365edo: Difference between revisions

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== Theory ==

365edo does not have good harmonics of 3, 5, 7 and as such could benefit from octave stretching.

365edo does not have good harmonics of 3, 5, 7 and as such could benefit from octave stretching. In the 2.9.15 subgroup, it can be regarded as every other step of [[730edo]], with one step amounting to two [[Woolhouse unit]]s.

Nonetheless, it does temper out [[2401/2400]], [[3136/3125]] and [[6144/6125]] on the patent val in the 7-limit, with an optimal stretch of -0.52 cents. In the 11 limit, 365edo tempers out [[3025/3024]], 3388/3375, 14641/14580. In 13-limit it tempers out 352/351, 1001/1000, and 1716/1715. In the 23-limit it tempers out 595/594, 1496/1495, 1729/1725, 3136/3135 in the 23-limit.

=== Relationship to the length of the year ===

An octave stretch of -0.796 cents would compress 365edo to an interesting intepretation: the pure 2/1 would represent 365.24219edo, which is the length of solar days in a tropical year. In 23-limit, 365eeffgghiii val's octave stretch of -0.79428 cents is very close, and makes 2/1 correspond to 365.241917 days, or 365 days 5h 48m 21.7s, which is only about 20 seconds short of the tropical year in the present era. Such a temperament eliminates 300/299, 875/874, 1729/1725, 3060/3059, 4235/4232.

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 == Theory ==
 {{Harmonics in equal|365}}
-edo does not have good harmonics of 3, 5, 7 and as such could benefit from octave stretching.
+edo does not have good harmonics of 3, 5, 7 and as such could benefit from octave stretching. In the 2.9.15 subgroup, it can be regarded as every other step of [[730edo]], with one step amounting to two [[Woolhouse unit]]s.
 Nonetheless, it does temper out [[2401/2400]], [[3136/3125]] and [[6144/6125]] on the patent val in the 7-limit, with an optimal stretch of -0.52 cents. In the 11 limit, 365edo tempers out [[3025/3024]], 3388/3375, 14641/14580. In 13-limit it tempers out 352/351, 1001/1000, and 1716/1715. In the 23-limit it tempers out 595/594, 1496/1495, 1729/1725, 3136/3135 in the 23-limit.
+=== Relationship to the length of the year ===
 An octave stretch of -0.796 cents would compress 365edo to an interesting intepretation: the pure 2/1 would represent 365.24219edo, which is the length of solar days in a tropical year. In 23-limit, 365eeffgghiii val's octave stretch of -0.79428 cents is very close, and makes 2/1 correspond to 365.241917 days, or 365 days 5h 48m 21.7s, which is only about 20 seconds short of the tropical year in the present era. Such a temperament eliminates 300/299, 875/874, 1729/1725, 3060/3059, 4235/4232.