# 364edo

 ← 363edo 364edo 365edo →
Prime factorization 22 × 7 × 13
Step size 3.2967¢
Fifth 213\364 (702.198¢)
Semitones (A1:m2) 35:27 (115.4¢ : 89.01¢)
Consistency limit 21
Distinct consistency limit 21

364 equal divisions of the octave (abbreviated 364edo or 364ed2), also called 364-tone equal temperament (364tet) or 364 equal temperament (364et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 364 equal parts of about 3.3 ¢ each. Each step represents a frequency ratio of 21/364, or the 364th root of 2.

## Theory

364edo is consistent through the 21-odd-limit. The equal temperament tempers out 1600000/1594323 (amity comma) and [-65 0 28 (oquatonic comma) in the 5-limit; 65625/65536 (horwell comma), 390625/388962 (dimcomp comma), and 420175/419904 (wizma) in the 7-limit (supporting fifthplus and oquatonic); 1375/1372, 6250/6237, 19712/19683, and 41503/41472 in the 11-limit (as well as 9801/9800); 625/624, 1716/1715, 2080/2079, 2200/2197, and 14641/14625 in the 13-limit (as well as 4096/4095, 4225/4224, and 10985/10976); 715/714, 1089/1088, 1225/1224, 1275/1274, 2025/2023, and 8624/8619 in the 17-limit (as well as 2431/2430, 4914/4913, and 5832/5831); 1216/1215, 1331/1330, 1540/1539, and 1729/1728 in the 19-limit.

### Prime harmonics

Approximation of prime harmonics in 364edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.00 +0.24 -0.60 +0.40 -0.77 +0.13 +0.54 -0.81 +1.40 -1.01 -1.08
Relative (%) +0.0 +7.4 -18.2 +12.3 -23.3 +4.0 +16.4 -24.6 +42.3 -30.5 -32.7
Steps
(reduced)
364
(0)
577
(213)
845
(117)
1022
(294)
1259
(167)
1347
(255)
1488
(32)
1546
(90)
1647
(191)
1768
(312)
1803
(347)

### Subsets and supersets

Since 364 factors into 22 × 7 × 13, 364edo has subset edos 2, 4, 7, 13, 14, 26, 28, 52, 91, 182.

### Miscellaneous properties

364edo can act as "pseudo-24024edo" in a sense that it can replicate being a multiple of 11edo, 12edo, 13edo and 14edo. It has 13 and 14 as its divisors, while at the same time supporting the Supermajor[11] scale from 91edo, which is a very precise temperament, and WorldCalendar[12] scale, which mimics 12edo. While it does not exactly replicate 11edo and 12edo, it comes close enough in harmonic parameters these edos are sought after.

## Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve Stretch (¢)
Tuning Error
Absolute (¢) Relative (%)
2.3 [577 -364 [364 577]] -0.0766 0.0766 2.32
2.3.5 1600000/1594323, [-65 0 28 [364 577 845]] +0.0350 0.1698 5.15
2.3.5.7 65625/65536, 390625/388962, 420125/419904 [364 577 845 1022]] -0.0098 0.1662 5.04
2.3.5.7.11 1375/1372, 6250/6237, 19712/19683, 41503/41472 [364 577 845 1022 1259]] +0.0366 0.1753 5.32
2.3.5.7.11.13 625/624, 1375/1372, 2080/2079, 2200/2197, 14641/14625 [364 577 845 1022 1259 1347]] +0.0245 0.1622 4.92
2.3.5.7.11.13.17 625/624, 715/714, 1089/1088, 1225/1224, 2025/2023, 2200/2197 [364 577 845 1022 1259 1347 1488]] +0.0022 0.1599 4.85
2.3.5.7.11.13.17.19 625/624, 715/714, 1089/1088, 1216/1215, 1225/1224, 1331/1330, 1729/1728 [364 577 845 1022 1259 1347 1488 1546]] +0.0257 0.1620 4.91

### Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve
Generator* Cents* Associated
Ratio*
Temperaments
1 103\364 339.56 243/200 Amity / paramity
1 125\364 412.09 80/63 Witch
1 149\364 491.21 3645/2744 Fifthplus
1 151\364 497.80 4/3 Gary
2 57\364 187.91 49/44 Semiwitch
4 30\364 98.90 18/17 World calendar
13 151\364
(11\364)
497.80
(36.26)
4/3
(?)
Aluminium
26 151\364
(11\364)
497.80
(36.26)
4/3
(?)
Iron
28 151\364
(5\364)
497.80
(16.48)
4/3
(105/104)
Oquatonic
91 151\364
(3\364)
497.80
(3.30)
4/3
(176/175)
Protactinium

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

## Scales

• WorldCalendar[12]: 31 30 30 31 30 30 31 30 30 31 30 30