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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|313}}
{{ED intro}}


== Theory ==
== Theory ==
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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|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]] (¢)
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| 32805/32768, {{monzo| -1 49 -33 }}
| 32805/32768, {{monzo| -1 49 -33 }}
| {{mapping| 313 496 727 }}
| {{mapping| 313 496 727 }}
| -0.055
| −0.055
| 0.254
| 0.254
| 6.64
| 6.64
Line 39: Line 40:
| 6144/6125, 19683/19600, 40500000/40353607
| 6144/6125, 19683/19600, 40500000/40353607
| {{mapping| 313 496 727 879 }}
| {{mapping| 313 496 727 879 }}
| -0.143
| −0.143
| 0.268
| 0.268
| 6.99
| 6.99
Line 46: Line 47:
| 540/539, 5632/5625, 8019/8000, 43923/43904
| 540/539, 5632/5625, 8019/8000, 43923/43904
| {{mapping| 313 496 727 879 1083 }}
| {{mapping| 313 496 727 879 1083 }}
| -0.158
| −0.158
| 0.242
| 0.242
| 6.30
| 6.30
Line 53: Line 54:
| 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 }}
| {{mapping| 313 496 727 879 1083 1158 }}
| -0.091
| −0.091
| 0.267
| 0.267
| 6.97
| 6.97
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=== 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
|-
! Periods<br />per 8ve
! Generator*
! Generator*
! Cents*
! Cents*
! Associated<br>Ratio
! Associated<br />ratio*
! Temperaments
! Temperaments
|-
|-
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| 498.40
| 498.40
| 4/3
| 4/3
| [[Helmholtz]]
| [[Helmholtz (temperament)|Helmholtz]]
|-
|-
| 1
| 1
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| [[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 ==
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{| class="wikitable right-2"
{| class="wikitable right-2"
|+Madagascar[9] (or Barbados[9]) scale
|+ style="font-size: 105%;" | Madagascar[9] (Barbados[9]) scale
|-
! Step
! Step
! Cents
! Cents
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| 53 (53\313)
| 53 (53\313)
| 203.195
| 203.195
| [[9/8]] (-0.715 ¢)
| [[9/8]] (−0.715¢)
|-
|-
| 12 (65\313)
| 12 (65\313)
| 249.201
| 249.201
| [[15/13]] (+1.46 ¢)
| [[15/13]] (+1.46¢)
|-
|-
| 53 (118\313)
| 53 (118\313)
| 452.396
| 452.396
| [[13/10]] (-1,818 ¢)
| [[13/10]] (−1,818¢)
|-
|-
| 12 (130\313)
| 12 (130\313)
| 498.403
| 498.403
| [[4/3]] (+0.358 ¢)
| [[4/3]] (+0.358¢)
|-
|-
| 53 (183\313)
| 53 (183\313)
| 701.597
| 701.597
| [[3/2]] (-0.358 ¢)
| [[3/2]] (−0.358¢)
|-
|-
| 12 (195\313)
| 12 (195\313)
| 747.604
| 747.604
| [[20/13]] (+1.818 ¢)
| [[20/13]] (+1.818¢)
|-
|-
| 53 (248\313)
| 53 (248\313)
| 950.799
| 950.799
| [[26/15]] (-1.46 ¢)
| [[26/15]] (−1.46¢)
|-
|-
| 12 (260\313)
| 12 (260\313)
| 996.805
| 996.805
| [[16/9]] (+0.715 ¢)
| [[16/9]] (+0.715¢)
|-
|-
| 53 (313\313)
| 53 (313\313)
| 1200.000
| 1200.000
| [[2/1]] (±0 ¢)
| [[2/1]] (0¢)
|}
|}
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
<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 ==
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; [[User:Francium|Francium]]
; [[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] – hemischis in 313edo tuning
* "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:Albus]]
[[Category:Hemischis]]
[[Category:Hemischis]]
[[Category:Hera]]
[[Category:Hera]]
[[Category:Albus]]
[[Category:Listen]]
[[Category:Listen]]
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