1861edo: Difference between revisions
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Created page with "{{Infobox ET}} {{EDO intro|1861}} == Theory == 1861et tempers out 369140625/369098752, 537109375/536870912 and 3025/3024 in the 11-limit; 1181640625/1181599328, 225000/224..." |
Rework as a dual-fifth temp. Suspend the plain-fifth interpretations |
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| Line 1: | Line 1: | ||
{{Infobox ET}} | {{Infobox ET}} | ||
{{EDO intro|1861}} | {{EDO intro|1861}} | ||
== Theory == | == Theory == | ||
1861edo is only [[consistent]] to the [[5-odd-limit]], and the 3rd harmonic is about halfway between its steps. It has a reasonable approximation of the 2.9.5.7.11 [[subgroup]]. | |||
===Odd harmonics=== | |||
=== Odd harmonics === | |||
{{Harmonics in equal|1861}} | {{Harmonics in equal|1861}} | ||
==Regular temperament properties== | === Subsets and supersets === | ||
1861edo is the 284th [[prime edo]]. 3722edo, which doubles it, provides a good correction to the harmonic 3. | |||
== 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 simple badness|Relative]] (%) | ||
|- | |- | ||
|2. | | 2.9 | ||
| | | {{monzo| -5899 1861 }} | ||
|{{val|1861 | | {{val| 1861 5899 }} | ||
| | | +0.0234 | ||
| 0. | | 0.0234 | ||
| | | 3.63 | ||
|} | |} | ||
Revision as of 05:14, 25 April 2023
| ← 1860edo | 1861edo | 1862edo → |
Theory
1861edo is only consistent to the 5-odd-limit, and the 3rd harmonic is about halfway between its steps. It has a reasonable approximation of the 2.9.5.7.11 subgroup.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.248 | -0.070 | -0.314 | -0.149 | -0.001 | +0.311 | +0.178 | +0.149 | -0.253 | -0.066 | -0.225 |
| Relative (%) | +38.5 | -10.8 | -48.8 | -23.0 | -0.2 | +48.2 | +27.7 | +23.2 | -39.3 | -10.3 | -34.9 | |
| Steps (reduced) |
2950 (1089) |
4321 (599) |
5224 (1502) |
5899 (316) |
6438 (855) |
6887 (1304) |
7271 (1688) |
7607 (163) |
7905 (461) |
8174 (730) |
8418 (974) | |
Subsets and supersets
1861edo is the 284th prime edo. 3722edo, which doubles it, provides a good correction to the harmonic 3.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.9 | [-5899 1861⟩ | ⟨1861 5899] | +0.0234 | 0.0234 | 3.63 |