365edo

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← 364edo365edo366edo →
Prime factorization 5 × 73
Step size 3.28767¢
Fifth 214\365 (703.562¢)
Semitones (A1:m2) 38:25 (124.9¢ : 82.19¢)
Sharp fifth 214\365 (703.562¢)
Flat fifth 213\365 (700.274¢)
Major 2nd 62\365 (203.836¢)
Consistency limit 7
Distinct consistency limit 7

The 365 equal divisions of the octave (365edo), or the 365(-tone) equal temperament (365tet, 365et) when viewed from a regular temperament perspective, divides the octave into 365 equal parts of about 3.29 cents each.

Theory

Approximation of odd harmonics in 365edo
Harmonic 3 5 7 9 11 13 15 17 19 21
Error absolute (¢) +1.61 +1.63 +1.04 -0.07 +1.01 +1.12 -0.05 +0.25 -1.62 -0.64
relative (%) +49 +50 +32 -2 +31 +34 -2 +8 -49 -20
Steps
(reduced)
579
(214)
848
(118)
1025
(295)
1157
(62)
1263
(168)
1351
(256)
1426
(331)
1492
(32)
1550
(90)
1603
(143)

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

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.

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.

Approaches