439edo: Difference between revisions
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Created page with "{{Infobox ET}} {{EDO intro|439}} == Theory == 439et tempers out 703125/702464 in the 7-limit; 55296000/55240493, 100663296/100656875, 820125/819896, 2097152/2096325, 75937..." |
→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 |
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| Line 7: | Line 7: | ||
===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" | ||
! rowspan="2" |[[Subgroup]] | ! rowspan="2" | [[Subgroup]] | ||
! rowspan="2" |[[Comma list|Comma List]] | ! rowspan="2" | [[Comma list|Comma List]] | ||
! rowspan="2" |[[Mapping]] | ! rowspan="2" | [[Mapping]] | ||
! rowspan="2" |Optimal<br>8ve Stretch (¢) | ! rowspan="2" | Optimal<br>8ve Stretch (¢) | ||
! colspan="2" |Tuning Error | ! colspan="2" | Tuning Error | ||
|- | |- | ||
![[TE error|Absolute]] (¢) | ! [[TE error|Absolute]] (¢) | ||
![[TE simple badness|Relative]] (%) | ! [[TE simple badness|Relative]] (%) | ||
|- | |- | ||
|2.3 | | 2.3 | ||
|{{monzo|696 -439}} | | {{monzo| 696 -439 }} | ||
|{{val|439 696}} | | {{val| 439 696 }} | ||
| -0.1737 | | -0.1737 | ||
| 0.1737 | | 0.1737 | ||
| 6. | | 6.36 | ||
|- | |- | ||
|2.3. | | style="border-top: double;" | 2.3.5 | ||
|15625/15552, {{monzo| | | style="border-top: double;" | 15625/15552, {{monzo| 115 -74 1 }} | ||
|{{val|439 696 | | style="border-top: double;" | {{val| 439 696 1019 }} (439) | ||
| -0. | | style="border-top: double;" | +0.0122 | ||
| 0. | | style="border-top: double;" | 0.2988 | ||
| | | style="border-top: double;" | 10.9 | ||
|- | |- | ||
|2.3. | | 2.3.5.7 | ||
| | | 10976/10935, 15625/15552, {{monzo| -25 6 -3 8 }} | ||
|{{val|439 696 | | {{val| 439 696 1019 1232 }} (439) | ||
| | | +0.1135 | ||
| 0. | | 0.3127 | ||
| | | 11.4 | ||
|- | |- | ||
|2.3. | | style="border-top: double;" | 2.3.5 | ||
| | | style="border-top: double;" | {{monzo| 24 -21 4 }}, {{monzo| 36 11 -23 }} | ||
|{{val|439 696 | | style="border-top: double;" | {{val| 439 696 1020 }} (439c) | ||
| -0. | | style="border-top: double;" | -0.3801 | ||
| 0. | | style="border-top: double;" | 0.3244 | ||
| | | style="border-top: double;" | 11.9 | ||
|- | |- | ||
|2.3. | | 2.3.5.7 | ||
| | | 3136/3125, 2097152/2083725, 43046721/42875000 | ||
|{{val|439 696 | | {{val| 439 696 1020 1233 }} (439cd) | ||
| -0. | | -0.4241 | ||
| 0. | | 0.2911 | ||
| | | 10.7 | ||
|} | |} | ||
Revision as of 19:49, 22 April 2023
| ← 438edo | 439edo | 440edo → |
Theory
439et tempers out 703125/702464 in the 7-limit; 55296000/55240493, 100663296/100656875, 820125/819896, 2097152/2096325, 759375/758912, 131072/130977, 352947/352000, 85937500/85766121, 1879453125/1879048192, 184549376/184528125, 184877/184320, 3025/3024 and 1771561/1771470 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 |