365edo
| ← 364edo | 365edo | 366edo → |
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
| 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 (%) | +49 | +50 | +32 | -2 | +31 | +34 | -2 | +8 | -49 | -20 | -10 | |
| Steps (reduced) |
579 (214) |
848 (118) |
1025 (295) |
1157 (62) |
1263 (168) |
1351 (256) |
1426 (331) |
1492 (32) |
1550 (90) |
1603 (143) |
1651 (191) | |
365edo does not have good harmonics of 3, 5, 7 and as such could benefit from octave stretching. In the 2.5/3.9.15 subgroup, it can be regarded as every other step of 730edo, with one step amounting to two Woolhouse units.
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, 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.