Harmonisma: Difference between revisions
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created page for the harmonisma |
clarify something that confused me when I read this |
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== Temperaments == | == Temperaments == | ||
Equal temperaments where this comma is tempered with very high accuracy will have an interval corresponding to a "sharp fifth" of (ideally) 706.7 to 706.9 cents, corresponding to the range of fifths from 13/11 * 14/11 on the lower end and 11/9 * 16/13 on the higher end. However, such temperaments are generally very precise, so [[224edo]], [[270edo]] and [[311edo]] offer slightly more manageable tunings. For less accurate temperaments still, 10648/10647 is notable as a comma of [[Subgroup_temperaments#Parapyth_.28Rank_3.29|parapyth]]. | Equal temperaments where this comma is tempered with very high accuracy will have an interval corresponding to a "sharp fifth" of (ideally) 706.7 to 706.9 cents, corresponding to the range of fifths from 13/11 * 14/11 on the lower end and 11/9 * 16/13 on the higher end. (This interval is not mapped to 3/2.) However, such temperaments are generally very precise, so [[224edo]], [[270edo]] and [[311edo]] offer slightly more manageable tunings. For less accurate temperaments still, 10648/10647 is notable as a comma of [[Subgroup_temperaments#Parapyth_.28Rank_3.29|parapyth]]. | ||
[[Category:13-limit]] | [[Category:13-limit]] | ||
[[Category:Unnoticeable comma]] | [[Category:Unnoticeable comma]] | ||
[[Category:Interval ratio]] | [[Category:Interval ratio]] | ||
Revision as of 19:33, 16 June 2021
| Interval information |
reduced
10648/10647, the harmonisma, is a no-5's 13-limit unnoticeable comma of about 0.1626 cents. It is equal to (16/13 * 11/9)/(14/11 * 13/11).
Temperaments
Equal temperaments where this comma is tempered with very high accuracy will have an interval corresponding to a "sharp fifth" of (ideally) 706.7 to 706.9 cents, corresponding to the range of fifths from 13/11 * 14/11 on the lower end and 11/9 * 16/13 on the higher end. (This interval is not mapped to 3/2.) However, such temperaments are generally very precise, so 224edo, 270edo and 311edo offer slightly more manageable tunings. For less accurate temperaments still, 10648/10647 is notable as a comma of parapyth.