Sensi: Difference between revisions
m added 65edo |
|||
| Line 19: | Line 19: | ||
The structure whereby 5/3 is split into two supermajor thirds is obviously xenharmonic as this cannot occur in [[12edo]]. But particularly, as the simplest [[EDO]]s with similar structures are [[8edo]] and [[11edo]] (whence the 8-note ([[3L 5s]], checkertonic) and 11-note ([[8L 3s]], flanatonic) [[MOS scale]]s), sensi has a very xenmelodic character compared to many other ways of organizing the 7-limit (such as [[superpyth]], which is based on the familiar [[chain of fifths]], and even [[porcupine]], which is fundamentally heptatonic). | The structure whereby 5/3 is split into two supermajor thirds is obviously xenharmonic as this cannot occur in [[12edo]]. But particularly, as the simplest [[EDO]]s with similar structures are [[8edo]] and [[11edo]] (whence the 8-note ([[3L 5s]], checkertonic) and 11-note ([[8L 3s]], flanatonic) [[MOS scale]]s), sensi has a very xenmelodic character compared to many other ways of organizing the 7-limit (such as [[superpyth]], which is based on the familiar [[chain of fifths]], and even [[porcupine]], which is fundamentally heptatonic). | ||
Equal temperaments that support sensi include [[19edo]] (generator 7\19; [[soft]] checkertonic), [[27edo]] (generator 10\27; [[supersoft]] checkertonic), | Equal temperaments that support sensi include [[19edo]] (generator 7\19; [[soft]] checkertonic), [[27edo]] (generator 10\27; [[supersoft]] checkertonic), as well as [[46edo]] (generator 17\46; {{nowrap| L/s {{=}} 7/5 }}), and [[65edo]] (generator 24\65; {{nowrap| L/s {{=}} 10/7 }}), more optimized for sensi temperament. | ||
See [[Sensipent family #Sensi]] for more technical data, and [[Sensi extensions]] for extensions of sensi that include the [[11/1|11th harmonic]]. | See [[Sensipent family #Sensi]] for more technical data, and [[Sensi extensions]] for extensions of sensi that include the [[11/1|11th harmonic]]. | ||
| Line 359: | Line 359: | ||
| | | | ||
|- | |- | ||
| 4\11 | | [[11edo|4\11]] | ||
| | | | ||
| 436.364 | | 436.364 | ||
| Line 379: | Line 379: | ||
| | | | ||
|- | |- | ||
| 7\19 | | [[19edo|7\19]] | ||
| | | | ||
| 442.105 | | 442.105 | ||
| Line 408: | Line 408: | ||
| 443.025 | | 443.025 | ||
| | | | ||
|- | |||
| [[65edo|24\65]] | |||
| | |||
| 443.077 | |||
| 65f val | |||
|- | |- | ||
| | | | ||
| Line 414: | Line 419: | ||
| 2.3.5.7.13-subgroup 15- and 21-odd-limit minimax | | 2.3.5.7.13-subgroup 15- and 21-odd-limit minimax | ||
|- | |- | ||
| 17\46 | | [[46edo|17\46]] | ||
| | | | ||
| 443.478 | | 443.478 | ||
| Line 433: | Line 438: | ||
| 443.756 | | 443.756 | ||
| 7-odd-limit minimax | | 7-odd-limit minimax | ||
|- | |||
| [[73edo|27\73]] | |||
| | |||
| 443.836 | |||
| | |||
|- | |- | ||
| | | | ||
| Line 444: | Line 454: | ||
| | | | ||
|- | |- | ||
| 10\27 | | [[27edo|10\27]] | ||
| | | | ||
| 444.444 | | 444.444 | ||
| Line 469: | Line 479: | ||
| | | | ||
|- | |- | ||
| 3\8 | | [[8edo|3\8]] | ||
| | | | ||
| 450.000 | | 450.000 | ||