439edo: Difference between revisions
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== Theory == | == Theory == | ||
Revision as of 05:52, 9 July 2023
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This page presents a novelty topic.
It may contain ideas which are less likely to find practical applications in music, or numbers or structures that are arbitrary or exceedingly small, large, or complex. Novelty topics are often developed by a single person or a small group. As such, this page may also contain idiosyncratic terms, notation, or conceptual frameworks. |
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| ← 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 |