363edo
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Prime factorization
3 × 112
Step size
3.30579¢
Fifth
212\363 (700.826¢)
Semitones (A1:m2)
32:29 (105.8¢ : 95.87¢)
Dual sharp fifth
213\363 (704.132¢) (→71\121)
Dual flat fifth
212\363 (700.826¢)
Dual major 2nd
62\363 (204.959¢)
Consistency limit
7
Distinct consistency limit
7
| ← 362edo | 363edo | 364edo → |
363 equal divisions of the octave (abbreviated 363edo or 363ed2), also called 363-tone equal temperament (363tet) or 363 equal temperament (363et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 363 equal parts of about 3.31 ¢ each. Each step represents a frequency ratio of 21/363, or the 363rd root of 2.
Uinsg the patent val, the equal temperament tempers out 2401/2400 and 78732/78125 in the 7-limit; 243/242, 441/440 and 540/539 in the 11-limit; 351/350, 1716/1715 and 1575/1573 in the 13-limit; and provides the optimal patent val for jovis temperament.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | -1.13 | +0.46 | -0.23 | +1.05 | +0.75 | -0.86 | -0.67 | +0.83 | +0.01 | -1.36 | -0.18 |
| relative (%) | -34 | +14 | -7 | +32 | +23 | -26 | -20 | +25 | +0 | -41 | -5 | |
| Steps (reduced) |
575 (212) |
843 (117) |
1019 (293) |
1151 (62) |
1256 (167) |
1343 (254) |
1418 (329) |
1484 (32) |
1542 (90) |
1594 (142) |
1642 (190) | |
Subsets and supersets
Since 363 factors into 3 × 112, 363edo has subset edos 3, 11, 33, and 121.