User:Francium/6091edo: Difference between revisions
Created page with "{{Infobox ET}} {{ED intro}} == Theory == 6091edo is consistent to the 9-odd-limit, tempering out 184528125/184473632, 8796093022208/8792724609375 and {{monzo|-15 42 -21 -1}} in the 7-limit. It has a remarkably low relative error in its harmonics 3, 23, 29 and 31/1, being strong in the 2.3.5.19.23.29.31 subgroup, tempering out 655371/655360, 323116128/323078125, 183353344/183347145, 484416/484375, 32506245/32505856 an..." |
+music |
||
| Line 61: | Line 61: | ||
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct | <nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct | ||
== Music == | |||
; [[Francium]] | |||
* "Hammin" from ''Bumbos'' (2026) – [https://open.spotify.com/track/0PHcvPz6zasF4TXV1lLc4H Spotify] | [https://francium223.bandcamp.com/track/hammin Bandcamp] | [https://www.youtube.com/watch?v=OO2wf9vS33M YouTube] – in Hamity, 6091edo tuning | |||
Revision as of 12:21, 2 February 2026
| ← 6090edo | 6091edo | 6092edo → |
6091 equal divisions of the octave (abbreviated 6091edo or 6091ed2), also called 6091-tone equal temperament (6091tet) or 6091 equal temperament (6091et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 6091 equal parts of about 0.197 ¢ each. Each step represents a frequency ratio of 21/6091, or the 6091st root of 2.
Theory
6091edo is consistent to the 9-odd-limit, tempering out 184528125/184473632, 8796093022208/8792724609375 and [-15 42 -21 -1⟩ in the 7-limit. It has a remarkably low relative error in its harmonics 3, 23, 29 and 31/1, being strong in the 2.3.5.19.23.29.31 subgroup, tempering out 655371/655360, 323116128/323078125, 183353344/183347145, 484416/484375, 32506245/32505856 and 46405467/46400000.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0000 | -0.0013 | +0.0268 | +0.0790 | -0.0784 | -0.0745 | +0.0520 | -0.0249 | -0.0031 | +0.0074 | -0.0019 |
| Relative (%) | +0.0 | -0.7 | +13.6 | +40.1 | -39.8 | -37.8 | +26.4 | -12.6 | -1.6 | +3.8 | -1.0 | |
| Steps (reduced) |
6091 (0) |
9654 (3563) |
14143 (1961) |
17100 (4918) |
21071 (2798) |
22539 (4266) |
24897 (533) |
25874 (1510) |
27553 (3189) |
29590 (5226) |
30176 (5812) | |
Subsets and supersets
6091edo is the 795th prime edo.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [-9654 6091⟩ | [⟨6091 9654]] | +0.0004 | 0.0004 | 0.20 |
| 2.3.5 | [91 -12 -31⟩, [-103 169 -71⟩ | [⟨6091 9654 14143]] | −0.0036 | 0.0056 | 2.8 |
| 2.3.5.7 | 184528125/184473632, 8796093022208/8792724609375, [-15 42 -21 -1⟩ | [⟨6091 9654 14143 17100]] | −0.0097 | 0.0117 | 5.94 |
Rank-2 temperaments
| Periods per 8ve |
Generator* | Cents* | Associated Ratio* |
Temperaments |
|---|---|---|---|---|
| 1 | 671\6091 | 132.1950 | [-38 5 13⟩ | Astro |
* octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct