496edo: Difference between revisions
Created page with "496 EDO divides the octave into steps of 2.42 cents each. ==Theory== {{primes in edo|496|columns=15}}" |
That "compound scale" is not really a temperament so moving accordingly |
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{{Infobox ET}} | |||
{{ED intro}} | |||
==Theory== | == Theory == | ||
{{ | 496edo is [[enfactoring|enfactored]] in the 11-limit, with the same tuning as [[248edo]], but the [[patent val]]s differ on the mapping for 13. In the 13-limit patent val, it tempers out [[4225/4224]]. | ||
496edo is good with the 2.3.11.19 [[subgroup]]. For higher limits, it has good approximations of [[31/1|31]], [[37/1|37]], and [[47/1|47]]. In the 2.3.11.19 subgroup, it tempers out 131072/131043. | |||
=== Odd harmonics === | |||
{{Harmonics in equal|496}} | |||
=== Subsets and supersets === | |||
496 is the 3rd {{w|perfect number}}, factoring into {{factorization|496}}. Its nontrivial divisors are {{EDOs| 2, 4, 8, 16, 31, 62, 124, 248 }}, the most notable being 31. | |||
== Scales == | |||
Since 496edo is enfactored 248edo, in the 11-limit it can represent a [[compound scale|compound]] of two chains of 11-limit [[bischismic]] temperaments, interlaced. | |||
Latest revision as of 21:30, 10 May 2026
| ← 495edo | 496edo | 497edo → |
496 equal divisions of the octave (abbreviated 496edo or 496ed2), also called 496-tone equal temperament (496tet) or 496 equal temperament (496et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 496 equal parts of about 2.42 ¢ each. Each step represents a frequency ratio of 21/496, or the 496th root of 2.
Theory
496edo is enfactored in the 11-limit, with the same tuning as 248edo, but the patent vals differ on the mapping for 13. In the 13-limit patent val, it tempers out 4225/4224.
496edo is good with the 2.3.11.19 subgroup. For higher limits, it has good approximations of 31, 37, and 47. In the 2.3.11.19 subgroup, it tempers out 131072/131043.
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) | |
Subsets and supersets
496 is the 3rd perfect number, factoring into 24 × 31. Its nontrivial divisors are 2, 4, 8, 16, 31, 62, 124, 248, the most notable being 31.
Scales
Since 496edo is enfactored 248edo, in the 11-limit it can represent a compound of two chains of 11-limit bischismic temperaments, interlaced.