# 373edo

 ← 372edo 373edo 374edo →
Prime factorization 373 (prime)
Step size 3.21716¢
Fifth 218\373 (701.34¢)
Semitones (A1:m2) 34:29 (109.4¢ : 93.3¢)
Consistency limit 15
Distinct consistency limit 15

373 equal divisions of the octave (abbreviated 373edo or 373ed2), also called 373-tone equal temperament (373tet) or 373 equal temperament (373et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 373 equal parts of about 3.22 ¢ each. Each step represents a frequency ratio of 21/373, or the 373rd root of 2.

## Theory

373edo is distinctly consistent to the 15-odd-limit. It has a flat tendency, with harmonics 3 through 13 all tuned flat. The equal temperament tempers out [8 14 -13 (parakleisma) and [-51 19 9 (untriton comma) in the 5-limit; 2401/2400 (breedsma), 65625/65536 (horwell comma), and 43046721/42875000 in the 7-limit; 3025/3024, 8019/8000, 24057/24010, and 496125/495616 in the 11-limit; 729/728, 1001/1000, 1716/1715, 4225/4224, and 10648/10647 in the 13-limit, enabling squbemic chords and sinbadmic chords. It supports the hemitert temperament.

### Prime harmonics

Approximation of prime harmonics in 373edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.00 -0.61 -0.25 -0.46 -1.18 -0.85 +1.21 -1.53 -0.93 -0.09 +0.27
Relative (%) +0.0 -19.1 -7.9 -14.3 -36.8 -26.4 +37.6 -47.7 -28.9 -2.7 +8.5
Steps
(reduced)
373
(0)
591
(218)
866
(120)
1047
(301)
1290
(171)
1380
(261)
1525
(33)
1584
(92)
1687
(195)
1812
(320)
1848
(356)

### Subsets and supersets

373edo is the 74th prime edo.

## Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve Stretch (¢)
Tuning Error
Absolute (¢) Relative (%)
2.3 [-591 373 [373 591]] +0.1939 0.1939 6.03
2.3.5 [8 14 -13, [-51 19 9 [373 591 866]] +0.1658 0.1632 5.07
2.3.5.7 2401/2400, 65625/65536, 43046721/42875000 [373 591 866 1047]] +0.1654 0.1413 4.39
2.3.5.7.11 2401/2400, 3025/3024, 8019/8000, 65625/65536 [373 591 866 1047 1290]] +0.2008 0.1449 4.50
2.3.5.7.11.13 729/728, 1001/1000, 1716/1715, 3025/3024, 4225/4224 [373 591 866 1047 1290 1380]] +0.2056 0.1327 4.12

### Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve
Generator* Cents* Associated
Ratio*
Temperaments
1 12\373 38.61 45/44 Hemitert
1 24\373 77.21 256/245 Tertiaseptal
1 98\373 315.28 6/5 Parakleismic (5-limit)
1 111\373 357.10 768/625 Dodifo (5-limit)
1 162\373 521.18 875/648 Maviloid
1 183\373 588.74 45/32 Untriton (5-limit)

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

Francium