439edo: Difference between revisions
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 |
||
| 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 | ||
|} | |} | ||