9ed9/8: Difference between revisions
Jump to navigation
Jump to search
m Infobox ET added |
ArrowHead294 (talk | contribs) No edit summary |
||
| Line 354: | Line 354: | ||
==See also== | ==See also== | ||
*[http://en.wikipedia.org/wiki/Ottoman_classical_music Ottoman classical music - Wikipedia] | * [http://en.wikipedia.org/wiki/Ottoman_classical_music Ottoman classical music - Wikipedia] | ||
*[http://en.wikipedia.org/wiki/Makam Makam - Wikipedia] | * [http://en.wikipedia.org/wiki/Makam Makam - Wikipedia] | ||
[[Category:Equal-step tuning]] | [[Category:Equal-step tuning]] | ||
[[Category:Edonoi]] | [[Category:Edonoi]] | ||
[[Category:Whole tone]] | [[Category:Whole tone]] | ||
Revision as of 04:32, 24 May 2024
| ← 8ed9/8 | 9ed9/8 | 10ed9/8 → |
(convergent)
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).
| 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 |