243edo: Difference between revisions
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The ''243 equal division'' divides the octave into 243 equal parts of 4.938 cents each. It tempers out the semicomma (5-limit orwell comma) 2109375/2097152 in the 5-limit, and 2401/2400 and 4375/4374 in the 7-limit. In the 11-limit it tempers out 243/242 and 441/440, and provides the [[ | The '''243 equal division''' divides the octave into 243 equal parts of 4.938 cents each. It tempers out the [[semicomma]] (5-limit orwell comma) 2109375/2097152 in the 5-limit, and [[2401/2400]] and [[4375/4374]] in the 7-limit. In the 11-limit it tempers out [[243/242]] and [[441/440]], and provides the [[optimal patent val]] for the [[Ragismic microtemperaments #Ennealimmal|ennealimnic temperament]]. In the 13-limit it tempers out [[364/363]] and [[625/624]], and provides the optimal temperament for 13-limit ennealimnic and the rank-3 [[Breed family #Jovial|jovial temperament]], and in the 17-limit it tempers out 375/374 and 595/594 and provides the optimal patent val for 17-limit ennealimnic. | ||
=== Prime harmonics === | |||
{{Harmonics in equal|243}} | |||
[[Category:Equal divisions of the octave]] | |||
Revision as of 11:54, 4 March 2022
The 243 equal division divides the octave into 243 equal parts of 4.938 cents each. It tempers out the semicomma (5-limit orwell comma) 2109375/2097152 in the 5-limit, and 2401/2400 and 4375/4374 in the 7-limit. In the 11-limit it tempers out 243/242 and 441/440, and provides the optimal patent val for the ennealimnic temperament. In the 13-limit it tempers out 364/363 and 625/624, and provides the optimal temperament for 13-limit ennealimnic and the rank-3 jovial temperament, and in the 17-limit it tempers out 375/374 and 595/594 and provides the optimal patent val for 17-limit ennealimnic.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | -0.72 | -1.13 | -0.92 | +1.77 | -1.02 | -1.25 | -1.22 | -1.11 | -2.42 | +0.64 |
| Relative (%) | +0.0 | -14.6 | -22.9 | -18.7 | +35.8 | -20.7 | -25.3 | -24.6 | -22.6 | -48.9 | +13.0 | |
| Steps (reduced) |
243 (0) |
385 (142) |
564 (78) |
682 (196) |
841 (112) |
899 (170) |
993 (21) |
1032 (60) |
1099 (127) |
1180 (208) |
1204 (232) | |