247edo: Difference between revisions
Jump to navigation
Jump to search
m Harmonics template |
mNo edit summary |
||
| Line 4: | Line 4: | ||
== Theory == | == 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 family|compton]] fifth). It tempers out [[126/125]], [[243/242]] and [[1029/1024]] in the 11-limit patent mapping, so it [[support]]s the ''hemivalentino'' temperament (31&61e). | 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 [[support]]s the ''hemivalentino'' temperament (31&61e). | ||
{{Harmonics in equal|247}} | {{Harmonics in equal|247|columns=15}} | ||
[[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | [[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | ||
Revision as of 07:29, 25 January 2024
| ← 246edo | 247edo | 248edo → |
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).
| 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) | |