367edo

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← 366edo367edo368edo →
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 367-tone equal temperament (367tet), 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 of 367edo 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 (%) +32 -15 -30 -36 +39 -6 +17 -10 +1 +2 -15
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

Music

Francium