15ed7: Difference between revisions
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'''[[Ed7|Division of the 7th harmonic]] into 15 equal parts''' (15ed7) is related to the [[Ragismic microtemperaments|supermajor temperament]], which tempers out 4375/4374 and 52734375/52706752. The step size is about 224.5884 cents, corresponding to 5.3431 [[edo]]. | '''[[Ed7|Division of the 7th harmonic]] into 15 equal parts''' (15ed7) is related to the [[Ragismic microtemperaments|supermajor temperament]], which tempers out 4375/4374 and 52734375/52706752. The step size is about 224.5884 cents, corresponding to 5.3431 [[edo]]. | ||
== Harmonics == | |||
{{Harmonics in equal|15|7|1}} | |||
{{Harmonics in equal|15|7|1|collapsed=1|start=12}} | |||
== Intervals == | |||
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Latest revision as of 19:20, 1 August 2025
| ← 14ed7 | 15ed7 | 16ed7 → |
Division of the 7th harmonic into 15 equal parts (15ed7) is related to the supermajor temperament, which tempers out 4375/4374 and 52734375/52706752. The step size is about 224.5884 cents, corresponding to 5.3431 edo.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -77.1 | -105.2 | +70.5 | -91.3 | +42.3 | +0.0 | -6.6 | +14.1 | +56.3 | -108.7 | -34.8 |
| Relative (%) | -34.3 | -46.9 | +31.4 | -40.6 | +18.8 | +0.0 | -2.9 | +6.3 | +25.1 | -48.4 | -15.5 | |
| Steps (reduced) |
5 (5) |
8 (8) |
11 (11) |
12 (12) |
14 (14) |
15 (0) |
16 (1) |
17 (2) |
18 (3) |
18 (3) |
19 (4) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +51.2 | -77.1 | +28.1 | -83.6 | +36.0 | -63.0 | +68.0 | -20.8 | -105.2 | +38.8 | -38.2 |
| Relative (%) | +22.8 | -34.3 | +12.5 | -37.2 | +16.0 | -28.0 | +30.3 | -9.3 | -46.9 | +17.3 | -17.0 | |
| Steps (reduced) |
20 (5) |
20 (5) |
21 (6) |
21 (6) |
22 (7) |
22 (7) |
23 (8) |
23 (8) |
23 (8) |
24 (9) |
24 (9) | |
Intervals
| degree | cents value | corresponding JI intervals |
comments |
|---|---|---|---|
| 0 | 0.0000 | exact 1/1 | |
| 1 | 224.5884 | ||
| 2 | 449.1768 | 35/27 | |
| 3 | 673.7652 | ||
| 4 | 898.3536 | 42/25 | |
| 5 | 1122.9420 | 21/11, 44/23 | |
| 6 | 1347.5304 | 98/45 | |
| 7 | 1572.1188 | 119/48 | |
| 8 | 1796.7072 | 48/17 | |
| 9 | 2021.2955 | 45/14 | |
| 10 | 2245.8839 | 11/3 | |
| 11 | 2470.4723 | 25/6 | |
| 12 | 2695.0607 | ||
| 13 | 2919.6491 | 27/5 | |
| 14 | 3144.2375 | ||
| 15 | 3368.8259 | exact 7/1 | harmonic seventh plus two octaves |
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