cents), as befits a tuning [[support|supporting]] [[meantone]], but the major third is less than a cent sharp (of just 5/4), making it slightly sharp of [[quarter-comma meantone]]. 31's approximation of 7/4, a cent flat, is also very close to just. It is a very tone-efficient melodic approximation of the [[11-limit]] (and specifically the [[11-odd-limit]]), although it conflates 9/7 with 14/11 and 11/8 with 15/11. Many [[7-limit]] JI scales are well-approximated in 31 (with tempering, of course). It also maps all [[15-odd-limit]] intervals consistently, with the sole exceptions of 13/9, 13/11, 18/13, and 22/13. | 31edo's perfect fifth is flat of the just interval 3/2 (over five cents), as befits a tuning [[support|supporting]] [[meantone]], but the major third is less than a cent sharp (of just 5/4), making it slightly sharp of [[quarter-comma meantone]]. 31's approximation of 7/4, a cent flat, is also very close to just. It is a very tone-efficient melodic approximation of the [[11-limit]] (and specifically the [[11-odd-limit]]), although it conflates 9/7 with 14/11 and 11/8 with 15/11. Many [[7-limit]] JI scales are well-approximated in 31 (with tempering, of course). It also maps all [[15-odd-limit]] intervals consistently, with the sole exceptions of 13/9, 13/11, 18/13, and 22/13. | ||