584edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{EDO intro|584}} | {{EDO intro|584}} | ||
==Theory== | ==Theory== | ||
584et tempers out 48828125/48771072 and 67108864/66976875 in the 7-limit (hemiluna temperament), and 12005/11979, [[131072/130977]], [[5632/5625]], 537109375/536870912, 9453125/9437184, 160083/160000 and 391314/390625 in the 11-limit. | |||
{{Harmonics in equal|584}} | {{Harmonics in equal|584}} | ||
==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| 463 -292}} | |||
|{{val| 584 926}} | |||
| -0.2476 | |||
| 0.2475 | |||
| 12.05 | |||
|- | |||
|2.3.5 | |||
|{{monzo| 3 -18 11}}, {{monzo| 21 -20 4}} | |||
|{{val| 584 926 1356}} | |||
| -0.1633 | |||
| 0.2346 | |||
| 11.42 | |||
|- | |||
|2.3.5.7 | |||
|1500625/1492992, 1605632/1594323, 235298/234375 | |||
|{{val| 584 926 1356 1639}} | |||
| -0.0319 | |||
| 0.3052 | |||
| 14.85 | |||
|- | |||
|2.3.5.7.11 | |||
|5632/5625, 160083/160000, 26411/26244, 968000/964467 | |||
|{{val| 584 926 1356 1639 2020}} | |||
| +0.0111 | |||
| 0.2862 | |||
| 13.93 | |||
|- | |||
|2.3.5.7.11.13 | |||
|2080/2079, 1001/1000, 4096/4095, 85750/85293, 983125/979776 | |||
|{{val| 584 926 1356 1639 2020 2161}} | |||
| +0.0145 | |||
| 0.2613 | |||
| 12.72 | |||
|} | |||
==Scales== | ==Scales== | ||
* [[Hemiluna14]] | * [[Hemiluna14]] | ||
==Music== | ==Music== | ||
* [https://www.youtube.com/watch?v=7qF6IwKB8Iw Are You From The Moon?] by Francium | * [https://www.youtube.com/watch?v=7qF6IwKB8Iw Are You From The Moon?] by Francium | ||
Revision as of 19:37, 26 March 2023
| ← 583edo | 584edo | 585edo → |
Theory
584et tempers out 48828125/48771072 and 67108864/66976875 in the 7-limit (hemiluna temperament), and 12005/11979, 131072/130977, 5632/5625, 537109375/536870912, 9453125/9437184, 160083/160000 and 391314/390625 in the 11-limit.
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.785 | -0.012 | -1.018 | -0.485 | -0.633 | -0.117 | +0.772 | -0.161 | +0.432 | -0.233 | +0.493 |
| Relative (%) | +38.2 | -0.6 | -49.5 | -23.6 | -30.8 | -5.7 | +37.6 | -7.8 | +21.0 | -11.3 | +24.0 | |
| Steps (reduced) |
926 (342) |
1356 (188) |
1639 (471) |
1851 (99) |
2020 (268) |
2161 (409) |
2282 (530) |
2387 (51) |
2481 (145) |
2565 (229) |
2642 (306) | |
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [463 -292⟩ | ⟨584 926] | -0.2476 | 0.2475 | 12.05 |
| 2.3.5 | [3 -18 11⟩, [21 -20 4⟩ | ⟨584 926 1356] | -0.1633 | 0.2346 | 11.42 |
| 2.3.5.7 | 1500625/1492992, 1605632/1594323, 235298/234375 | ⟨584 926 1356 1639] | -0.0319 | 0.3052 | 14.85 |
| 2.3.5.7.11 | 5632/5625, 160083/160000, 26411/26244, 968000/964467 | ⟨584 926 1356 1639 2020] | +0.0111 | 0.2862 | 13.93 |
| 2.3.5.7.11.13 | 2080/2079, 1001/1000, 4096/4095, 85750/85293, 983125/979776 | ⟨584 926 1356 1639 2020 2161] | +0.0145 | 0.2613 | 12.72 |
Scales
Music
- Are You From The Moon? by Francium