439edo: Difference between revisions
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→Regular temperament properties: 2.3.15 is equivalent to 2.3.5 and 2.3.15.35 is equivalent to 2.3.5.7. Rework to address alternative vals |
→Theory: rework to address alternative vals |
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{{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. | |||
===Prime harmonics=== | |||
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 === | |||
{{Harmonics in equal|439}} | {{Harmonics in equal|439}} | ||
===Subsets and supersets=== | |||
=== Subsets and supersets === | |||
439edo is the 85th [[prime edo]]. | 439edo is the 85th [[prime edo]]. | ||
== Regular temperament properties == | == Regular temperament properties == | ||
{| class="wikitable center-4 center-5 center-6" | {| class="wikitable center-4 center-5 center-6" | ||
Revision as of 19:59, 22 April 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 |