167edo - Revision history

FloraC: Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"

2026-03-13T13:32:51Z

Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"

← Older revision		Revision as of 13:32, 13 March 2026
Line 130:		Line 130:
	\| [[Whoops]]		\| [[Whoops]]
	\|}		\|}
	<nowiki />* [[Normal ~~lists~~\|Octave-reduced form]], reduced to the first half-octave, and [[~~Normal lists~~\|minimal form]] in parentheses if 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

	== Scales ==		== Scales ==

Francium: /* Music */ +link

2025-07-03T12:01:11Z

Music: +link

← Older revision		Revision as of 12:01, 3 July 2025
Line 141:		Line 141:
	* "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://francium223.bandcamp.com/track/dont-bother Bandcamp] \| [https://www.youtube.com/watch?v=kzlP4bWfQf8 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]]		[[Category:Listen]]

Francium: /* Music */ +music

2025-07-01T13:30:17Z

Music: +music

← Older revision		Revision as of 13:30, 1 July 2025
Line 137:		Line 137:
	== Music ==		== Music ==
	; [[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]		* "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://francium223.bandcamp.com/track/dont-bother Bandcamp] \| [https://www.youtube.com/watch?v=kzlP4bWfQf8 YouTube]

	[[Category:Listen]]		[[Category:Listen]]

Francium: changed EDO intro to ED intro

2025-02-19T18:04:59Z

changed EDO intro to ED intro

← Older revision		Revision as of 18:04, 19 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 14:59, 16 January 2025

2025-01-16T14:59:40Z

← Older revision		Revision as of 14:59, 16 January 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro~~\|167~~}}		{{EDO intro}}

	== Theory ==		== Theory ==
Line 32:		Line 32:
	\| {{monzo\| 265 -167 }}		\| {{monzo\| 265 -167 }}
	\| {{mapping\| 167 265 }}		\| {{mapping\| 167 265 }}
	\| ~~−0~~.7056		\| −0.7056
	\| 0.7052		\| 0.7052
	\| 9.81		\| 9.81
Line 39:		Line 39:
	\| 393216/390625, {{monzo\| 31 -21 1 }}		\| 393216/390625, {{monzo\| 31 -21 1 }}
	\| {{mapping\| 167 265 388 }}		\| {{mapping\| 167 265 388 }}
	\| ~~−0~~.7158		\| −0.7158
	\| 0.5759		\| 0.5759
	\| 8.01		\| 8.01
Line 46:		Line 46:
	\| 2401/2400, 3136/3125, 179200/177147		\| 2401/2400, 3136/3125, 179200/177147
	\| {{mapping\| 167 265 388 469 }}		\| {{mapping\| 167 265 388 469 }}
	\| ~~−0~~.6467		\| −0.6467
	\| 0.5129		\| 0.5129
	\| 7.14		\| 7.14
Line 53:		Line 53:
	\| 896/891, 2200/2187, 2401/2400, 3136/3125		\| 896/891, 2200/2187, 2401/2400, 3136/3125
	\| {{mapping\| 167 265 388 469 578 }}		\| {{mapping\| 167 265 388 469 578 }}
	\| ~~−0~~.6315		\| −0.6315
	\| 0.4598		\| 0.4598
	\| 6.40		\| 6.40
Line 60:		Line 60:
	\| 325/324, 352/351, 364/363, 1001/1000, 1716/1715		\| 325/324, 352/351, 364/363, 1001/1000, 1716/1715
	\| {{mapping\| 167 265 388 469 578 618 }}		\| {{mapping\| 167 265 388 469 578 618 }}
	\| ~~−0~~.5349		\| −0.5349
	\| 0.4721		\| 0.4721
	\| 6.57		\| 6.57
Line 67:		Line 67:
	\| 256/255, 325/324, 352/351, 364/363, 442/441, 1001/1000		\| 256/255, 325/324, 352/351, 364/363, 442/441, 1001/1000
	\| {{mapping\| 167 265 388 469 578 618 683 }}		\| {{mapping\| 167 265 388 469 578 618 683 }}
	\| ~~−0~~.5573		\| −0.5573
	\| 0.4405		\| 0.4405
	\| 6.13		\| 6.13
Line 130:		Line 130:
	\| [[Whoops]]		\| [[Whoops]]
	\|}		\|}
	<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 lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if distinct

	== Scales ==		== Scales ==
Line 137:		Line 137:
	== Music ==		== Music ==
	; [[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] – helayo in 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]

	[[Category:Listen]]		[[Category:Listen]]

ArrowHead294: Partial undo

2024-11-16T12:19:25Z

Partial undo

← Older revision		Revision as of 12:19, 16 November 2024
Line 18:		Line 18:

	== Regular temperament properties ==		== 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		\| 2.3
Line 61:		Line 70:
	\| 0.4405		\| 0.4405
	\| 6.13		\| 6.13
	~~{{comma basis end}~~}		\|}

	=== Rank-2 temperaments ===		=== 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		\| 1
Line 113:		Line 129:
	\| 242/175		\| 242/175
	\| [[Whoops]]		\| [[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 it is distinct

	== Scales ==		== Scales ==

ArrowHead294 at 05:02, 16 November 2024

2024-11-16T05:02:42Z

← Older revision		Revision as of 05:02, 16 November 2024
Line 18:		Line 18:

