373edo
| ← 372edo | 373edo | 374edo → |
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
| 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 | -19 | -8 | -14 | -37 | -26 | +38 | -48 | -29 | -3 | +8 | |
| 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
| 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