57edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
'''57edo''' divides the [[Octave|octave]] into 57 parts of size 21.053¢. It can be used to tune [[Mothra_temperament|mothra temperament]], and is an excellent tuning for the 2.5/3.7.11.13.17.19 [[just_intonation_subgroup|just intonation subgroup]]. One way to describe 57 is that it has a [[5-limit|5-limit]] part consisting of three versions of 19, plus a no-threes no-fives part which is much more accurate. A good generator to exploit the 2.5/3.7.11.13.17.19 aspect of 57 is the approximate 11/8, which is 26\57. This gives the [[19-limit|19-limit]] 46&57 temperament [[Sensipent_family|Heinz]]. | '''57edo''' divides the [[Octave|octave]] into 57 parts of size 21.053¢. It can be used to tune [[Mothra_temperament|mothra temperament]], and is an excellent tuning for the 2.5/3.7.11.13.17.19 [[just_intonation_subgroup|just intonation subgroup]]. One way to describe 57 is that it has a [[5-limit|5-limit]] part consisting of three versions of 19, plus a no-threes no-fives part which is much more accurate. A good generator to exploit the 2.5/3.7.11.13.17.19 aspect of 57 is the approximate [[11/8]], which is 26\57. This gives the [[19-limit|19-limit]] 46&57 temperament [[Sensipent_family|Heinz]]. | ||
[[5-limit|5-limit]] [[comma]]s: 81/80, 3125/3072 | [[5-limit|5-limit]] [[comma]]s: [[81/80]], [[3125/3072]] | ||
[[7-limit|7-limit]] commas: 81/80, 3125/3072, 1029/1024 | [[7-limit|7-limit]] commas: 81/80, 3125/3072, [[1029/1024]] | ||
[[11-limit|11-limit]] commas: 99/98, 385/384, 441/440, 625/616 | [[11-limit|11-limit]] commas: [[99/98]], [[385/384]], [[441/440]], [[625/616]] | ||
==Just approximation== | ==Just approximation== | ||