57edo: Difference between revisions
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= | =57 tone equal temperament= | ||
''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|comma]]s: 81/80, 3125/3072 | [[5-limit|5-limit]] [[Comma|comma]]s: 81/80, 3125/3072 | ||
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<u>'''Modes of | <u>'''Modes of 57edo'''</u> | ||
2 1 2 1 2 1 2 1 2 1 1 2 1 2 1 2 1 2 1 2 1 1 2 1 2 1 2 1 2 1 2 1 1 - 3MOS of type 18L 21s (augene) | 2 1 2 1 2 1 2 1 2 1 1 2 1 2 1 2 1 2 1 2 1 1 2 1 2 1 2 1 2 1 2 1 1 - 3MOS of type 18L 21s (augene) | ||