# 365edo

 ← 364edo 365edo 366edo →
Prime factorization 5 × 73
Step size 3.28767¢
Fifth 214\365 (703.562¢)
Semitones (A1:m2) 38:25 (124.9¢ : 82.19¢)
Dual sharp fifth 214\365 (703.562¢)
Dual flat fifth 213\365 (700.274¢)
Dual major 2nd 62\365 (203.836¢)
Consistency limit 7
Distinct consistency limit 7

365 equal divisions of the octave (abbreviated 365edo or 365ed2), also called 365-tone equal temperament (365tet) or 365 equal temperament (365et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 365 equal parts of about 3.29 ¢ each. Each step represents a frequency ratio of 21/365, or the 365th root of 2.

## Theory

365edo is consistent to the 7-odd-limit, but both harmonics 3 and 5 are about halfway between its steps. As every other step of 730edo, it is suitable for a 2.9.15 subgroup interpretation, in which case it is identical to 730edo.

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, and hereby tunes the hemiwürschmidt temperament. In the 11-limit, it tempers out 3025/3024, 3388/3375, 14641/14580; in the 13-limit, 352/351, 1001/1000, and 1716/1715.

### Odd harmonics

Approximation of odd harmonics in 365edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) +1.61 +1.63 +1.04 -0.07 +1.01 +1.12 -0.05 +0.25 -1.62 -0.64 -0.33
Relative (%) +48.9 +49.6 +31.5 -2.3 +30.7 +34.0 -1.5 +7.6 -49.4 -19.6 -10.0
Steps
(reduced)
579
(214)
848
(118)
1025
(295)
1157
(62)
1263
(168)
1351
(256)
1426
(331)
1492
(32)
1550
(90)
1603
(143)
1651
(191)

### Subsets and supersets

Since 365 factors into 5 × 73, 365edo contains 5edo and 73edo as subsets. A step of 365edo is exactly 2 Woolhouse units (2\730).

### Miscellaneous properties

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. A comma basis for the 365eeffgghiii val in the 23-limit is {256/255, 300/299, 352/351, 456/455, 896/891, 1225/1224, 3136/3125, 13608/13585}.