1361edo: Difference between revisions
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Created page with "{{Infobox ET}} {{EDO intro|1361}} == Theory == 1361edo is consistent in the 17-odd-limit, tempering out 3025/3024, 1716/1715, 2500/2499, 4225/4224..." |
Misc. cleanup. Request explanation |
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== Theory == | == Theory == | ||
1361edo is [[consistent]] in the [[17-odd-limit]], [[tempering out]] [[3025/3024]], [[1716/1715]], [[2500/2499]], [[4225/4224]], [[57375/57344]] and 3536379/3536000. Using the 2.3.5.13.17.43 [[subgroup]], it tempers out [[2925/2924]]. It [[support]]s [[galaxy]] and [[geb]]. | 1361edo is [[consistent]] in the [[17-odd-limit]]. As an equal temperament, it [[tempering out|tempers out]] [[3025/3024]], [[1716/1715]], [[2500/2499]], [[4225/4224]], [[57375/57344]] and 3536379/3536000. Using the 2.3.5.13.17.43 [[subgroup]]<!-- todo: explain why this subgroup is good to consider -->, it tempers out [[2925/2924]]. It [[support]]s [[galaxy]] and [[geb]]. | ||
=== Prime harmonics === | === Prime harmonics === | ||
| Line 13: | Line 13: | ||
== 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 | ! rowspan="2" | [[Comma list]] | ||
! rowspan="2" |[[Mapping]] | ! rowspan="2" | [[Mapping]] | ||
! rowspan="2" |Optimal<br>8ve | ! rowspan="2" | Optimal<br>8ve stretch (¢) | ||
! colspan="2" |Tuning | ! colspan="2" | Tuning error | ||
|- | |- | ||
![[TE error|Absolute]] (¢) | ! [[TE error|Absolute]] (¢) | ||
![[TE simple badness|Relative]] (%) | ! [[TE simple badness|Relative]] (%) | ||
|- | |- | ||
| 2.3 | | 2.3 | ||
| {{monzo|-2157 1361}} | | {{monzo| -2157 1361 }} | ||
| {{mapping|1361 2157}} | | {{mapping| 1361 2157 }} | ||
| 0.0373 | | 0.0373 | ||
| 0.0373 | | 0.0373 | ||
| Line 30: | Line 30: | ||
|- | |- | ||
| 2.3.5 | | 2.3.5 | ||
| {{monzo|-31 43 -16}}, {{monzo|-67 -9 35}} | | {{monzo| -31 43 -16 }}, {{monzo| -67 -9 35 }} | ||
| {{mapping|1361 2157 3160}} | | {{mapping| 1361 2157 3160 }} | ||
| 0.0431 | | 0.0431 | ||
| 0.0315 | | 0.0315 | ||
| Line 37: | Line 37: | ||
|- | |- | ||
| 2.3.5.7 | | 2.3.5.7 | ||
| 703125/702464, 14348907/14336000, {{monzo|37 2 -4 -11}} | | 703125/702464, 14348907/14336000, {{monzo| 37 2 -4 -11 }} | ||
| {{mapping|1361 2157 3160 3821}} | | {{mapping| 1361 2157 3160 3821 }} | ||
| 0.0174 | | 0.0174 | ||
| 0.0522 | | 0.0522 | ||
| Line 45: | Line 45: | ||
| 2.3.5.7.11 | | 2.3.5.7.11 | ||
| 3025/3024, 759375/758912, 14348907/14336000, 262766592/262609375 | | 3025/3024, 759375/758912, 14348907/14336000, 262766592/262609375 | ||
| {{mapping|1361 2157 3160 3821 4708}} | | {{mapping| 1361 2157 3160 3821 4708 }} | ||
| 0.0285 | | 0.0285 | ||
| 0.0517 | | 0.0517 | ||
| Line 51: | Line 51: | ||
|- | |- | ||
| 2.3.5.7.11.13 | | 2.3.5.7.11.13 | ||
| 3025/3024 | | 1716/1715, 3025/3024, 4225/4224, 91125/91091, 131107977/131072000 | ||
| {{mapping|1361 2157 3160 3821 4708 5036}} | | {{mapping| 1361 2157 3160 3821 4708 5036 }} | ||
| 0.0356 | | 0.0356 | ||
| 0.0498 | | 0.0498 | ||
| Line 58: | Line 58: | ||
|- | |- | ||
| 2.3.5.7.11.13.17 | | 2.3.5.7.11.13.17 | ||
| | | 1716/1715, 2500/2499, 3025/3024, 4225/4224, 57375/57344, 3536379/3536000 | ||
| {{mapping|1361 2157 3160 3821 4708 5036 5563}} | | {{mapping| 1361 2157 3160 3821 4708 5036 5563 }} | ||
| 0.0317 | | 0.0317 | ||
| 0.0471 | | 0.0471 | ||
| 5.34 | | 5.34 | ||
|} | |} | ||
Revision as of 16:36, 10 January 2025
| ← 1360edo | 1361edo | 1362edo → |
Theory
1361edo is consistent in the 17-odd-limit. As an equal temperament, it tempers out 3025/3024, 1716/1715, 2500/2499, 4225/4224, 57375/57344 and 3536379/3536000. Using the 2.3.5.13.17.43 subgroup, it tempers out 2925/2924. It supports galaxy and geb.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.118 | -0.127 | +0.167 | -0.253 | -0.263 | -0.033 | -0.379 | +0.381 | +0.254 | +0.299 |
| Relative (%) | +0.0 | -13.4 | -14.4 | +19.0 | -28.6 | -29.8 | -3.7 | -42.9 | +43.2 | +28.8 | +33.9 | |
| Steps (reduced) |
1361 (0) |
2157 (796) |
3160 (438) |
3821 (1099) |
4708 (625) |
5036 (953) |
5563 (119) |
5781 (337) |
6157 (713) |
6612 (1168) |
6743 (1299) | |
Subsets and supersets
1361edo is the 218th prime edo.
Regular temperament properties
| Subgroup | Comma list | Mapping | Optimal 8ve stretch (¢) |
Tuning error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [-2157 1361⟩ | [⟨1361 2157]] | 0.0373 | 0.0373 | 4.23 |
| 2.3.5 | [-31 43 -16⟩, [-67 -9 35⟩ | [⟨1361 2157 3160]] | 0.0431 | 0.0315 | 3.57 |
| 2.3.5.7 | 703125/702464, 14348907/14336000, [37 2 -4 -11⟩ | [⟨1361 2157 3160 3821]] | 0.0174 | 0.0522 | 5.92 |
| 2.3.5.7.11 | 3025/3024, 759375/758912, 14348907/14336000, 262766592/262609375 | [⟨1361 2157 3160 3821 4708]] | 0.0285 | 0.0517 | 5.86 |
| 2.3.5.7.11.13 | 1716/1715, 3025/3024, 4225/4224, 91125/91091, 131107977/131072000 | [⟨1361 2157 3160 3821 4708 5036]] | 0.0356 | 0.0498 | 5.65 |
| 2.3.5.7.11.13.17 | 1716/1715, 2500/2499, 3025/3024, 4225/4224, 57375/57344, 3536379/3536000 | [⟨1361 2157 3160 3821 4708 5036 5563]] | 0.0317 | 0.0471 | 5.34 |