Pajara: Difference between revisions
→Scala files: add file |
→Interval chains: oops |
||
| (3 intermediate revisions by 2 users not shown) | |||
| Line 30: | Line 30: | ||
There are two different mappings of the 11-limit. One is just called ''pajara'' and is slightly more complex but suffers almost no loss of accuracy compared to the 7-limit. It is best tuned flat of 22edo, with the optimum at around 707-708 cents. The other, called ''pajarous'' to avoid confusion, maps the 11th harmonic slightly simpler, but it equates [[12/11]] with [[10/9]], and the only tuning equating [[11/10]] with both is 22edo. | There are two different mappings of the 11-limit. One is just called ''pajara'' and is slightly more complex but suffers almost no loss of accuracy compared to the 7-limit. It is best tuned flat of 22edo, with the optimum at around 707-708 cents. The other, called ''pajarous'' to avoid confusion, maps the 11th harmonic slightly simpler, but it equates [[12/11]] with [[10/9]], and the only tuning equating [[11/10]] with both is 22edo. | ||
In the following tables, odd harmonics | In the following tables, odd harmonics 1–21 and their inverses are in '''bold'''. | ||
{| class="wikitable center-1 right-2 right-4" | {| class="wikitable center-1 right-2 right-4" | ||
| Line 48: | Line 48: | ||
| '''1/1''' | | '''1/1''' | ||
| 600.0 | | 600.0 | ||
| 7/5, 10/7 | | 7/5, 10/7, 17/12, 24/17 | ||
|- | |- | ||
| 1 | | 1 | ||
| 707. | | 707.4 | ||
| '''3/2''' | | '''3/2''', '''32/21''' | ||
| 107. | | 107.4 | ||
| 15/14, 16/15, 21/20 | | 15/14, '''16/15''', '''17/16''',<br>18/17, 21/20 | ||
|- | |- | ||
| 2 | | 2 | ||
| 214. | | 214.7 | ||
| '''8/7''', '''9/8''' | | '''8/7''', '''9/8''', 17/15 | ||
| 814. | | 814.7 | ||
| '''8/5''' | | '''8/5''', 34/21 | ||
|- | |- | ||
| 3 | | 3 | ||
| | | 922.1 | ||
| 12/7 | | 12/7, 17/10 | ||
| | | 322.1 | ||
| 6/5 | | 6/5, 17/14 | ||
|- | |- | ||
| 4 | | 4 | ||
| | | 429.5 | ||
| 9/7, 14/11 | | 9/7, 14/11 | ||
| | | 1029.5 | ||
| 9/5, 20/11 | | 9/5, 20/11 | ||
|- | |- | ||
| 5 | | 5 | ||
| | | 1136.9 | ||
| 21/11, 27/14, 48/25, <br>64/33, 96/49 | | 21/11, 27/14, 48/25, <br>64/33, 96/49 | ||
| | | 536.9 | ||
| 15/11, 27/20 | | 15/11, 27/20 | ||
|- | |- | ||
| 6 | | 6 | ||
| | | 644.2 | ||
| '''16/11''' | | '''16/11''', 36/25, 72/49 | ||
| | | 44.2 | ||
| 45/44, 56/55, 81/80 | | 45/44, 56/55, 81/80 | ||
|} | |} | ||
| Line 103: | Line 103: | ||
| '''1/1''' | | '''1/1''' | ||
| 600.0 | | 600.0 | ||
| 7/5, 10/7 | | 7/5, 10/7, 17/12, 24/17 | ||
|- | |- | ||
| 1 | | 1 | ||
| 709. | | 709.5 | ||
| '''3/2''' | | '''3/2''', '''32/21''' | ||
| 109. | | 109.5 | ||
| 15/14, 16/15, 21/20 | | 15/14, '''16/15''', '''17/16''',<br>18/17, 21/20 | ||
|- | |- | ||
| 2 | | 2 | ||
| 219.1 | | 219.1 | ||
| '''8/7''', '''9/8''' | | '''8/7''', '''9/8''', 17/15 | ||
| 819.1 | | 819.1 | ||
| '''8/5''' | | '''8/5''', 34/21 | ||
|- | |- | ||
| 3 | | 3 | ||
| 928. | | 928.6 | ||
| 12/7 | | 12/7, 17/10 | ||
| 328. | | 328.6 | ||
| 6/5, 11/9 | | 6/5, 11/9, 17/14 | ||
|- | |- | ||
| 4 | | 4 | ||
| 438.2 | | 438.2 | ||
| 9/7 | | 9/7, 22/17 | ||
| 1038.2 | | 1038.2 | ||
| 9/5, 11/6 | | 9/5, 11/6 | ||
|- | |- | ||
| 5 | | 5 | ||
| 1147. | | 1147.7 | ||
| 27/14, 48/25, 55/28, <br>88/45, 96/49 | | 27/14, 48/25, 55/28, <br>88/45, 96/49 | ||
| 547. | | 547.7 | ||
| '''11/8''', 27/20 | | '''11/8''', 27/20 | ||
|- | |- | ||
| Line 141: | Line 141: | ||
| 22/21, 33/32, 81/80 | | 22/21, 33/32, 81/80 | ||
|} | |} | ||
<nowiki/>* In 11- | <nowiki/>* In 2.3.5.7.11.17-subgroup CWE tuning, octave-reduced | ||
== Chords and harmony == | == Chords and harmony == | ||
| Line 314: | Line 314: | ||
| 11/8 | | 11/8 | ||
| 708.114 | | 708.114 | ||
| | | 11- and 15-odd-limit minimax | ||
|- | |||
| | |||
|36/35 | |||
|708.128 | |||
|9-odd-limit minimax | |||
|- | |- | ||
| | | | ||
| Line 330: | Line 335: | ||
| 709.091 | | 709.091 | ||
| Upper bound of 11-odd-limit diamond monotone | | Upper bound of 11-odd-limit diamond monotone | ||
|- | |||
| | |||
|48/35 | |||
|709.363 | |||
|7-odd-limit minimax | |||
|- | |- | ||
| | | | ||