1361edo: Difference between revisions
Misc. cleanup. Request explanation |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
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]] | 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|clarify|comment=explain why this subgroup is good to consider}}, it tempers out [[2925/2924]]. It [[support]]s [[galaxy]] and [[geb]]. | ||
=== Prime harmonics === | === Prime harmonics === | ||
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== 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 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]] (%) | ||
| Line 25: | Line 26: | ||
| {{monzo| -2157 1361 }} | | {{monzo| -2157 1361 }} | ||
| {{mapping| 1361 2157 }} | | {{mapping| 1361 2157 }} | ||
| 0.0373 | | +0.0373 | ||
| 0.0373 | | 0.0373 | ||
| 4.23 | | 4.23 | ||
| Line 32: | Line 33: | ||
| {{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 | ||
| 3.57 | | 3.57 | ||
| Line 39: | Line 40: | ||
| 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 | ||
| 5.92 | | 5.92 | ||
| Line 46: | Line 47: | ||
| 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 | ||
| 5.86 | | 5.86 | ||
| Line 53: | Line 54: | ||
| 1716/1715, 3025/3024, 4225/4224, 91125/91091, 131107977/131072000 | | 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 | ||
| 5.65 | | 5.65 | ||
| Line 60: | Line 61: | ||
| 1716/1715, 2500/2499, 3025/3024, 4225/4224, 57375/57344, 3536379/3536000 | | 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 | ||
|} | |} | ||
== Music == | |||
; [[Francium]] | |||
* "The Nights Get Better and Better." from ''Random Sentences'' (2025) – [https://open.spotify.com/track/11VP8L05cT6pDNQX8SJ0u6 Spotify] | [https://francium223.bandcamp.com/track/the-nights-get-better-and-better Bandcamp] | [https://www.youtube.com/watch?v=WmjKnu0OzLQ Bandcamp] – in Beattic, 1361edo tuning | |||