673edo
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Prime factorization
673 (prime)
Step size
1.78306¢
Fifth
394\673 (702.526¢)
Semitones (A1:m2)
66:49 (117.7¢ : 87.37¢)
Consistency limit
5
Distinct consistency limit
5
| ← 672edo | 673edo | 674edo → |
673 equal divisions of the octave (abbreviated 673edo or 673ed2), also called 673-tone equal temperament (673tet) or 673 equal temperament (673et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 673 equal parts of about 1.78 ¢ each. Each step represents a frequency ratio of 21/673, or the 673rd root of 2.
Theory
673edo is consistent to the 5-odd-limit. Using the 2.3.5.17.19.41 subgroup, it tempers out 4624/4617, 131072/130815, 53136/53125, 10584064/10546875 and 19178125/19131876.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.571 | +0.611 | -0.624 | -0.641 | -0.352 | -0.706 | -0.602 | +0.245 | +0.258 | -0.053 | -0.637 |
| Relative (%) | +32.0 | +34.2 | -35.0 | -36.0 | -19.7 | -39.6 | -33.7 | +13.8 | +14.5 | -3.0 | -35.7 | |
| Steps (reduced) |
1067 (394) |
1563 (217) |
1889 (543) |
2133 (114) |
2328 (309) |
2490 (471) |
2629 (610) |
2751 (59) |
2859 (167) |
2956 (264) |
3044 (352) | |
Subsets and supersets
673edo is the 122nd prime EDO. 2019edo, which triples it, gives a good correction to the harmonic 7.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [1067 -673⟩ | [⟨673 1067]] | -0.1801 | 0.1801 | 10.10 |
| 2.3.5 | [32 -7 -9⟩, [19 -53 28⟩ | [⟨673 1067 1563]] | -0.2077 | 0.1521 | 8.53 |
Rank-2 temperaments
| Periods per 8ve |
Generator* | Cents* | Associated Ratio* |
Temperaments |
|---|---|---|---|---|
| 1 | 31\673 | 55.275 | 16875/16384 | Escapade |
* octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct