379edo: Difference between revisions
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Created page with "{{Infobox ET}} {{EDO intro|379}} It is the 75th prime edo. == Theory == 379 tempers out 4096000/4084101, 5120/5103 and 2401/2400 in the 7-limit; 2097152/2096325, 1..." |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{EDO intro|379}} | {{EDO intro|379}} | ||
== Theory == | ==Theory== | ||
379 tempers out 4096000/4084101, [[5120/5103]] and [[2401/2400]] in the 7-limit; 2097152/2096325, 1953125/1951488, [[6250/6237]], 42875/42768, 5767168/5764801, 180224/180075, [[5632/5625]], 537109375/536870912, 422576/421875, 9453125/9437184, 166375/165888, 67110351/67108864, 3294225/3294172, 43923/43904, 102487/102400, 20614528/20588575, 644204/643125 and 781258401/781250000 in the 11-limit. It provides the optimal patent val for the [[subneutral]] temperament. | 379 tempers out 4096000/4084101, [[5120/5103]] and [[2401/2400]] in the 7-limit; 2097152/2096325, 1953125/1951488, [[6250/6237]], 42875/42768, 5767168/5764801, 180224/180075, [[5632/5625]], 537109375/536870912, 422576/421875, 9453125/9437184, 166375/165888, 67110351/67108864, 3294225/3294172, 43923/43904, 102487/102400, 20614528/20588575, 644204/643125 and 781258401/781250000 in the 11-limit. It provides the optimal patent val for the [[subneutral]] temperament. | ||
379edo is the 75th [[prime edo]]. | |||
{{Harmonics in equal|379}} | {{Harmonics in equal|379}} | ||
==Regular temperament properties== | |||
{| class="wikitable center-4 center-5 center-6" | |||
! rowspan="2" |[[Subgroup]] | |||
! rowspan="2" |[[Comma list|Comma List]] | |||
! rowspan="2" |[[Mapping]] | |||
! rowspan="2" |Optimal<br>8ve Stretch (¢) | |||
! colspan="2" |Tuning Error | |||
|- | |||
![[TE error|Absolute]] (¢) | |||
![[TE simple badness|Relative]] (%) | |||
|- | |||
|2.3 | |||
|{{monzo| 601 -379}} | |||
|{{val| 379 601}} | |||
| -0.2989 | |||
|0.2988 | |||
|9.43 | |||
|- | |||
|2.3.5 | |||
|{{monzo| 35 -25 2}}, {{monzo| 38 -2 -15}} | |||
|{{val| 379 601 880}} | |||
| -0.1944 | |||
|0.2852 | |||
|9.01 | |||
|- | |||
|2.3.5.7 | |||
|5120/5103, 2401/2400, {{monzo| -23 -11 15 2}} | |||
|{{val| 379 601 880 1064}} | |||
| -0.1493 | |||
|0.2591 | |||
|8.18 | |||
|- | |||
|2.3.5.7.11 | |||
|5120/5103, 5632/5625, 2401/2400, 166375/165888 | |||
|{{val| 379 601 880 1064 1311}} | |||
| -0.0967 | |||
|0.2545 | |||
|8.04 | |||
|- | |||
|2.3.5.7.11.13 | |||
|325/324, 1001/1000, 1716/1715, 5120/5103, 6656/6655 | |||
|{{val| 379 601 880 1064 1311 1402}} | |||
| -0.014 | |||
|0.2969 | |||
|9.38 | |||
|} | |||
==Scales== | ==Scales== | ||
* [[Subneutral31]] | *[[Subneutral31]] | ||
Revision as of 18:35, 26 March 2023
| ← 378edo | 379edo | 380edo → |
Theory
379 tempers out 4096000/4084101, 5120/5103 and 2401/2400 in the 7-limit; 2097152/2096325, 1953125/1951488, 6250/6237, 42875/42768, 5767168/5764801, 180224/180075, 5632/5625, 537109375/536870912, 422576/421875, 9453125/9437184, 166375/165888, 67110351/67108864, 3294225/3294172, 43923/43904, 102487/102400, 20614528/20588575, 644204/643125 and 781258401/781250000 in the 11-limit. It provides the optimal patent val for the subneutral temperament. 379edo is the 75th prime edo.
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.95 | -0.03 | +0.04 | -1.27 | -0.39 | -1.48 | +0.91 | -0.47 | +0.11 | +0.99 | -1.36 |
| Relative (%) | +29.9 | -1.1 | +1.2 | -40.2 | -12.5 | -46.7 | +28.8 | -14.8 | +3.5 | +31.2 | -43.0 | |
| Steps (reduced) |
601 (222) |
880 (122) |
1064 (306) |
1201 (64) |
1311 (174) |
1402 (265) |
1481 (344) |
1549 (33) |
1610 (94) |
1665 (149) |
1714 (198) | |
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [601 -379⟩ | ⟨379 601] | -0.2989 | 0.2988 | 9.43 |
| 2.3.5 | [35 -25 2⟩, [38 -2 -15⟩ | ⟨379 601 880] | -0.1944 | 0.2852 | 9.01 |
| 2.3.5.7 | 5120/5103, 2401/2400, [-23 -11 15 2⟩ | ⟨379 601 880 1064] | -0.1493 | 0.2591 | 8.18 |
| 2.3.5.7.11 | 5120/5103, 5632/5625, 2401/2400, 166375/165888 | ⟨379 601 880 1064 1311] | -0.0967 | 0.2545 | 8.04 |
| 2.3.5.7.11.13 | 325/324, 1001/1000, 1716/1715, 5120/5103, 6656/6655 | ⟨379 601 880 1064 1311 1402] | -0.014 | 0.2969 | 9.38 |