25ed7
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Prime factorization
52
Step size
134.753¢
Octave
9\25ed7 (1212.78¢)
Twelfth
14\25ed7 (1886.54¢)
Consistency limit
8
Distinct consistency limit
4
| ← 24ed7 | 25ed7 | 26ed7 → |
Division of the 7th harmonic into 25 equal parts (25ed7) is related to 9edo, but with the 7/1 rather than the 2/1 being just. The octave is about 12.7773 cents stretched and the step size is about 134.7530 cents.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +12.8 | -15.4 | +25.6 | +43.5 | -2.6 | +0.0 | +38.3 | -30.8 | +56.3 | +26.0 | +10.1 |
| Relative (%) | +9.5 | -11.4 | +19.0 | +32.3 | -2.0 | +0.0 | +28.4 | -22.9 | +41.8 | +19.3 | +7.5 | |
| Steps (reduced) |
9 (9) |
14 (14) |
18 (18) |
21 (21) |
23 (23) |
25 (0) |
27 (2) |
28 (3) |
30 (5) |
31 (6) |
32 (7) | |
Intervals
| degree | cents value | corresponding JI intervals |
comments |
|---|---|---|---|
| 0 | 0.0000 | exact 1/1 | |
| 1 | 134.7530 | (27/25), 13/12 | |
| 2 | 269.5061 | 7/6 | |
| 3 | 404.2591 | 24/19, 91/72 | |
| 4 | 539.0121 | 15/11 | |
| 5 | 673.7652 | 28/19 | |
| 6 | 808.5182 | (147/92) | |
| 7 | 943.2713 | 19/11 | |
| 8 | 1078.0243 | 28/15 | |
| 9 | 1212.7773 | 161/80 | |
| 10 | 1347.5304 | 24/11 | |
| 11 | 1482.2834 | 40/17 | |
| 12 | 1617.0364 | 28/11 | |
| 13 | 1751.7895 | 11/4 | |
| 14 | 1886.5425 | 119/40 | |
| 15 | 2021.2955 | 77/24 | |
| 16 | 2156.0486 | 80/23 | |
| 17 | 2290.8016 | 15/4 | |
| 18 | 2425.5547 | 77/19 | |
| 19 | 2560.3077 | (92/21) | |
| 20 | 2695.0607 | 19/4 | |
| 21 | 2829.8138 | 77/15 | |
| 22 | 2964.5668 | 72/13, 133/24 | |
| 23 | 3099.3198 | 6/1 | |
| 24 | 3234.0729 | 84/13, (175/27) | |
| 25 | 3368.8259 | exact 7/1 | harmonic seventh plus two octaves |
25ed7 as a generator
25ed7 can also be thought of as a generator of the 23-limit temperament which tempers out 169/168, 176/175, 208/207, 221/220, 247/245, 256/255, and 361/360, which is a cluster temperament with nine clusters of notes in an octave. This temperament is supported by 9edo, 71edo (using 71d val), 80edo, and 89edo among others.