313edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
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{{Harmonics in equal|313}} | {{Harmonics in equal|313}} | ||
=== | === Subsets and supersets === | ||
313edo is the 65th [[prime edo]]. | 313edo is the 65th [[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 | ! 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]] (¢) | ||
| Line 24: | Line 25: | ||
| 2.3 | | 2.3 | ||
| {{monzo| -496 313 }} | | {{monzo| -496 313 }} | ||
| | | {{mapping| 313 496 }} | ||
| +0.113 | | +0.113 | ||
| 0.113 | | 0.113 | ||
| Line 31: | Line 32: | ||
| 2.3.5 | | 2.3.5 | ||
| 32805/32768, {{monzo| -1 49 -33 }} | | 32805/32768, {{monzo| -1 49 -33 }} | ||
| | | {{mapping| 313 496 727 }} | ||
| | | −0.055 | ||
| 0.254 | | 0.254 | ||
| 6.64 | | 6.64 | ||
| Line 38: | Line 39: | ||
| 2.3.5.7 | | 2.3.5.7 | ||
| 6144/6125, 19683/19600, 40500000/40353607 | | 6144/6125, 19683/19600, 40500000/40353607 | ||
| | | {{mapping| 313 496 727 879 }} | ||
| | | −0.143 | ||
| 0.268 | | 0.268 | ||
| 6.99 | | 6.99 | ||
| Line 45: | Line 46: | ||
| 2.3.5.7.11 | | 2.3.5.7.11 | ||
| 540/539, 5632/5625, 8019/8000, 43923/43904 | | 540/539, 5632/5625, 8019/8000, 43923/43904 | ||
| | | {{mapping| 313 496 727 879 1083 }} | ||
| | | −0.158 | ||
| 0.242 | | 0.242 | ||
| 6.30 | | 6.30 | ||
| Line 52: | Line 53: | ||
| 2.3.5.7.11.13 | | 2.3.5.7.11.13 | ||
| 351/350, 540/539, 676/675, 4096/4095, 43923/43904 | | 351/350, 540/539, 676/675, 4096/4095, 43923/43904 | ||
| | | {{mapping| 313 496 727 879 1083 1158 }} | ||
| | | −0.091 | ||
| 0.267 | | 0.267 | ||
| 6.97 | | 6.97 | ||
| Line 60: | Line 61: | ||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{| class="wikitable center-all left-5" | {| class="wikitable center-all left-5" | ||
! Periods<br>per 8ve | |+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | ||
! Generator | |- | ||
! Cents | ! Periods<br />per 8ve | ||
! Associated<br> | ! Generator* | ||
! Cents* | |||
! Associated<br />ratio* | |||
! Temperaments | ! Temperaments | ||
|- | |- | ||
| Line 82: | Line 85: | ||
| 498.40 | | 498.40 | ||
| 4/3 | | 4/3 | ||
| [[Helmholtz]] | | [[Helmholtz (temperament)|Helmholtz]] | ||
|- | |- | ||
| 1 | | 1 | ||
| Line 90: | Line 93: | ||
| [[Vydubychi]] | | [[Vydubychi]] | ||
|} | |} | ||
<nowiki />* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct | |||
== Scales == | == Scales == | ||
* [[Hemischis14]] | |||
* [[Madagascar19]] | * [[Madagascar19]] | ||
* Madagascar[9] (or Barbados[9]): | * Madagascar[9] (or Barbados[9]): | ||
{| class="wikitable right-2" | {| class="wikitable right-2" | ||
|+Madagascar[9] ( | |+ style="font-size: 105%;" | Madagascar[9] (Barbados[9]) scale | ||
|- | |||
! Step | ! Step | ||
! Cents | ! Cents | ||
| Line 103: | Line 109: | ||
| 53 (53\313) | | 53 (53\313) | ||
| 203.195 | | 203.195 | ||
| [[9/8]] ( | | [[9/8]] (−0.715¢) | ||
|- | |- | ||
| 12 (65\313) | | 12 (65\313) | ||
| 249.201 | | 249.201 | ||
| [[15/13]] (+1. | | [[15/13]] (+1.46¢) | ||
|- | |- | ||
| 53 (118\313) | | 53 (118\313) | ||
| 452.396 | | 452.396 | ||
| [[13/10]] ( | | [[13/10]] (−1,818¢) | ||
|- | |- | ||
| 12 (130\313) | | 12 (130\313) | ||
| 498.403 | | 498.403 | ||
| [[4/3]] (+0. | | [[4/3]] (+0.358¢) | ||
|- | |- | ||
| 53 (183\313) | | 53 (183\313) | ||
| 701.597 | | 701.597 | ||
| [[3/2]] ( | | [[3/2]] (−0.358¢) | ||
|- | |- | ||
| 12 (195\313) | | 12 (195\313) | ||
| 747.604 | | 747.604 | ||
| [[20/13]] (+1. | | [[20/13]] (+1.818¢) | ||
|- | |- | ||
| 53 (248\313) | | 53 (248\313) | ||
| 950.799 | | 950.799 | ||
| [[26/15]] ( | | [[26/15]] (−1.46¢) | ||
|- | |- | ||
| 12 (260\313) | | 12 (260\313) | ||
| 996.805 | | 996.805 | ||
| [[16/9]] (+0. | | [[16/9]] (+0.715¢) | ||
|- | |- | ||
| 53 (313\313) | | 53 (313\313) | ||
| 1200.000 | | 1200.000 | ||
| [[2/1]] ( | | [[2/1]] (0¢) | ||
|} | |} | ||
<nowiki />* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct | |||
== Music == | == Music == | ||
{{ | {{Catrel| 313edo tracks }} | ||
; [[User:Francium|Francium]] | |||
* "Calling Voices" from ''HemischisMatic EP'' (2023) – [https://open.spotify.com/track/6NdgC4jYz5TIvxV09kdpuk Spotify] | [https://francium223.bandcamp.com/track/calling-voices Bandcamp] | [https://youtu.be/ls51r_AICak?si=iaiiHo-Q-Q-74LN9 YouTube] – in Hemischis, 313edo tuning | |||
* "Fried Rolled Up Trousers With Fish Sauce" from ''Unsuspecting Tyrant Double-Decker Beef Fort'' (2026) – [https://open.spotify.com/track/4Gnz6Dagdkg5C35osK1HXa Spotify] | [https://francium223.bandcamp.com/track/fried-rolled-up-trousers-with-fish-sauce Bandcamp] | [https://www.youtube.com/watch?v=ZSq62yTs3p0 YouTube] | |||
* [ | ; [[Sevish]] | ||
* ''[[Desert Island Rain]]'' | |||
* ''[[Disorient]]'' | |||
* ''[[Never Coming Home]]'' | |||
* ''[[Never Coming Home (Remix)]]'' | |||
* ''[[Septillion Reptilians]]'' | |||
[[Category: | [[Category:Albus]] | ||
[[Category:Hemischis]] | [[Category:Hemischis]] | ||
[[Category:Hera]] | [[Category:Hera]] | ||
[[Category: | [[Category:Listen]] | ||