25ed5

From Xenharmonic Wiki
Jump to navigation Jump to search

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

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.