494edo: Difference between revisions
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The '''494 equal temperament''' is a very strong [[13-limit|13]]- and [[17-limit]] equal temperament. | {{Infobox ET | ||
| Prime factorization = 2 × 13 × 19 | |||
| Step size = 2.42915¢ | |||
| Fifth = 289\494 (702.02¢) | |||
| Semitones = 47:37 (114.17¢ : 89.88¢) | |||
| Consistency = 17 | |||
}} | |||
The '''494 equal divisions of the octave''' ('''494edo'''), or the '''494(-tone) equal temperament''' ('''494tet''', '''494et''') when viewed from a [[regular temperament]] perspective, divides the [[octave]] into 494 [[equal]] parts of about 2.43 [[cent]]s each. It is a very strong [[13-limit|13]]- and [[17-limit]] equal temperament. The step size is close to [[729/728]], the squbema, and a step is a '''squb'''. | |||
== Theory == | |||
494edo is a [[The Riemann zeta function and tuning #Zeta EDO lists|zeta peak and zeta peak integer edo]] and uniquely [[consistent]] through the [[17-odd-limit]]. It [[tempering out|tempers out]] the [[enneadeca]], {{monzo| -14 -19 19 }}, the [[tricot comma]], {{monzo| 39 -29 3 }}, and the [[kwazy comma]], {{monzo| -53 10 16 }} in the [[5-limit]]. In the [[7-limit]], it tempers out [[4375/4374]] and [[703125/702464]]; in the [[11-limit]] [[3025/3024]] and [[9801/9800]]; in the [[13-limit]] [[1716/1715]], [[2080/2079]], [[4096/4095]], [[4225/4224]] and [[6656/6655]]; and in the 17-limit, [[1156/1155]], 1275/1274, 2431/2430, and 2500/2499. Not until [[1506edo|1506]] do we reach a division with a lower 13- or 17-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]], and it is the first past [[72edo|72]] with a lower 17-limit relative error. 494 is divisible by 2, 13, 19, 26, 38 and 247. | |||
=== Prime harmonics === | |||
{{Harmonics in equal|494|prec=3}} | |||
== Intervals == | == Intervals == | ||
{{ | {{Main| Table of 494edo intervals }} | ||
[[Category:17-limit]] | [[Category:17-limit]] | ||
Revision as of 15:34, 28 January 2022
| ← 493edo | 494edo | 495edo → |
The 494 equal divisions of the octave (494edo), or the 494(-tone) equal temperament (494tet, 494et) when viewed from a regular temperament perspective, divides the octave into 494 equal parts of about 2.43 cents each. It is a very strong 13- and 17-limit equal temperament. The step size is close to 729/728, the squbema, and a step is a squb.
Theory
494edo is a zeta peak and zeta peak integer edo and uniquely consistent through the 17-odd-limit. It tempers out the enneadeca, [-14 -19 19⟩, the tricot comma, [39 -29 3⟩, and the kwazy comma, [-53 10 16⟩ in the 5-limit. In the 7-limit, it tempers out 4375/4374 and 703125/702464; in the 11-limit 3025/3024 and 9801/9800; in the 13-limit 1716/1715, 2080/2079, 4096/4095, 4225/4224 and 6656/6655; and in the 17-limit, 1156/1155, 1275/1274, 2431/2430, and 2500/2499. Not until 1506 do we reach a division with a lower 13- or 17-limit relative error, and it is the first past 72 with a lower 17-limit relative error. 494 is divisible by 2, 13, 19, 26, 38 and 247.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | +0.069 | -0.079 | +0.405 | +0.099 | -0.042 | -0.502 | -1.157 | +0.875 | +0.382 | -0.906 |
| Relative (%) | +0.0 | +2.9 | -3.2 | +16.7 | +4.1 | -1.7 | -20.7 | -47.6 | +36.0 | +15.7 | -37.3 | |
| Steps (reduced) |
494 (0) |
783 (289) |
1147 (159) |
1387 (399) |
1709 (227) |
1828 (346) |
2019 (43) |
2098 (122) |
2235 (259) |
2400 (424) |
2447 (471) | |