31edo: Difference between revisions

BudjarnLambeth (talk | contribs)
BudjarnLambeth (talk | contribs)
Basic theory: Restored prime harmonics table to default number of columns (not sure why there were less than usual. If there was a reason why, then feel free to change it back)
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== Basic theory ==
== Basic theory ==
{{Harmonics in equal|31|columns=9}}
{{Harmonics in equal|31}}


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 the fact that it equates 14/11 with 9/7 and 11/8 with 15/11 could potentially be considered too much tuning damage. Many [[7-limit]] JI scales are well-approximated in 31 (with tempering, of course).
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 the fact that it equates 14/11 with 9/7 and 11/8 with 15/11 could potentially be considered too much tuning damage. Many [[7-limit]] JI scales are well-approximated in 31 (with tempering, of course).