# 367edo

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 ← 366edo 367edo 368edo →
Prime factorization 367 (prime)
Step size 3.26975¢
Fifth 215\367 (702.997¢)
Semitones (A1:m2) 37:26 (121¢ : 85.01¢)
Consistency limit 5
Distinct consistency limit 5

367 equal divisions of the octave (abbreviated 367edo or 367ed2), also called 367-tone equal temperament (367tet) or 367 equal temperament (367et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 367 equal parts of about 3.27 ¢ each. Each step represents a frequency ratio of 21/367, or the 367th root of 2.

## Theory

367et is only consistent to the 5-odd-limit, with three mappings possible for the 7-limit:

• 367 582 852 1030] (patent val)
• 367 582 852 1031] (367d val)
• 367 582 853 1031] (367cd val)

Using the patent val, it tempers out 15625/15552 and [102 -57 -5 in the 5-limit; 5120/5103 and 40353607/39858075 in the 7-limit.

Using the 367d val, it tempers out 15625/15552 and [102 -57 -5 in the 5-limit; 2460375/2458624 and 2097152/2083725 in the 7-limit.

Using the 367cd val, it tempers out 268435456/263671875 and [33 -34 9 in the 5-limit; 5120/5103, 7558272/7503125 and 235298/234375 in the 7-limit.

### Odd harmonics

Approximation of odd harmonics in 367edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) +1.04 -0.48 -0.98 -1.19 +1.27 -0.20 +0.56 -0.32 +0.03 +0.06 -0.48
Relative (%) +31.9 -14.8 -29.9 -36.2 +38.9 -6.1 +17.1 -9.9 +1.1 +2.0 -14.7
Steps
(reduced)
582
(215)
852
(118)
1030
(296)
1163
(62)
1270
(169)
1358
(257)
1434
(333)
1500
(32)
1559
(91)
1612
(144)
1660
(192)

### Subsets and supersets

367edo is the 73rd prime edo. 1101edo, which triples it, gives a good correction to the harmonic 7.

## Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve Stretch (¢)
Tuning Error
Absolute (¢) Relative (%)
2.3 [582 -367 [367 582]] -0.3288 0.3287 10.05
2.3.5 15625/15552, [102 -57 -5 [367 582 852]] -0.1500 0.3688 11.28

### Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve
Generator* Cents* Associated
Ratio*
Temperaments
1 28\367 91.55 [46 -7 -15 Gross
1 97\367 317.17 6/5 Hanson

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

Francium