181edo: Difference between revisions
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== Regular temperament properties == | == Regular temperament properties == | ||
{ | {{comma basis begin}} | ||
|- | |- | ||
| 2.3 | | 2.3 | ||
| {{monzo| 287 -181 }} | | {{monzo| 287 -181 }} | ||
| {{mapping| 181 287 }} | | {{mapping| 181 287 }} | ||
| | | −0.255 | ||
| 0.255 | | 0.255 | ||
| 3.84 | | 3.84 | ||
| Line 70: | Line 62: | ||
| 0.404 | | 0.404 | ||
| 6.09 | | 6.09 | ||
{{comma basis end}} | |||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{ | {{rank-2 begin}} | ||
|- | |- | ||
| 1 | | 1 | ||
| Line 116: | Line 102: | ||
| 7/5 | | 7/5 | ||
| [[Cotritone]] (181f) | | [[Cotritone]] (181f) | ||
{{rank-2 end}} | |||
{{orf}} | |||
== Music == | == Music == | ||
; [[Francium]] | ; [[Francium]] | ||
* "Today Or Tomorrow?" from ''Questions'' (2024) | * "Today Or Tomorrow?" from ''Questions'' (2024) – [https://open.spotify.com/track/24RikcnTP33a6v9vXyNPwh Spotify] | [https://francium223.bandcamp.com/track/today-or-tomorrow Bandcamp] | [https://www.youtube.com/watch?v=ipUyBAHIvlk YouTube] – slurpee in 181edo tuning | ||
== See also == | == See also == | ||
* [[181edo and stretched hemififths]] | * [[181edo and stretched hemififths]] | ||
[[Category:Listen]] | |||
Revision as of 03:51, 16 November 2024
| ← 180edo | 181edo | 182edo → |
Theory
181et tempers out 2109375/2097152 (semicomma) and [14 -22 9⟩ in the 5-limit; 2401/2400, 5120/5103, and 390625/387072 in the 7-limit (supporting the hemififths and the cotritone). Using the patent val, it tempers out 385/384, 1375/1372, 2200/2187, and 4000/3993 in the 11-limit; 325/324, 352/351, 847/845, and 1575/1573 in the 13-limit.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | +0.81 | -1.78 | -0.87 | -1.04 | +1.46 | +1.12 | +0.83 | +1.56 | -1.95 | +1.93 |
| Relative (%) | +0.0 | +12.2 | -26.9 | -13.1 | -15.7 | +22.0 | +16.9 | +12.5 | +23.5 | -29.5 | +29.0 | |
| Steps (reduced) |
181 (0) |
287 (106) |
420 (58) |
508 (146) |
626 (83) |
670 (127) |
740 (16) |
769 (45) |
819 (95) |
879 (155) |
897 (173) | |
Subsets and supersets
181edo is the 42nd prime edo.
Regular temperament properties
Template:Comma basis begin |- | 2.3 | [287 -181⟩ | [⟨181 287]] | −0.255 | 0.255 | 3.84 |- | 2.3.5 | 2109375/2097152, [14 -22 9⟩ | [⟨181 287 420]] | +0.086 | 0.525 | 7.92 |- | 2.3.5.7 | 2401/2400, 5120/5103, 390625/387072 | [⟨181 287 420 508]] | +0.142 | 0.465 | 7.01 |- | 2.3.5.7.11 | 385/384, 1375/1372, 2200/2187, 4000/3993 | [⟨181 287 420 508 626]] | +0.174 | 0.421 | 6.35 |- | 2.3.5.7.11.13 | 325/324, 352/351, 385/384, 1375/1372, 1575/1573 | [⟨181 287 420 508 626 670]] | +0.079 | 0.439 | 6.62 |- | 2.3.5.7.11.13.17 | 325/324, 352/351, 375/374, 385/384, 595/594, 1275/1274 | [⟨181 287 420 508 626 670 740]] | +0.028 | 0.425 | 6.40 |- | 2.3.5.7.11.13.17.19 | 325/324, 352/351, 375/374, 385/384, 400/399, 595/594, 1275/1274 | [⟨181 287 420 508 626 670 740 769]] | +0.000 | 0.404 | 6.09 Template:Comma basis end
Rank-2 temperaments
Template:Rank-2 begin |- | 1 | 18\181 | 119.34 | 15/14 | Septidiasemi |- | 1 | 35\181 | 232.04 | 8/7 | Quadrawell |- | 1 | 39\181 | 258.56 | [-32 13 5⟩ | Lafa |- | 1 | 41\181 | 271.82 | 75/64 | Orson |- | 1 | 53\181 | 351.38 | 49/40 | Hemififths (7-limit) |- | 1 | 88\181 | 583.43 | 7/5 | Cotritone (181f) Template:Rank-2 end Template:Orf
Music
- "Today Or Tomorrow?" from Questions (2024) – Spotify | Bandcamp | YouTube – slurpee in 181edo tuning