167edo: Difference between revisions

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== Theory ==

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== Regular temperament properties ==

{~~{comma basis begin}}~~

{| class="wikitable center-4 center-5 center-6"

|-

! rowspan="2" | [[Subgroup]]

! rowspan="2" | [[Comma list]]

! rowspan="2" | [[Mapping]]

! rowspan="2" | Optimal<br />8ve stretch (¢)

! colspan="2" | Tuning error

|-

! [[TE error|Absolute]] (¢)

! [[TE simple badness|Relative]] (%)

|-

| 2.3

| {{monzo| 265 -167 }}

| {{mapping| 167 265 }}

| ~~−0~~.7056

| −0.7056

| 0.7052

| 9.81

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| 393216/390625, {{monzo| 31 -21 1 }}

| {{mapping| 167 265 388 }}

| ~~−0~~.7158

| −0.7158

| 0.5759

| 8.01

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| 2401/2400, 3136/3125, 179200/177147

| {{mapping| 167 265 388 469 }}

| ~~−0~~.6467

| −0.6467

| 0.5129

| 7.14

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Line 53:

| 896/891, 2200/2187, 2401/2400, 3136/3125

| {{mapping| 167 265 388 469 578 }}

| ~~−0~~.6315

| −0.6315

| 0.4598

| 6.40

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| 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

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| 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

~~{{comma basis end}~~}

|}

=== Rank-2 temperaments ===

{{rank-2 ~~begin}}~~

{| class="wikitable center-all left-5"

|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator

|-

! Periods<br />per 8ve

! Generator*

! Cents*

! Associated<br />ratio*

! Temperaments

|-

| 1

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| 242/175

| [[Whoops]]

~~{{rank-2 end}~~}

|}

~~{{orf}}~~

<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct

== Scales ==

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== Music ==

; [[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]

* "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]

* "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]

* "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]]

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|167}}
+{{ED intro}}
 == Theory ==
@@ Line 18: / Line 18: @@
 == Regular temperament properties ==
-{{comma basis begin}}
+{| class="wikitable center-4 center-5 center-6"
+|-
+! rowspan="2" | [[Subgroup]]
+! rowspan="2" | [[Comma list]]
+! rowspan="2" | [[Mapping]]
+! rowspan="2" | Optimal<br />8ve stretch (¢)
+! colspan="2" | Tuning error
+|-
+! [[TE error|Absolute]] (¢)
+! [[TE simple badness|Relative]] (%)
 |-
 | 2.3
 | {{monzo| 265 -167 }}
 | {{mapping| 167 265 }}
-| &minus;0.7056
+| −0.7056
 | 0.7052
 | 9.81
@@ Line 30: / Line 39: @@
 | 393216/390625, {{monzo| 31 -21 1 }}
 | {{mapping| 167 265 388 }}
-| &minus;0.7158
+| −0.7158
 | 0.5759
 | 8.01
@@ Line 37: / Line 46: @@
 | 2401/2400, 3136/3125, 179200/177147
 | {{mapping| 167 265 388 469 }}
-| &minus;0.6467
+| −0.6467
 | 0.5129
 | 7.14
@@ Line 44: / Line 53: @@
 | 896/891, 2200/2187, 2401/2400, 3136/3125
 | {{mapping| 167 265 388 469 578 }}
-| &minus;0.6315
+| −0.6315
 | 0.4598
 | 6.40
@@ Line 51: / Line 60: @@
 | 325/324, 352/351, 364/363, 1001/1000, 1716/1715
 | {{mapping| 167 265 388 469 578 618 }}
-| &minus;0.5349
+| −0.5349
 | 0.4721
 | 6.57
@@ Line 58: / Line 67: @@
 | 256/255, 325/324, 352/351, 364/363, 442/441, 1001/1000
 | {{mapping| 167 265 388 469 578 618 683 }}
-| &minus;0.5573
+| −0.5573
 | 0.4405
 | 6.13
-{{comma basis end}}
+|}
 === Rank-2 temperaments ===
-{{rank-2 begin}}
+{| class="wikitable center-all left-5"
+|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
+|-
+! Periods<br />per 8ve
+! Generator*
+! Cents*
+! Associated<br />ratio*
+! Temperaments
 |-
 | 1
@@ Line 113: / Line 129: @@
 | 242/175
 | [[Whoops]]
-{{rank-2 end}}
+|}
-{{orf}}
+<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
 == Scales ==
@@ Line 121: / Line 137: @@
 == Music ==
 ; [[Francium]]
-* "way too random partying" from ''Helayo EP'' (2023) &ndash; [https://open.spotify.com/track/4yf5R4eVOxK2fgZEZRfCqU Spotify] | [https://francium223.bandcamp.com/track/way-too-random-partying Bandcamp] | [https://youtu.be/33T11NI7EQQ?si=mZ57p2EN4uvPCVo7 YouTube] &ndash; 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) &ndash; [https://open.spotify.com/track/5h0JcJ4YTQV20CB9N8S8Af Spotify] | [https://francium223.bandcamp.com/track/moving-on Bandcamp] | [https://www.youtube.com/watch?v=FSjU0-w6XVE YouTube]
+* "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) &ndash; [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]
+* "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) &ndash; [https://open.spotify.com/track/0ILOgCY4pzx7S3B51wA9ee Spotify] | [https://francium223.bandcamp.com/track/funky-mans-love Bandcamp] | [https://www.youtube.com/watch?v=4Evj3vX8ZDY 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]]