439edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{EDO intro|439}} | {{EDO intro|439}} | ||
== Theory == | == Theory == | ||
439edo is in[[consistent]] in the 5-odd-limit. In the 7-limit, the [[patent val]] {{val| 439 696 1019 1232 }}, and the 439cd val {{val| 439 696 '''1020''' '''1233''' }} are about as viable. | 439edo is in[[consistent]] in the 5-odd-limit. In the 7-limit, the [[patent val]] {{val| 439 696 1019 1232 }}, and the 439cd val {{val| 439 696 '''1020''' '''1233''' }} are about as viable. | ||
| Line 27: | Line 28: | ||
| 2.3 | | 2.3 | ||
| {{monzo| 696 -439 }} | | {{monzo| 696 -439 }} | ||
| {{ | | {{mapping| 439 696 }} | ||
| -0.1737 | | -0.1737 | ||
| 0.1737 | | 0.1737 | ||
| Line 34: | Line 35: | ||
| style="border-top: double;" | 2.3.5 | | style="border-top: double;" | 2.3.5 | ||
| style="border-top: double;" | 15625/15552, {{monzo| 115 -74 1 }} | | style="border-top: double;" | 15625/15552, {{monzo| 115 -74 1 }} | ||
| style="border-top: double;" | {{ | | style="border-top: double;" | {{mapping| 439 696 1019 }} (439) | ||
| style="border-top: double;" | +0.0122 | | style="border-top: double;" | +0.0122 | ||
| style="border-top: double;" | 0.2988 | | style="border-top: double;" | 0.2988 | ||
| Line 41: | Line 42: | ||
| 2.3.5.7 | | 2.3.5.7 | ||
| 10976/10935, 15625/15552, {{monzo| -25 6 -3 8 }} | | 10976/10935, 15625/15552, {{monzo| -25 6 -3 8 }} | ||
| {{ | | {{mapping| 439 696 1019 1232 }} (439) | ||
| +0.1135 | | +0.1135 | ||
| 0.3127 | | 0.3127 | ||
| Line 48: | Line 49: | ||
| style="border-top: double;" | 2.3.5 | | style="border-top: double;" | 2.3.5 | ||
| style="border-top: double;" | {{monzo| 24 -21 4 }}, {{monzo| 36 11 -23 }} | | style="border-top: double;" | {{monzo| 24 -21 4 }}, {{monzo| 36 11 -23 }} | ||
| style="border-top: double;" | {{ | | style="border-top: double;" | {{mapping| 439 696 1020 }} (439c) | ||
| style="border-top: double;" | -0.3801 | | style="border-top: double;" | -0.3801 | ||
| style="border-top: double;" | 0.3244 | | style="border-top: double;" | 0.3244 | ||
| Line 55: | Line 56: | ||
| 2.3.5.7 | | 2.3.5.7 | ||
| 3136/3125, 2097152/2083725, 43046721/42875000 | | 3136/3125, 2097152/2083725, 43046721/42875000 | ||
| {{ | | {{mapping| 439 696 1020 1233 }} (439cd) | ||
| -0.4241 | | -0.4241 | ||
| 0.2911 | | 0.2911 | ||
| Line 62: | Line 63: | ||
== Music == | == Music == | ||
* [https:// | ; [[User:Francium|Francium]] | ||
* "In The Black Hole" from ''Helayo EP'' (2023) – [https://open.spotify.com/track/3M2keEmTeY1J1j4cugAjXG Spotify] | [https://francium223.bandcamp.com/track/in-the-black-hole Bandcamp] | [https://youtu.be/ouGndPvLLso?si=fEI5pzfIydWHPF2l YouTube] – helayo in 439edo tuning | |||
Revision as of 13:18, 21 October 2023
| ← 438edo | 439edo | 440edo → |
Theory
439edo is inconsistent in the 5-odd-limit. In the 7-limit, the patent val ⟨439 696 1019 1232], and the 439cd val ⟨439 696 1020 1233] are about as viable.
The patent val tempers out 10976/10935, 15625/15552 and 703125/702464 in the 7-limit; 3025/3024, 4375/4356, 14700/14641, 59290/59049, 131072/130977, and 184877/184320 in the 11-limit.
The 439cd val tempers out 3136/3125, 2097152/2083725, and 4096000/4084101 in the 7-limit; 3136/3125, 15488/15435, 16384/16335, 19712/19683, 24057/24010, 43923/43750, 43923/43904, and 46656/46585 in the 11-limit.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | +0.55 | -0.89 | -1.17 | +0.85 | -1.35 | -1.08 | +0.44 | +0.43 | +0.95 | +0.29 |
| Relative (%) | +0.0 | +20.1 | -32.6 | -42.9 | +31.0 | -49.3 | -39.6 | +16.0 | +15.6 | +34.6 | +10.8 | |
| Steps (reduced) |
439 (0) |
696 (257) |
1019 (141) |
1232 (354) |
1519 (202) |
1624 (307) |
1794 (38) |
1865 (109) |
1986 (230) |
2133 (377) |
2175 (419) | |
Subsets and supersets
439edo is the 85th prime edo.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [696 -439⟩ | [⟨439 696]] | -0.1737 | 0.1737 | 6.36 |
| 2.3.5 | 15625/15552, [115 -74 1⟩ | [⟨439 696 1019]] (439) | +0.0122 | 0.2988 | 10.9 |
| 2.3.5.7 | 10976/10935, 15625/15552, [-25 6 -3 8⟩ | [⟨439 696 1019 1232]] (439) | +0.1135 | 0.3127 | 11.4 |
| 2.3.5 | [24 -21 4⟩, [36 11 -23⟩ | [⟨439 696 1020]] (439c) | -0.3801 | 0.3244 | 11.9 |
| 2.3.5.7 | 3136/3125, 2097152/2083725, 43046721/42875000 | [⟨439 696 1020 1233]] (439cd) | -0.4241 | 0.2911 | 10.7 |