25ed5: Difference between revisions
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'''[[Ed5|Division of the 5th harmonic]] into 25 equal parts''' (25ED5) was first used in [[wikipedia:Karlheinz Stockhausen|Stockhausen’s]] [[wikipedia:Studie II|Elektronische Studie II]]. The step size is about 111.4525 cents. This tuning is very similar to [[17edt|17ED3]] but compressed by several cents. | '''[[Ed5|Division of the 5th harmonic]] into 25 equal parts''' (25ED5) was first used in [[wikipedia:Karlheinz Stockhausen|Stockhausen’s]] [[wikipedia:Studie II|Elektronische Studie II]]. The step size is about 111.4525 cents. This tuning is very similar to [[17edt|17ED3]] but compressed by several cents. | ||
== Intervals == | |||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
| Line 139: | Line 140: | ||
| | just major third plus two octaves | | | just major third plus two octaves | ||
|} | |} | ||
== Harmonics == | |||
{{Harmonics in equal | |||
| steps = 25 | |||
| num = 5 | |||
| denom = 1 | |||
}} | |||
{{Harmonics in equal | |||
| steps = 25 | |||
| num = 5 | |||
| denom = 1 | |||
| start = 12 | |||
| collapsed = 1 | |||
}} | |||
== Related temperament == | == Related temperament == | ||
25de5 is strongly related to the 140 & 183 temperament ([[stockhausenic]]), which tempers out 703125/702464 ([[meter]]) and 4096000/4084101 (hemfiness comma) 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]]. | |||
== Music == | == Music == | ||
[https://www.youtube.com/watch?v=bwj6ZptPnDo Studie II] - [[wikipedia:Karlheinz Stockhausen|Karlheinz Stockhausen]] | [https://www.youtube.com/watch?v=bwj6ZptPnDo Studie II] - [[wikipedia:Karlheinz Stockhausen|Karlheinz Stockhausen]] | ||
[[ | 25th root of 5, strings and brass - [[Brian McLaren]], Undiscovered Worlds Vol. 4 (1998) | ||
Latest revision as of 12:03, 8 September 2026
| ← 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
25de5 is strongly related to the 140 & 183 temperament (stockhausenic), which tempers out 703125/702464 (meter) and 4096000/4084101 (hemfiness comma) 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.
Music
Studie II - Karlheinz Stockhausen
25th root of 5, strings and brass - Brian McLaren, Undiscovered Worlds Vol. 4 (1998)