45edo: Difference between revisions
Continue filling in table |
Still filling in table. |
||
| Line 1: | Line 1: | ||
'''45edo''' divides the octave into 45 equal parts of 26.667 [[cent]]s. It is the [[optimal patent val]] for [[flattone]] temperament, the [[7-limit]] 525/512 planar [[Avicennmic_temperaments|avicennmic]] temperament, the 11-limit [[calliope]] temperament tempering out [[45/44]] and [[81/80]], and the rank four temperament tempering out 45/44. It tempers out 81/80, 3125/3087, 525/512, 875/864 and 45/44. It is a flat-tending system in the 7-limit, with 3, 5 and 7 all flat, but the 11 is sharp. Also supports messed-up [[ennealimmal]], if you want. Since 45 is a multiple of 5 and 9, it can be used to model [[Indonesian]] music in both [[wikipedia:Slendro|Slendro]] (~ 5edo) and [[wikipedia:Pelog|Pelog]] (~ modes of 9edo) tunings. | '''45edo''' divides the octave into 45 equal parts of 26.667 [[cent]]s. It has two major thirds, each almost equally far from Just, but as the flat one is slightly closer, it qualifies as a meantone temperament, forming a good approximation to 2/5 comma meantone. It is the [[optimal patent val]] for [[flattone]] temperament, the [[7-limit]] 525/512 planar [[Avicennmic_temperaments|avicennmic]] temperament, the 11-limit [[calliope]] temperament tempering out [[45/44]] and [[81/80]], and the rank four temperament tempering out 45/44. It tempers out 81/80, 3125/3087, 525/512, 875/864 and 45/44. It is a flat-tending system in the 7-limit, with 3, 5 and 7 all flat, but the 11 is sharp. Also supports messed-up [[ennealimmal]], if you want. Since 45 is a multiple of 5 and 9, it can be used to model [[Indonesian]] music in both [[wikipedia:Slendro|Slendro]] (~ 5edo) and [[wikipedia:Pelog|Pelog]] (~ modes of 9edo) tunings. | ||
[[Category:Edo]] | [[Category:Edo]] | ||
| Line 22: | Line 22: | ||
| 0 | | 0 | ||
| 0¢ | | 0¢ | ||
| | |1:1 | ||
| | | 0 | ||
| | |0 | ||
| unison | | unison | ||
| 1 | | 1 | ||
| Line 67: | Line 67: | ||
| 5 | | 5 | ||
| 133.333 | | 133.333 | ||
| | |27:25 | ||
| | |133.238 | ||
| | |0.095 | ||
| | | | ||
| | | | ||
| Line 77: | Line 77: | ||
|160 | |160 | ||
|11:10 | |11:10 | ||
| | |165.004 | ||
|<nowiki>-5.004</nowiki> | |<nowiki>-5.004</nowiki> | ||
| | | | ||
| Line 131: | Line 131: | ||
|320 | |320 | ||
|6:5 | |6:5 | ||
| | |315.641 | ||
|4.359 | |4.359 | ||
| | | | ||
| Line 140: | Line 140: | ||
|346.666 | |346.666 | ||
|11:9 | |11:9 | ||
| | |347.408 | ||
| | | -0.741 | ||
| | | | ||
| | | | ||
| Line 149: | Line 149: | ||
|373.333 | |373.333 | ||
|5:4- | |5:4- | ||
| | |386.314 | ||
|<nowiki>-12.980</nowiki> | |<nowiki>-12.980</nowiki> | ||
| | | | ||
| Line 158: | Line 158: | ||
|400 | |400 | ||
|5:4+ | |5:4+ | ||
| | |386.314 | ||
|13.686 | |13.686 | ||
| | | | ||
| Line 202: | Line 202: | ||
| 20 | | 20 | ||
|533.333 | |533.333 | ||
| | |49:36 | ||
| | |533.742 | ||
| | | -0.409 | ||
| | | | ||
| | | | ||
| Line 213: | Line 213: | ||
|18:13 | |18:13 | ||
| | | | ||
| | |<nowiki>-3.382</nowiki> | ||
| | | | ||
| | | | ||
| Line 221: | Line 221: | ||
|586.666 | |586.666 | ||
|7:5 | |7:5 | ||
| | |582.512 | ||
| | |4.155 | ||
| | | | ||
| | | | ||
| Line 230: | Line 230: | ||
|613.333 | |613.333 | ||
|10:7 | |10:7 | ||
| | |617.488 | ||
| | |<nowiki>-4.155</nowiki> | ||
| | | | ||
| | | | ||
| Line 240: | Line 240: | ||
|13:9 | |13:9 | ||
| | | | ||
| | |3.382 | ||
| | | | ||
| | | | ||
| Line 247: | Line 247: | ||
| 25 | | 25 | ||
|666.666 | |666.666 | ||
| | |72:49 | ||
| | |66.258 | ||
| | |0.409 | ||
| | | | ||
| | | | ||
| Line 434: | Line 434: | ||
|D | |D | ||
|} | |} | ||
[[Category:Meantone]] | |||