# 180edo

 ← 179edo 180edo 181edo →
Prime factorization 22 × 32 × 5
Step size 6.66667¢
Fifth 105\180 (700¢) (→7\12)
Semitones (A1:m2) 15:15 (100¢ : 100¢)
Consistency limit 7
Distinct consistency limit 7
Special properties

180 equal divisions of the octave (abbreviated 180edo or 180ed2), also called 180-tone equal temperament (180tet) or 180 equal temperament (180et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 180 equal parts of about 6.67 ¢ each. Each step represents a frequency ratio of 21/180, or the 180th root of 2.

The equal temperament tempers out 531441/524288 (pythagorean comma) and 30958682112/30517578125 (trisedodge comma) in the 5-limit, as well as 31381059609/30517578125 (mowgli comma) and 274877906944/274658203125 (hemithirds comma); 1029/1024, 3136/3125, and 118098/117649 in the 7-limit.

Using the patent val, it tempers out 540/539, 2835/2816, 4000/3993, and 6912/6875 in the 11-limit; 351/350, 364/363, 1001/1000, and 1701/1690 in the 13-limit. Using the 180e val, it tempers out 385/384, 441/440, 3388/3375, and 216513/214375 in the 11-limit; 351/350, 1188/1183, 1287/1280, 1573/1568, and 3146/3125 in the 13-limit.

### Odd harmonics

Approximation of odd harmonics in 180edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) -1.96 +0.35 -2.16 +2.76 +2.02 -0.53 -1.60 +1.71 +2.49 +2.55 -1.61
Relative (%) -29.3 +5.3 -32.4 +41.3 +30.2 -7.9 -24.0 +25.7 +37.3 +38.3 -24.1
Steps
(reduced)
285
(105)
418
(58)
505
(145)
571
(31)
623
(83)
666
(126)
703
(163)
736
(16)
765
(45)
791
(71)
814
(94)

### Subsets and supersets

180edo is the 11th highly composite edo; its nontrivial subsets are: 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, and 90.