167edo: Difference between revisions

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@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|167}}
+{{ED intro}}
 == Theory ==
-et [[tempering out|tempers out]] the [[würschmidt comma]], 393216/390625, and the leapday comma, {{monzo| 31 -21 1 }}, in the [[5-limit]]; [[2401/2400]], [[3136/3125]], and 179200/177147 in the [[7-limit]]; [[896/891]], 2200/2187, and 3388/3375 in the [[11-limit]]; [[325/324]], [[352/351]], [[364/363]], [[1001/1000]], and [[1716/1715]] in the [[13-limit]], providing the [[optimal patent val]] for 11- and 13-limit [[Porwell temperaments|polypyth temperament]]; [[256/255]], [[442/441]], [[595/594]], [[715/714]], and [[936/935]] in the [[17-limit]]. It also [[support]]s the 11-limit [[Breedsmic temperaments #Unthirds|unthirds temperament]].
+et [[tempering out|tempers out]] the [[würschmidt comma]], 393216/390625, and the leapday comma, {{monzo| 31 -21 1 }}, in the [[5-limit]]; [[2401/2400]], [[3136/3125]], [[6144/6125]], and 179200/177147 in the [[7-limit]]; [[896/891]], [[2200/2187]], [[3025/3024]], [[3388/3375]], and [[4000/3993]] in the [[11-limit]]; [[325/324]], [[352/351]], [[364/363]], [[1001/1000]], and [[1716/1715]] in the [[13-limit]], providing the [[optimal patent val]] for 11- and 13-limit [[polypyth]] temperament; [[256/255]], [[442/441]], [[595/594]], [[715/714]], and [[936/935]] in the [[17-limit]]. It also [[support]]s the 11-limit [[unthirds]] temperament.
 edo also has a very close approximation to the [[golden magic]] scale.
@@ Line 13: / Line 13: @@
 === Subsets and supersets ===
 edo is the 39th [[prime edo]].
+== Intervals ==
+{{Main|Table of 167edo intervals}}
 == Regular temperament properties ==
 {| class="wikitable center-4 center-5 center-6"
+|-
 ! rowspan="2" | [[Subgroup]]
-! rowspan="2" | [[Comma list|Comma List]]
+! rowspan="2" | [[Comma list]]
 ! 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]] (¢)
@@ Line 28: / Line 32: @@
 | {{monzo| 265 -167 }}
 | {{mapping| 167 265 }}
-| -0.7056
+| −0.7056
 | 0.7052
 | 9.81
@@ Line 35: / Line 39: @@
 | 393216/390625, {{monzo| 31 -21 1 }}
 | {{mapping| 167 265 388 }}
-| -0.7158
+| −0.7158
 | 0.5759
 | 8.01
@@ Line 42: / Line 46: @@
 | 2401/2400, 3136/3125, 179200/177147
 | {{mapping| 167 265 388 469 }}
-| -0.6467
+| −0.6467
 | 0.5129
 | 7.14
@@ Line 49: / Line 53: @@
 | 896/891, 2200/2187, 2401/2400, 3136/3125
 | {{mapping| 167 265 388 469 578 }}
-| -0.6315
+| −0.6315
 | 0.4598
 | 6.40
@@ Line 56: / Line 60: @@
 | 325/324, 352/351, 364/363, 1001/1000, 1716/1715
 | {{mapping| 167 265 388 469 578 618 }}
-| -0.5349
+| −0.5349
 | 0.4721
 | 6.57
@@ Line 63: / Line 67: @@
 | 256/255, 325/324, 352/351, 364/363, 442/441, 1001/1000
 | {{mapping| 167 265 388 469 578 618 683 }}
-| -0.5573
+| −0.5573
 | 0.4405
 | 6.13
@@ Line 70: / Line 74: @@
 === Rank-2 temperaments ===
 {| class="wikitable center-all left-5"
