361edo: Difference between revisions
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== Regular temperament properties == | == Regular temperament properties == | ||
{ | {{comma basis begin}} | ||
|- | |- | ||
| 2.3 | | 2.3 | ||
| Line 43: | Line 34: | ||
| 0.1941 | | 0.1941 | ||
| 5.84 | | 5.84 | ||
{{comma basis end}} | |||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{ | {{rank-2 begin}} | ||
|- | |- | ||
| 1 | | 1 | ||
| Line 66: | Line 50: | ||
| 4/3<br />(225/224) | | 4/3<br />(225/224) | ||
| [[Enneadecal]] | | [[Enneadecal]] | ||
{{rank-2 end}} | |||
{{orf}} | {{orf}} | ||
Revision as of 01:40, 16 November 2024
| ← 360edo | 361edo | 362edo → |
Theory
361et is consistent to the 9-odd-limit with flat tunings of harmonics 3, 5, and 7. The equal temperament tempers out 4375/4374, 703125/702464, 2460375/2458624, 43046721/43025920, and 48828125/48771072 in the 7-limit. It supports the 5-limit submajor temperament.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.57 | -0.72 | -1.51 | -1.14 | +0.48 | +0.47 | -1.29 | +1.42 | +1.66 | +1.24 | -0.02 |
| Relative (%) | -17.1 | -21.6 | -45.5 | -34.3 | +14.5 | +14.1 | -38.8 | +42.6 | +49.8 | +37.3 | -0.6 | |
| Steps (reduced) |
572 (211) |
838 (116) |
1013 (291) |
1144 (61) |
1249 (166) |
1336 (253) |
1410 (327) |
1476 (32) |
1534 (90) |
1586 (142) |
1633 (189) | |
Subsets and supersets
361 factors into 192, with 19edo as its only edo subset.
Regular temperament properties
Template:Comma basis begin |- | 2.3 | [-572 361⟩ | [⟨361 572]] | 0.1798 | 0.1798 | 5.41 |- | 2.3.5 | [-36 11 8⟩, [-14 -19 19⟩ | [⟨361 572 838]] | 0.2230 | 0.1590 | 4.78 |- | 2.3.5.7 | 4375/4374, 823543/819200, 2460375/2458624 | [⟨361 572 838 1013]] | 0.3020 | 0.1941 | 5.84 Template:Comma basis end
Rank-2 temperaments
Template:Rank-2 begin
|-
| 1
| 166\361
| 551.80
| 48/35
| Emka
|-
| 19
| 150\361
(2\361)
| 498.61
(6.65)
| 4/3
(225/224)
| Enneadecal
Template:Rank-2 end
Template:Orf