332edo
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Prime factorization
22 × 83
Step size
3.61446¢
Fifth
194\332 (701.205¢) (→97\166)
Semitones (A1:m2)
30:26 (108.4¢ : 93.98¢)
Consistency limit
7
Distinct consistency limit
7
| ← 331edo | 332edo | 333edo → |
332 equal divisions of the octave (332edo), or 332-tone equal temperament (332tet), 332 equal temperament (332et) when viewed from a regular temperament perspective, is the tuning system that divides the octave into 332 equal parts of about 3.61 ¢ each.
Theory
332edo tempers out 118098/117649, 134217728/133984375, 29360128/29296875 and 2401/2400 in the 7-limit. It provides the optimal patent val for majvamoid and sedia.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | +0.0 | -2.0 | +13.7 | +31.2 | +48.7 | -40.5 | -5.0 | +2.5 | -28.3 | -29.6 | -45.0 |
| relative (%) | +0 | -2 | +14 | +31 | +49 | -41 | -5 | +2 | -28 | -30 | -45 | |
| Steps (reduced) |
12 (0) |
19 (7) |
28 (4) |
34 (10) |
42 (6) |
44 (8) |
49 (1) |
51 (3) |
54 (6) |
58 (10) |
59 (11) | |
Subsets and supersets
332 factors into 22 × 83, with subset edos 2, 4, 83, and 166.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [-263 166⟩ | [⟨332 526]] | 0.2367 | 0.2367 | 6.55 |
| 2.3.5 | [-13 17 -6⟩, [-53 10 16⟩ | [⟨332 526 771]] | 0.0955 | 0.2778 | 7.69 |
| 2.3.5.7 | 2401/2400, 19683/19600, 29360128/29296875 | [⟨332 526 771 932]] | 0.0851 | 0.2412 | 6.67 |
Rank-2 temperaments
| Periods per 8ve |
Generator* | Cents* | Associated Ratio* |
Temperaments |
|---|---|---|---|---|
| 1 | 33\332 | 119.28 | 15/14 | Septidiasemi |
| 1 | 75\332 | 271.08 | 1024/875 | Quasiorwell |
| 1 | 127\332 | 459.04 | 125/96 | Majvam |
| 1 | 143\332 | 516.87 | 27/20 | Gravity |
| 2 | 143\332 (23\332) |
516.87 (83.13) |
27/20 (21/20) |
Harry |
| 2 | 45\332 | 162.65 | 1125/1024 | Kwazy |
* octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct