373edo
| ← 372edo | 373edo | 374edo → |
The 373 equal divisions of the octave (373edo), or the 373(-tone) equal temperament (373tet, 373et) when viewed from a regular temperament perspective, is the equal division of the octave into 373 parts of about 3.22 cents each.
Theory
373edo is consistent to the 15-odd-limit, with harmonics 3 through 13 all tuned flat. It tempers out [8 14 -13⟩ (parakleisma) and [-51 19 9⟩ (untriton comma) in the 5-limit; 2401/2400 (breedsma), 65625/65536 (horwell), 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.
373edo is the 74th prime edo.
Prime harmonics
Script error: No such module "primes_in_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
| Periods per octave |
Generator (reduced) |
Cents (reduced) |
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) |