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]] | ||