25ed5
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Prime factorization
52
Step size
111.453¢
Octave
11\25ed5 (1225.98¢)
Twelfth
17\25ed5 (1894.69¢)
Consistency limit
3
Distinct consistency limit
3
| ← 24ed5 | 25ed5 | 26ed5 → |
Division of the 5th harmonic into 25 equal parts (25ED5) was first used in Stockhausen’s Elektronische Studie II. The step size is about 111.4525 cents. This tuning is very similar to 17ED3 but compressed by several cents.
Intervals
| degree | cents value | corresponding JI intervals |
comments |
|---|---|---|---|
| 0 | 0.0000 | exact 1/1 | |
| 1 | 111.4525 | 16/15 | |
| 2 | 222.9051 | 25/22, 33/29 | |
| 3 | 334.3576 | 17/14, 40/33 | |
| 4 | 445.8102 | 22/17 | |
| 5 | 557.2627 | 40/29 | |
| 6 | 668.7153 | 25/17 | |
| 7 | 780.1678 | 11/7, 80/51 | |
| 8 | 891.6204 | 176/105 | pseudo-5/3 |
| 9 | 1003.0729 | 25/14 | |
| 10 | 1114.5255 | 40/21 | |
| 11 | 1225.9780 | 65/32, 128/63, 132/65 |
|
| 12 | 1337.4306 | 13/6 | |
| 13 | 1448.8831 | 30/13 | |
| 14 | 1560.3357 | 32/13 | |
| 15 | 1671.7882 | 21/8 | |
| 16 | 1783.2408 | 14/5 | |
| 17 | 1894.6933 | 224/75 | pseudo-3/1 |
| 18 | 2006.1459 | 35/11, 51/16 | |
| 19 | 2117.5984 | 17/5 | |
| 20 | 2229.0510 | 29/8 | |
| 21 | 2340.5035 | 58/15, 85/22 | |
| 22 | 2451.9561 | 33/8, 70/17, 136/33 |
|
| 23 | 2563.4086 | 22/5 | |
| 24 | 2674.8612 | 75/16 | |
| 25 | 2786.3137 | exact 5/1 | just major third plus two octaves |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +26.0 | -7.3 | +52.0 | +0.0 | +18.7 | -25.2 | -33.5 | -14.5 | +26.0 | -27.6 | +44.7 |
| Relative (%) | +23.3 | -6.5 | +46.6 | +0.0 | +16.8 | -22.7 | -30.1 | -13.0 | +23.3 | -24.7 | +40.1 | |
| Steps (reduced) |
11 (11) |
17 (17) |
22 (22) |
25 (0) |
28 (3) |
30 (5) |
32 (7) |
34 (9) |
36 (11) |
37 (12) |
39 (14) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +17.6 | +0.7 | -7.3 | -7.5 | -1.0 | +11.5 | +29.3 | +52.0 | -32.5 | -1.6 | +32.9 |
| Relative (%) | +15.8 | +0.7 | -6.5 | -6.8 | -0.9 | +10.3 | +26.3 | +46.6 | -29.2 | -1.4 | +29.5 | |
| Steps (reduced) |
40 (15) |
41 (16) |
42 (17) |
43 (18) |
44 (19) |
45 (20) |
46 (21) |
47 (22) |
47 (22) |
48 (23) |
49 (24) | |
Related temperament
25ED5 is strongly related to 140&183 temperament (stockhausenic, named by Xenllium), which tempers out 703125/702464 (meter comma) and 4096000/4084101 (hemfiness comma, named by Xenllium) in the 7-limit; 1375/1372, 5632/5625, and 35937/35840 in the 11-limit; 676/675, 1001/1000, 1573/1568, and 4096/4095 in the 13-limit.
Etymology
25ed5 is sometimes called "McLaren" or "Stockhausen" according to the main Ed5 article. Stockhausen is named for Karlheinz Stockhausen who used this scale. McLaren might be named after Brian McLaren.