2207edo
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Prime factorization
2207 (prime)
Step size
0.543725¢
Fifth
1291\2207 (701.948¢)
Semitones (A1:m2)
209:166 (113.6¢ : 90.26¢)
Consistency limit
5
Distinct consistency limit
5
| ← 2206edo | 2207edo | 2208edo → |
2207 equal divisions of the octave (abbreviated 2207edo or 2207ed2), also called 2207-tone equal temperament (2207tet) or 2207 equal temperament (2207et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 2207 equal parts of about 0.544 ¢ each. Each step represents a frequency ratio of 21/2207, or the 2207th root of 2.
Theory
2207edo is consistent to the 5-odd-limit, but its harmonic 5 is about halfway its steps. It is strong in the 2.3.11.17.31 subgroup. Using the 2.3.7.11.17.37 subgroup, it tempers out 3774/3773.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.007 | -0.269 | +0.091 | -0.013 | +0.019 | +0.070 | +0.268 | -0.017 | -0.096 | +0.085 | +0.271 |
| Relative (%) | -1.2 | -49.5 | +16.8 | -2.4 | +3.4 | +13.0 | +49.2 | -3.0 | -17.6 | +15.5 | +49.9 | |
| Steps (reduced) |
3498 (1291) |
5124 (710) |
6196 (1782) |
6996 (375) |
7635 (1014) |
8167 (1546) |
8623 (2002) |
9021 (193) |
9375 (547) |
9694 (866) |
9984 (1156) | |
Subsets and supersets
2207edo is the 329th prime edo. 4414edo, which doubles it, gives a good correction to the harmonic 5.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [-3498 2207⟩ | [⟨2207 3498]] | 0.0021 | 0.0021 | 0.39 |