247edo: Difference between revisions
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Created page with "The '''247 equal divisions of the octave''' ('''247EDO'''), or the '''247(-tone) equal temperament''' ('''247TET''', '''247ET''') when viewed from a regular temperament pe..." |
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== Theory == | == Theory == | ||
247EDO is the largest number EDO that interval representing 3/2 is flatter than that of [[12EDO]] (700¢) | In 247EDO, 144 degree represents [[3/2]] (2.36¢ flat), 80 degree represents [[5/4]] (2.35¢ sharp), 199 degree represents [[7/4]] (2.02¢ flat), and 113 degree represents [[11/8]] (2.33¢ flat). 247EDO lacks consistency to the 5 and higher odd-limit. It is the largest number EDO that interval representing 3/2 is flatter than that of [[12EDO]] (700¢, [[Compton family|compton]] fifth). It tempers out [[126/125]], [[243/242]] and [[1029/1024]] in the 11-limit patent mapping, so it supports the ''hemivalentino'' temperament (31&61e). | ||
{{Odd harmonics in edo|edo=247|prec=2}} | {{Odd harmonics in edo|edo=247|prec=2}} | ||
[[Category:Equal divisions of the octave]] | [[Category:Equal divisions of the octave]] | ||
Revision as of 12:49, 20 October 2021
The 247 equal divisions of the octave (247EDO), or the 247(-tone) equal temperament (247TET, 247ET) when viewed from a regular temperament perspective, is the equal division of the octave into 247 parts of 4.8583 cents each.
Theory
In 247EDO, 144 degree represents 3/2 (2.36¢ flat), 80 degree represents 5/4 (2.35¢ sharp), 199 degree represents 7/4 (2.02¢ flat), and 113 degree represents 11/8 (2.33¢ flat). 247EDO lacks consistency to the 5 and higher odd-limit. It is the largest number EDO that interval representing 3/2 is flatter than that of 12EDO (700¢, compton fifth). It tempers out 126/125, 243/242 and 1029/1024 in the 11-limit patent mapping, so it supports the hemivalentino temperament (31&61e).
| Odd 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 (%) | -49 | +48 | -42 | +3 | -48 | -1 | -0 | +40 | -24 | +10 | -32 | -3 | -46 | +8 | +31 | |
| 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) | |