User:Francium/7297edo
| ← 7296edo | 7297edo | 7298edo → |
7297 equal divisions of the octave (abbreviated 7297edo or 7297ed2), also called 7297-tone equal temperament (7297tet) or 7297 equal temperament (7297et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 7297 equal parts of about 0.164 ¢ each. Each step represents a frequency ratio of 21/7297, or the 7297th root of 2.
Theory
7297edo is consistent to the 7-limit, although its harmonic 3 is about halfway its steps. It is strong in the 2.9.5.13.19 subgroup, tempering out 1220703125/1220607063, 41864013671875/41856138215424, 882632959197184/882592301503125 and 90647705078125/90628500150792.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.0775 | -0.0180 | -0.0442 | +0.0094 | -0.0777 | -0.0179 | +0.0690 | -0.0356 | -0.0209 | +0.0427 | -0.0710 |
| Relative (%) | -47.1 | -10.9 | -26.9 | +5.7 | -47.3 | -10.9 | +41.9 | -21.6 | -12.7 | +26.0 | -43.2 | |
| Steps (reduced) |
11565 (4268) |
16943 (2349) |
20485 (5891) |
23131 (1240) |
25243 (3352) |
27002 (5111) |
28509 (6618) |
29826 (638) |
30997 (1809) |
32051 (2863) |
33008 (3820) | |
Subsets and supersets
7297edo is the 930th prime edo. 14594edo, which doubles it, gives a good correction to its harmonic 3, but it is only consistent to the 5-limit. 43782edo, which is the sixfold of 7297edo, ensures its consistency.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.9 | [23131 -7297⟩ | [⟨7297 23131]] | −0.0015 | 0.0015 | 0.91 |
| 2.9.5 | [-34 -53 87⟩, [269 -79 -8⟩ | [⟨7297 23131 16943]] | +0.0016 | 0.0045 | 2.73 |
| 2.9.5.7 | 96889010407/96855122250, 193119049072265625/193091834023510016, [57 -25 12 -2⟩ | [⟨7297 23131 16943 20485]] | +0.0051 | 0.0073 | 4.44 |
| 2.9.5.7.11 | 3294225/3294172, 6576668672/6576582375, 1722499009/1721868840, 19073486328125/19070548180992 | [⟨7297 23131 16943 20485 25243]] | +0.0086 | 0.0095 | 5.77 |
| 2.9.5.7.11.13 | 10648/10647, 3764768/3764475, 19140625/19140264, 708883245/708837376, 120955835/120932352 | [⟨7297 23131 16943 20485 25243 27002]] | +0.0080 | 0.0088 | 5.35 |
| 2.9.5.7.11.13.17 | 426496/426465, 194481/194480, 10648/10647, 3408075/3407872, 66406250/66405339, 406174769/406093824 | [⟨7297 23131 16943 20485 25243 27002 29826]] | +0.0081 | 0.0081 | 4.92 |
| 2.9.5.7.11.13.17.19 | 10241/10240, 426496/426465, 194481/194480, 1549184/1549125, 10648/10647, 1484406/1484375, 739375/739328 | [⟨7297 23131 16943 20485 25243 27002 29826 30997]] | +0.0077 | 0.0077 | 4.68 |