179edo: Difference between revisions
Jump to navigation
Jump to search
m Infobox ET added |
Cleanup |
||
| Line 1: | Line 1: | ||
{{Infobox ET}} | {{Infobox ET}} | ||
{{EDO intro|179}} | |||
179edo doesn't approximate any odd harmonic up to 23 with less than 22% error on [[21/16]]. Nonetheless, it is consistent in the 7-limit and there are anumber of temperaments to be considered. | |||
179edo tempers out the parakleisma, 1224440064/1220703125 in the 5-limit, and [[support]]s parakleismic and its extensions, providing the optimal patent val for 11- and 13-limit [[Ragismic_microtemperaments|parkleismic temperament]]. In the 7-limit it tempers out 3136/3125, 4375/4374 and 10976/10935, in the 11-limit 176/175 and 1375/1372 and in the 13-limit 169/168, 325/324, 351/350 and 352/351, providing the optimal patent val for 11- and 13-limit [[Valinorismic_temperaments#Ulmo|ulmo temperament]]. | |||
=== Odd harmonics === | |||
{{Harmonics in equal|179}} | |||
=== Subsets and supersets === | |||
179edo is the 41st [[prime edo]]. | |||
[[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | [[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | ||
[[Category:Prime EDO]] | [[Category:Prime EDO]] | ||
Revision as of 15:08, 22 October 2023
| ← 178edo | 179edo | 180edo → |
179edo doesn't approximate any odd harmonic up to 23 with less than 22% error on 21/16. Nonetheless, it is consistent in the 7-limit and there are anumber of temperaments to be considered.
179edo tempers out the parakleisma, 1224440064/1220703125 in the 5-limit, and supports parakleismic and its extensions, providing the optimal patent val for 11- and 13-limit parkleismic temperament. In the 7-limit it tempers out 3136/3125, 4375/4374 and 10976/10935, in the 11-limit 176/175 and 1375/1372 and in the 13-limit 169/168, 325/324, 351/350 and 352/351, providing the optimal patent val for 11- and 13-limit ulmo temperament.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +1.96 | +2.51 | +3.24 | -2.79 | -1.60 | -2.54 | -2.24 | +2.31 | -2.54 | -1.51 | +1.89 |
| Relative (%) | +29.2 | +37.5 | +48.3 | -41.7 | -23.8 | -37.9 | -33.3 | +34.4 | -37.9 | -22.5 | +28.2 | |
| Steps (reduced) |
284 (105) |
416 (58) |
503 (145) |
567 (30) |
619 (82) |
662 (125) |
699 (162) |
732 (16) |
760 (44) |
786 (70) |
810 (94) | |
Subsets and supersets
179edo is the 41st prime edo.