25ed5: Difference between revisions
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'''[[Ed5|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 [[17edt|17ED3]] but compressed by several cents. | |||
{| class="wikitable" | |||
|- | |||
! | degree | |||
! | cents value | |||
! | corresponding <br>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 | |||
| | [[65/64|65/32]], [[64/63|128/63]], <br>[[66/65|132/65]] | |||
| | | |||
|- | |||
| | 12 | |||
| | 1337.4306 | |||
| | [[13/6]] | |||
| | | |||
|- | |||
| | 13 | |||
| | 1448.8831 | |||
| | [[15/13|30/13]] | |||
| | | |||
|- | |||
| | 14 | |||
| | 1560.3357 | |||
| | [[16/13|32/13]] | |||
| | | |||
|- | |||
| | 15 | |||
| | 1671.7882 | |||
| | [[21/16|21/8]] | |||
| | | |||
|- | |||
| | 16 | |||
| | 1783.2408 | |||
| | [[7/5|14/5]] | |||
| | | |||
|- | |||
| | 17 | |||
| | 1894.6933 | |||
| | 224/75 | |||
| | pseudo-[[3/1]] | |||
|- | |||
| | 18 | |||
| | 2006.1459 | |||
| | 35/11, 51/16 | |||
| | | |||
|- | |||
| | 19 | |||
| | 2117.5984 | |||
| | [[17/10|17/5]] | |||
| | | |||
|- | |||
| | 20 | |||
| | 2229.0510 | |||
| | [[29/16|29/8]] | |||
| | | |||
|- | |||
| | 21 | |||
| | 2340.5035 | |||
| | 58/15, 85/22 | |||
| | | |||
|- | |||
| | 22 | |||
| | 2451.9561 | |||
| | [[33/32|33/8]], [[35/34|70/17]], <br>[[34/33|136/33]] | |||
| | | |||
|- | |||
| | 23 | |||
| | 2563.4086 | |||
| | [[11/10|22/5]] | |||
| | | |||
|- | |||
| | 24 | |||
| | 2674.8612 | |||
| | [[75/64|75/16]] | |||
| | | |||
|- | |||
| | 25 | |||
| | 2786.3137 | |||
| | '''exact [[5/1]]''' | |||
| | just major third plus two octaves | |||
|} | |||
[[Category:Ed5]] | [[Category:Ed5]] | ||
Revision as of 04:11, 3 May 2021
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.
| 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 |