31edo: Difference between revisions
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== Basic theory == | == Basic theory == | ||
{| | {{Odd harmonics in edo|edo=31}} | ||
31edo perfect fifth is flat of the just interval 3/2 (over five cents), as befits a tuning 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]], although the fact that it equates 14/11 with 9/7, and 11/8 with 15/11, may be too off for some. Many [[7-limit]] JI scales are well-approximated in 31 (with tempering, of course). | 31edo perfect fifth is flat of the just interval 3/2 (over five cents), as befits a tuning 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]], although the fact that it equates 14/11 with 9/7, and 11/8 with 15/11, may be too off for some. Many [[7-limit]] JI scales are well-approximated in 31 (with tempering, of course). | ||