# 363edo

 ← 362edo 363edo 364edo →
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

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

Approximation of odd harmonics in 363edo
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 (%) -34.1 +14.0 -7.0 +31.7 +22.6 -26.0 -20.1 +25.1 +0.2 -41.1 -5.3
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.