57edo: Difference between revisions

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~~'''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]].

== Theory ==

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]]

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[[11-limit|11-limit]] commas: [[99/98]], [[385/384]], [[441/440]], [[625/616]]

==~~Just approximation~~==

===Odd harmonics===

==Intervals==

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 {{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&amp;57 temperament [[Sensipent_family|Heinz]].
+{{EDO intro|57}}
+== Theory ==
+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&amp;57 temperament [[Sensipent_family|Heinz]].
 [[5-limit|5-limit]] [[comma]]s: [[81/80]], [[3125/3072]]
@@ Line 8: / Line 10: @@
 [[11-limit|11-limit]] commas: [[99/98]], [[385/384]], [[441/440]], [[625/616]]
-==Just approximation==
+===Odd harmonics===
-{{Primes in edo|57}}
+{{harmonics in equal|57}}
 ==Intervals==