496edo: Difference between revisions
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{{Infobox ET}} | |||
{{EDO intro|496}} | {{EDO intro|496}} | ||
==Theory== | ==Theory== | ||
Revision as of 06:37, 9 July 2023
| ← 495edo | 496edo | 497edo → |
Theory
496edo is strongly related to the 248edo, but the patent vals differ on the mapping for 13. As such, in the 11-limit it supports a compound of two chains of 11-limit bischismic temperaments. In the 13-limit patent val, first step where 496edo is not contorted, it tempers out 4225/4224.
496edo is good with the 2.3.11.19 subgroup, for low-complexity just intonation. Higher limits that it appreciates are 31, 37, and 47. In the 2.3.11.19 subgroup, 496edo tempers out 131072/131043.
496 is the 3rd perfect number, and its divisors are 1, 2, 4, 8, 16, 31, 62, 124, 248, the most notable being 31.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.34 | +0.78 | -1.08 | -0.68 | +0.29 | -1.01 | +0.44 | -0.92 | +0.07 | +0.99 | +0.76 |
| Relative (%) | -14.1 | +32.4 | -44.8 | -28.3 | +12.2 | -41.8 | +18.2 | -38.2 | +2.8 | +41.1 | +31.3 | |
| Steps (reduced) |
786 (290) |
1152 (160) |
1392 (400) |
1572 (84) |
1716 (228) |
1835 (347) |
1938 (450) |
2027 (43) |
2107 (123) |
2179 (195) |
2244 (260) | |