251edo: Difference between revisions
Review |
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== Regular temperament properties == | == Regular temperament properties == | ||
{ | {{comma basis begin}} | ||
|- | |- | ||
| 2.3 | | 2.3 | ||
| Line 46: | Line 38: | ||
| 0.2322 | | 0.2322 | ||
| 4.86 | | 4.86 | ||
{{comma basis end}} | |||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{ | {{rank-2 begin}} | ||
|- | |- | ||
| 1 | | 1 | ||
| Line 86: | Line 72: | ||
| 512/375 | | 512/375 | ||
| [[Maquila]] | | [[Maquila]] | ||
{{rank-2 end}} | |||
{{orf}} | |||
== Music == | == Music == | ||
; [[Francium]] | ; [[Francium]] | ||
* "hope in dark times" from ''hope in dark times'' (2024) | * "hope in dark times" from ''hope in dark times'' (2024) – [https://open.spotify.com/track/1zSiYXz46ugWAmqySaEN2A Spotify] | [https://francium223.bandcamp.com/track/hope-in-dark-times Bandcamp] | [https://www.youtube.com/watch?v=yHl3oku_NmY YouTube] | ||
[[Category:Listen]] | [[Category:Listen]] | ||
Revision as of 03:04, 16 November 2024
| ← 250edo | 251edo | 252edo → |
Theory
251et tempers out 1600000/1594323 (amity comma) and [49 -6 -17⟩ (maquila comma) in the 5-limit; 4375/4374, 5120/5103, and 40500000/40353607 in the 7-limit, supporting amity, supermajor, and acrokleismic.
Using the patent val ⟨251 398 583 705 868], it tempers out 1331/1323, 1375/1372, 16896/16807, and 24057/24010 in the 11-limit; 352/351, 676/675, 847/845, and 1573/1568 in the 13-limit.
Using the 251e val ⟨251 398 583 705 869], it tempers out 540/539, 5632/5625, 6250/6237, and 12005/11979 in the 11-limit; 364/363, 676/675, 1716/1715, and 3584/3575 in the 13-limit.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.83 | +0.94 | +1.69 | +1.67 | -1.52 | +0.91 | +1.77 | +0.22 | -1.10 | -2.26 | -1.98 |
| Relative (%) | +17.4 | +19.6 | +35.4 | +34.9 | -31.7 | +19.0 | +37.0 | +4.7 | -23.0 | -47.2 | -41.4 | |
| Steps (reduced) |
398 (147) |
583 (81) |
705 (203) |
796 (43) |
868 (115) |
929 (176) |
981 (228) |
1026 (22) |
1066 (62) |
1102 (98) |
1135 (131) | |
Subsets and supersets
251edo is the 54th prime edo.
Regular temperament properties
Template:Comma basis begin |- | 2.3 | [398 -251⟩ | [⟨251 398]] | -0.2630 | 0.2630 | 5.50 |- | 2.3.5 | [9 -13 5⟩, [49 -6 -17⟩ | [⟨251 398 583]] | -0.3099 | 0.2247 | 4.70 |- | 2.3.5.7 | 4375/4374, 5120/5103, 40500000/40353607 | [⟨251 398 583 705]] | -0.3830 | 0.2322 | 4.86 Template:Comma basis end
Rank-2 temperaments
Template:Rank-2 begin |- | 1 | 66\251 | 315.54 | 6/5 | Acrokleismic |- | 1 | 71\251 | 339.44 | 243/200 | Amity |- | 1 | 91\251 | 435.06 | 9/7 | Supermajor |- | 1 | 96\251 | 458.96 | 125/96 | Majvam |- | 1 | 112\251 | 535.46 | 512/375 | Maquila Template:Rank-2 end Template:Orf