361edo

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← 360edo361edo362edo →
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 361-tone equal temperament (361tet), 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 of 361edo 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 -22 -46 -34 +15 +14 -39 +43 +50 +37 -1
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)
Enneadecal

* octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct