# 361edo

 ← 360edo 361edo 362edo →
Prime factorization 192
Step size 3.3241¢
Fifth 211\361 (701.385¢)
Semitones (A1:m2) 33:28 (109.7¢ : 93.07¢)
Consistency limit 9
Distinct consistency limit 9

361 equal divisions of the octave (abbreviated 361edo or 361ed2), also called 361-tone equal temperament (361tet) or 361 equal temperament (361et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 361 equal parts of about 3.32 ¢ each. Each step represents a frequency ratio of 21/361, or the 361st root of 2.

## Theory

361et is consistent to the 9-odd-limit with flat tunings of harmonics 3, 5, and 7. The equal temperament tempers out 4375/4374, 703125/702464, 2460375/2458624, 43046721/43025920, and 48828125/48771072 in the 7-limit. It supports the 5-limit submajor temperament.

### Odd harmonics

Approximation of odd harmonics in 361edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) -0.57 -0.72 -1.51 -1.14 +0.48 +0.47 -1.29 +1.42 +1.66 +1.24 -0.02
Relative (%) -17.1 -21.6 -45.5 -34.3 +14.5 +14.1 -38.8 +42.6 +49.8 +37.3 -0.6
Steps
(reduced)
572
(211)
838
(116)
1013
(291)
1144
(61)
1249
(166)
1336
(253)
1410
(327)
1476
(32)
1534
(90)
1586
(142)
1633
(189)

### Subsets and supersets

361 factors into 192, with 19edo as its only edo subset.

## Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve Stretch (¢)
Tuning Error
Absolute (¢) Relative (%)
2.3 [-572 361 [361 572]] 0.1798 0.1798 5.41
2.3.5 [-36 11 8, [-14 -19 19 [361 572 838]] 0.2230 0.1590 4.78
2.3.5.7 4375/4374, 823543/819200, 2460375/2458624 [361 572 838 1013]] 0.3020 0.1941 5.84

### Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve
Generator* Cents* Associated
Ratio*
Temperaments
1 166\361 551.80 48/35 Emka
19 150\361
(2\361)
498.61
(6.65)
4/3
(225/224)