| Prime factorization
|
32
|
| Step size
|
22.6567¢
|
| Octave
|
53\9ed9/8 (1200.8¢)
(convergent)
|
| Twelfth
|
84\9ed9/8 (1903.16¢) (→28\3ed9/8)
|
| Consistency limit
|
10
|
| Distinct consistency limit
|
4
|
9ED9/8 is the equal division of the Pythagorean whole tone into nine parts of 22.6567 cents each, corresponding to 52.9645 edo. This tuning is used in Ottoman classical music theory, in which ninth root of the 9/8 whole tone is treated as the minimum interval.
Intervals
| degree
|
cents value
|
ratio
|
| 0
|
0.0000
|
1/1
|
| 1
|
22.6567
|
(9/8)1/9
|
| 2
|
45.3133
|
(9/8)2/9
|
| 3
|
67.9700
|
(9/8)1/3
|
| 4
|
90.6267
|
(9/8)4/9
|
| 5
|
113.2833
|
(9/8)5/9
|
| 6
|
135.9400
|
(9/8)2/3
|
| 7
|
158.5967
|
(9/8)7/9
|
| 8
|
181.2533
|
(9/8)8/9
|
| 9
|
203.9100
|
9/8
|
| 10
|
226.5667
|
(9/8)10/9
|
| 11
|
249.2233
|
(9/8)11/9
|
| 12
|
271.8800
|
(9/8)4/3
|
| 13
|
294.5367
|
(9/8)13/9
|
| 14
|
317.1933
|
(9/8)14/9
|
| 15
|
339.8500
|
(9/8)5/3
|
| 16
|
362.5067
|
(9/8)16/9
|
| 17
|
385.1633
|
(9/8)17/9
|
| 18
|
407.8200
|
(9/8)2 = 81/64
|
| 19
|
430.4767
|
(9/8)19/9
|
| 20
|
453.1333
|
(9/8)20/9
|
| 21
|
475.7900
|
(9/8)7/3
|
| 22
|
498.4467
|
(9/8)22/9
|
| 23
|
521.1033
|
(9/8)23/9
|
| 24
|
543.7600
|
(9/8)8/3
|
| 25
|
566.4167
|
(9/8)25/9
|
| 26
|
589.0733
|
(9/8)26/9
|
| 27
|
611.7300
|
(9/8)3 = 729/512
|
| 28
|
634.3867
|
(9/8)28/9
|
| 29
|
657.0433
|
(9/8)29/9
|
| 30
|
679.7000
|
(9/8)10/3
|
| 31
|
702.3567
|
(9/8)31/9
|
| 32
|
725.0133
|
(9/8)32/9
|
| 33
|
747.6700
|
(9/8)11/3
|
| 34
|
770.3267
|
(9/8)34/9
|
| 35
|
792.9833
|
(9/8)35/9
|
| 36
|
815.6400
|
(9/8)4 = 6561/4096
|
| 37
|
838.2967
|
(9/8)37/9
|
| 38
|
860.9533
|
(9/8)38/9
|
| 39
|
883.6100
|
(9/8)13/3
|
| 40
|
906.2667
|
(9/8)40/9
|
| 41
|
928.9233
|
(9/8)41/9
|
| 42
|
951.5800
|
(9/8)14/3
|
| 43
|
974.2367
|
(9/8)43/9
|
| 44
|
996.8933
|
(9/8)44/9
|
| 45
|
1019.5500
|
(9/8)5 = 59049/32768
|
| 46
|
1042.2067
|
(9/8)46/9
|
| 47
|
1064.8633
|
(9/8)47/9
|
| 48
|
1087.5200
|
(9/8)16/3
|
| 49
|
1110.1767
|
(9/8)49/9
|
| 50
|
1132.8333
|
(9/8)50/9
|
| 51
|
1155.4900
|
(9/8)17/3
|
| 52
|
1178.1467
|
(9/8)52/9
|
| 53
|
1200.8033
|
(9/8)53/9
|
| 54
|
1223.4600
|
(9/8)6 = 531441/262144
|
Just approximation
15-odd-limit mappings
The following table shows how 15-odd-limit intervals are represented in 9ed9/8 (ordered by absolute error).
Direct mapping (even if inconsistent)
| Interval(s)
|
Error (abs, ¢)
|
| 9/8
|
0.000
|
| 3/2, 4/3
|
0.402
|
| 26/15
|
0.679
|
| 15/8, 5/3
|
0.749
|
| 16/9
|
0.803
|
| 13/10
|
1.081
|
| 5/4, 10/9
|
1.150
|
| 15/13
|
1.482
|
| 6/5, 16/15
|
1.552
|
| 20/13
|
1.884
|
| 9/5, 8/5
|
1.954
|
| 13/8, 13/9
|
2.231
|
| 13/12
|
2.633
|
| 16/13, 18/13
|
3.034
|
| 24/13
|
3.436
|
| 12/7
|
4.206
|
| 22/13
|
4.524
|
| 9/7, 8/7
|
4.607
|
| 7/6
|
5.009
|
| 13/11
|
5.327
|
| 7/4, 14/9
|
5.411
|
| 10/7
|
5.758
|
| 22/15
|
6.006
|
| 15/14
|
6.159
|
| 11/10
|
6.408
|
| 7/5
|
6.561
|
| 15/11
|
6.809
|
| 13/7
|
6.838
|
| 28/15
|
6.963
|
| 11/6
|
7.156
|
| 20/11
|
7.211
|
| 11/9, 11/8
|
7.558
|
| 14/13
|
7.642
|
| 12/11
|
7.960
|
| 18/11, 16/11
|
8.361
|
| 14/11
|
9.688
|
| 11/7
|
10.491
|
See also