247edo: Difference between revisions
Jump to navigation
Jump to search
mNo edit summary |
Expand on theory; +subsets and supersets |
||
| Line 1: | Line 1: | ||
{{Infobox ET}} | {{Infobox ET}} | ||
{{EDO intro}} | |||
[[Prime harmonic]]s [[3/1|3]], [[5/1|5]], [[7/1|7]], and [[11/1|11]] are all about halfway between 247edo's steps, so 247edo lacks [[consistency]] to the [[5-odd-limit|5]] and higher odd limits. It is the largest numbered edo that the closest approximation to 3/2 is flatter than that of [[12edo]] (700¢, [[Compton family|compton fifth]]). Using the [[patent val]], it tempers out [[126/125]], [[243/242]] and [[1029/1024]] in the 11-limit , so it [[support]]s the ''hemivalentino'' temperament (31 & 61e). | |||
As every other step of the monstrous [[494edo]], 247edo can be used in the 2.9.15.21 [[subgroup]]. | |||
=== Odd harmonics === | |||
{{Harmonics in equal|247|columns=15}} | {{Harmonics in equal|247|columns=15}} | ||
[[ | === Subsets and supersets === | ||
Since 247 factors into {{factorization|247}}, 247edo contains [[13edo]] and [[19edo]] as its subsets. 494edo, which doubles it, provides excellent correction to all the lower prime harmonics. | |||
Revision as of 15:32, 22 March 2024
| ← 246edo | 247edo | 248edo → |
Prime harmonics 3, 5, 7, and 11 are all about halfway between 247edo's steps, so 247edo lacks consistency to the 5 and higher odd limits. It is the largest numbered edo that the closest approximation to 3/2 is flatter than that of 12edo (700¢, compton fifth). Using the patent val, it tempers out 126/125, 243/242 and 1029/1024 in the 11-limit , so it supports the hemivalentino temperament (31 & 61e).
As every other step of the monstrous 494edo, 247edo can be used in the 2.9.15.21 subgroup.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | 25 | 27 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -2.36 | +2.35 | -2.02 | +0.14 | -2.33 | -0.04 | -0.01 | +1.93 | -1.16 | +0.47 | -1.55 | -0.16 | -2.22 | +0.38 | +1.52 |
| Relative (%) | -48.6 | +48.4 | -41.7 | +2.9 | -48.0 | -0.9 | -0.2 | +39.7 | -23.8 | +9.8 | -32.0 | -3.2 | -45.7 | +7.9 | +31.4 | |
| Steps (reduced) |
391 (144) |
574 (80) |
693 (199) |
783 (42) |
854 (113) |
914 (173) |
965 (224) |
1010 (22) |
1049 (61) |
1085 (97) |
1117 (129) |
1147 (159) |
1174 (186) |
1200 (212) |
1224 (236) | |
Subsets and supersets
Since 247 factors into 13 × 19, 247edo contains 13edo and 19edo as its subsets. 494edo, which doubles it, provides excellent correction to all the lower prime harmonics.