-|+Table of rank-2 temperaments by generator
+|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
-! Periods<br>per 8ve
+|-
-! Generator<br>(reduced)
+! Periods<br />per 8ve
-! Cents<br>(reduced)
+! Generator*
-! Associated<br>ratio
+! Cents*
+! Associated<br />ratio*
 ! Temperaments
 |-
-|1
+| 1
-|27\167
+| 27\167
-|194.01
+| 194.01
-|28/25
+| 28/25
-|[[Hemiwürschmidt]]
+| [[Hemiwürschmidt]]
 |-
-|1
+| 1
-|44\167
+| 44\167
-|316.17
+| 316.17
-|6/5
+| 6/5
-|[[Counterhanson]]
+| [[Counterhanson]]
 |-
-|1
+| 1
-|54\167
+| 54\167
-|388.02
+| 388.02
-|5/4
+| 5/4
-|[[Würschmidt]]
+| [[Würschmidt]]
 |-
-|1
+| 1
-|58\167
+| 58\167
-|416.77
+| 416.77
-|14/11
+| 14/11
-|[[Unthirds]]
+| [[Unthirds]] (11-limit)
 |-
-|1
+| 1
-|63\167
+| 63\167
-|452.69
+| 452.69
-|125/96
+| 125/96
-|[[Maja]]
+| [[Majo]]
 |-
-|1
+| 1
-|69\167
+| 69\167
-|495.81
+| 495.81
-|4/3
+| 4/3
-|[[Trisayo]] / [[polypyth]]
+| [[Polypyth]]
 |-
-|1
+| 1
-|70\167
+| 70\167
-|502.99
+| 502.99
-|147/110
+| 147/110
-|[[Quadrawürschmidt]]
+| [[Quadrawürschmidt]]
 |-
-|1
+| 1
-|78\167
+| 78\167
-|560.48
+| 560.48
-|864/625
+| 242/175
-|[[Whoosh]] / [[whoops]]
+| [[Whoops]]
 |}
+<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 ==
+* [[Helayo19]]
 == Music ==
-; [[User:Francium|Francium]]
+; [[Francium]]
-* "way too random partying" from ''Helayo EP'' (2023) – [https://open.spotify.com/track/4yf5R4eVOxK2fgZEZRfCqU Spotify] | [https://francium223.bandcamp.com/track/way-too-random-partying Bandcamp] | [https://youtu.be/33T11NI7EQQ?si=mZ57p2EN4uvPCVo7 YouTube] – helayo in 167edo tuning
+* "way too random partying" from ''Helayo EP'' (2023) – [https://open.spotify.com/track/4yf5R4eVOxK2fgZEZRfCqU Spotify] | [https://francium223.bandcamp.com/track/way-too-random-partying Bandcamp] | [https://youtu.be/33T11NI7EQQ?si=mZ57p2EN4uvPCVo7 YouTube] – in Helayo, 167edo tuning
+* "moving on" from ''hope in dark times'' (2024) – [https://open.spotify.com/track/5h0JcJ4YTQV20CB9N8S8Af Spotify] | [https://francium223.bandcamp.com/track/moving-on Bandcamp] | [https://www.youtube.com/watch?v=FSjU0-w6XVE YouTube]
+* "ordering the universal theme on wish" from ''End of Sartorius Membranes'' (2024) – [https://open.spotify.com/track/00S85fGWQBI19kRwC9GrJ2 Spotify] | [https://francium223.bandcamp.com/track/ordering-the-universal-theme-on-wish Bandcamp] | [https://www.youtube.com/watch?v=g70V2NIPq1I YouTube]
+* "Funky Man's Love" from ''Abbreviations Gone Wrong'' (2024) – [https://open.spotify.com/track/0ILOgCY4pzx7S3B51wA9ee Spotify] | [https://francium223.bandcamp.com/track/funky-mans-love Bandcamp] | [https://www.youtube.com/watch?v=4Evj3vX8ZDY YouTube]
+* "Don't Bother" from ''Don't'' (2025) – [https://open.spotify.com/track/5B9LMtfG3wTNgQX0PKBFO3 Spotify] | [https://francium223.bandcamp.com/track/dont-bother Bandcamp] | [https://www.youtube.com/watch?v=kzlP4bWfQf8 YouTube]
+[[Category:Listen]]