494edo
| ← 493edo | 494edo | 495edo → |
Theory
494 is a very strong 13- and 17-limit equal temperament. 494edo is a zeta peak and zeta peak integer edo and distinctly 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.
Since the step size is close to 729/728, the squbema, the accepted name for 494edo's step is squb.
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) | |
Subsets and supersets
Since 494 factors into 2 × 13 × 19, 494edo has subset edos 2, 13, 19, 26, 38, and 247.
988edo, which slices the edostep in two, provides a good correction of the 19th harmonic. 2964edo, which slices the edostep in six, provides an extremely precise correction of the 7th harmonic.
Intervals
Regular temperament properties
Template:Comma basis begin |- | 2.3 | [783 -494⟩ | [⟨494 783]] | −0.0219 | 0.0219 | 0.90 |- | 2.3.5 | [-14 -19 19⟩, [39 -23 3⟩ | [⟨494 783 1147]] | −0.0032 | 0.0318 | 1.31 |- | 2.3.5.7 | 4375/4374, 703125/702464, [21 3 1 -10⟩ | [⟨494 783 1147 1387]] | −0.0385 | 0.0670 | 2.76 |- | 2.3.5.7.11 | 3025/3024, 4375/4374, 131072/130977, 234375/234256 | [⟨494 783 1147 1387 1709]] | −0.0365 | 0.0600 | 2.47 |- | 2.3.5.7.11.13 | 1716/1715, 2080/2079, 3025/3024, 4096/4095, 31250/31213 | [⟨494 783 1147 1387 1709 1828]] | −0.0286 | 0.0576 | 2.37 |- | 2.3.5.7.11.13.17 | 1156/1155, 1275/1274, 1716/1715, 2080/2079, 2431/2430, 4096/4095 | [⟨494 783 1147 1387 1709 1828 2019]] | −0.0069 | 0.0752 | 3.09 Template:Comma basis end
- 494et has lower relative errors than any previous equal temperaments in the 13- and 17-limit. It is the first past 270 with a lower 13-limit relative error, and the first past 72 with a lower 17-limit relative error. It is narrowly beaten by 684 in terms of 13-limit absolute error and by 581 in terms of 17-limit absolute error. Not until 1506 do we reach an equal temperament with a lower relative error in either subgroup.
Rank-2 temperaments
Template:Rank-2 begin
|-
| 1
| 27\494
| 65.59
| 27/26
| Luminal
|-
| 1
| 119\494
| 289.07
| 13/11
| Moulin
|-
| 1
| 233\494
| 565.99
| 104/75
| Tricot / trillium
|-
| 2
| 67\494
| 162.75
| 1125/1024
| Kwazy
|-
| 2
| 86\494
| 208.91
| 44/39
| Abigail
|-
| 13
| 205\494
(15\494)
| 497.98
(36.43)
| 4/3
(?)
| Aluminium
|-
| 19
| 205\494
(3\494)
| 497.98
(7.29)
| 4/3
(225/224)
| Enneadecal
|-
| 38
| 205\494
(3\494)
| 497.98
(7.29)
| 4/3
(225/224)
| Hemienneadecal
|-
| 38
| 109\494
(5\494)
| 264.78
(12.15)
| 500/429
(144/143)
| Semihemienneadecal
Template:Rank-2 end
Template:Orf
Music
- Unknown piece in Abigail (2023)