	== Regular temperament properties ==		== Regular temperament properties ==
	{~~\| class="wikitable center-4 center-5 center-6"~~		{{comma basis begin}}
	~~! rowspan="2" \| [[Subgroup]]~~
	~~! rowspan="2" \| [[Comma list\|Comma List]]~~
	~~! rowspan="2" \| [[Mapping]]~~
	~~! rowspan="2" \| Optimal<br>8ve Stretch (¢)~~
	~~! colspan="2" \| Tuning Error~~
	\|-
	~~! [[TE error\|Absolute]] (¢)~~
	~~! [[TE simple badness\|Relative]] (%)~~
	\|-		\|-
	\| 2.3		\| 2.3
	\| {{monzo\| 265 -167 }}		\| {{monzo\| 265 -167 }}
	\| {{mapping\| 167 265 }}		\| {{mapping\| 167 265 }}
	\| -0.7056		\| −0.7056
	\| 0.7052		\| 0.7052
	\| 9.81		\| 9.81
Line 38:		Line 30:
	\| 393216/390625, {{monzo\| 31 -21 1 }}		\| 393216/390625, {{monzo\| 31 -21 1 }}
	\| {{mapping\| 167 265 388 }}		\| {{mapping\| 167 265 388 }}
	\| -0.7158		\| −0.7158
	\| 0.5759		\| 0.5759
	\| 8.01		\| 8.01
Line 45:		Line 37:
	\| 2401/2400, 3136/3125, 179200/177147		\| 2401/2400, 3136/3125, 179200/177147
	\| {{mapping\| 167 265 388 469 }}		\| {{mapping\| 167 265 388 469 }}
	\| -0.6467		\| −0.6467
	\| 0.5129		\| 0.5129
	\| 7.14		\| 7.14
Line 52:		Line 44:
	\| 896/891, 2200/2187, 2401/2400, 3136/3125		\| 896/891, 2200/2187, 2401/2400, 3136/3125
	\| {{mapping\| 167 265 388 469 578 }}		\| {{mapping\| 167 265 388 469 578 }}
	\| -0.6315		\| −0.6315
	\| 0.4598		\| 0.4598
	\| 6.40		\| 6.40
Line 59:		Line 51:
	\| 325/324, 352/351, 364/363, 1001/1000, 1716/1715		\| 325/324, 352/351, 364/363, 1001/1000, 1716/1715
	\| {{mapping\| 167 265 388 469 578 618 }}		\| {{mapping\| 167 265 388 469 578 618 }}
	\| -0.5349		\| −0.5349
	\| 0.4721		\| 0.4721
	\| 6.57		\| 6.57
Line 66:		Line 58:
	\| 256/255, 325/324, 352/351, 364/363, 442/441, 1001/1000		\| 256/255, 325/324, 352/351, 364/363, 442/441, 1001/1000
	\| {{mapping\| 167 265 388 469 578 618 683 }}		\| {{mapping\| 167 265 388 469 578 618 683 }}
	\| -0.5573		\| −0.5573
	\| 0.4405		\| 0.4405
	\| 6.13		\| 6.13
	\|}		{{comma basis end}}

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{~~\| class="wikitable center-all left-5"~~		{{rank-2 begin}}
	~~\|+Table of~~ rank-2 ~~temperaments by generator~~
	~~! Periods<br>per 8ve~~
	! Generator*
	! Cents*
	! Associated<br>Ratio*
	~~! Temperaments~~
	\|-		\|-
	\| 1		\| 1
Line 127:		Line 113:
	\| 242/175		\| 242/175
	\| [[Whoops]]		\| [[Whoops]]
	\|}		{{rank-2 end}}
	~~<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct~~		{{orf}}

	== Scales ==		== Scales ==
Line 135:		Line 121:
	== Music ==		== Music ==
	; [[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] – helayo in 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]

	[[Category:Listen]]		[[Category:Listen]]

Francium: /* Music */ +music

2024-10-06T12:10:27Z

Music: +music

← Older revision		Revision as of 12:10, 6 October 2024
Line 134:		Line 134:

	== Music ==		== 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] – helayo in 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]

	[[Category:Listen]]		[[Category:Listen]]

FloraC: +some commas; gen for whoops

2024-05-14T08:56:39Z

+some commas; gen for whoops

← Older revision		Revision as of 08:56, 14 May 2024
Line 3:		Line 3:

	== Theory ==		== Theory ==
	167et [[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 [[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.		167et [[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.

	167edo also has a very close approximation to the [[golden magic]] scale.		167edo also has a very close approximation to the [[golden magic]] scale.
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	\| 78\167		\| 78\167
	\| 560.48		\| 560.48
	\| ~~864~~/~~625~~		\| 242/175
	\| [[Whoops]]		\| [[Whoops]]
	\|}		\|}

FloraC: Cleanup

2024-05-05T08:44:40Z

Cleanup

← Older revision		Revision as of 08:44, 5 May 2024
Line 3:		Line 3:

	== Theory ==		== Theory ==
	167et [[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~~]].		167et [[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 [[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.

	167edo also has a very close approximation to the [[golden magic]] scale.		167edo also has a very close approximation to the [[golden magic]] scale.
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	\|+Table of rank-2 temperaments by generator		\|+Table of rank-2 temperaments by generator
	! Periods<br>per 8ve		! Periods<br>per 8ve
	! Generator~~<br>(reduced)~~		! Generator*
	! Cents~~<br>(reduced)~~		! Cents*
	! Associated<br>~~ratio~~		! Associated<br>Ratio*
	! Temperaments		! 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		\| 864/625
	\|[[~~Whoosh]] / [[whoops~~]]		\| [[Whoops]]
	\|}		\|}
			<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

	== Scales ==		== Scales ==
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	* "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] – helayo in 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]

	[[Category:Listen]]		[[Category:Listen]]