32edo - Revision history

CompactStar: /* Intervals */

2026-11-07T00:30:08Z

Intervals

← Older revision		Revision as of 00:30, 7 November 2026
Line 160:		Line 160:
	\| dup 4th, updim 5th		\| dup 4th, updim 5th
	\| ^^G, ^Ab		\| ^^G, ^Ab
	\| [[11/8]], [[48/35]], ''[[27/20]]''		\| [[11/8]], ''[[27/20]]'', [[48/35]]
	\|		\|
	\|-		\|-

CompactStar: /* Intervals */

2026-11-07T00:29:08Z

Intervals

← Older revision		Revision as of 00:29, 7 November 2026
Line 48:		Line 48:
	\| up unison, minor 2nd		\| up unison, minor 2nd
	\| ^D, Eb		\| ^D, Eb
	\| ''[[25/24]]'', [[45/44]], [[49/48]]		\| ''[[25/24]]'', ''[[28/27]]'', [[45/44]], [[49/48]]
	\| 46/45, 52/51, 51/50		\| 46/45, 52/51, 51/50
	\|-		\|-
Line 288:		Line 288:
	\| major 7th, down 8ve		\| major 7th, down 8ve
	\| C#, vD		\| C#, vD
	\| ''[[48/25]]'', [[88/45]], [[96/49]]		\| ''[[27/14]]'', ''[[48/25]]'', [[88/45]], [[96/49]]
	\| 45/23, 51/26, 100/51		\| 45/23, 51/26, 100/51
	\|-		\|-

CompactStar: /* As a tuning of other temperaments */

2026-11-06T10:32:10Z

As a tuning of other temperaments

← Older revision		Revision as of 10:32, 6 November 2026
Line 17:		Line 17:
	The patent val also tempers out [[2048/2025]] in the 5-limit, and [[50/49]] with [[64/63]] in the [[7-limit]], which means it [[support]]s [[pajara]], with a very sharp fifth of 712.5 cents which could be experimented with by those with a penchant for fifths even sharper than the fifth of [[27edo]]; this fifth is in fact very close to the [[minimax tuning]] of the pajara extension [[Diaschismic family #Pajaro\|pajaro]], using the 32f val.		The patent val also tempers out [[2048/2025]] in the 5-limit, and [[50/49]] with [[64/63]] in the [[7-limit]], which means it [[support]]s [[pajara]], with a very sharp fifth of 712.5 cents which could be experimented with by those with a penchant for fifths even sharper than the fifth of [[27edo]]; this fifth is in fact very close to the [[minimax tuning]] of the pajara extension [[Diaschismic family #Pajaro\|pajaro]], using the 32f val.

	The patent fifth of 32edo can be used to generate a very unequal [[archy]] (specifically [[oceanfront]]) [[5L 2s\|diatonic scale]], with a [[chromatic semitone]] of 5 steps and a [[diatonic semitone]] of only 1. The diatonic [[major third]] (which can sound like both a major third and a flat fourth depending on context) is an interseptimal interval of 450{{c}}, approximating [[9/7]] and [[13/10]], and the minor third is 262.5{{c}}, approximating [[7/6]]. In the 11-limit 32edo provides the [[optimal patent val]] for [[kangaroo]] temperament, tempering out [[55/54]], 64/63, and [[245/242]], whereas the 32c val is equally good for [[progress]]. Both temperaments are generated by a flat [[16/11]] such that three of them reduce to [[3/2]] and six of them reduce to [[8/7]]. The 15-note scale could potentially be used as a [[detempering]] of [[15edo]].		The patent fifth of 32edo can be used to generate a very unequal [[archy]] (specifically [[oceanfront]]) [[5L 2s\|diatonic scale]], with a [[chromatic semitone]] of 5 steps and a [[diatonic semitone]] of only 1. The diatonic [[major third]] (which can sound like both a major third and a flat fourth depending on context) is an interseptimal interval of 450{{c}}, approximating [[9/7]] and [[13/10]], and the minor third is 262.5{{c}}, approximating [[7/6]] and [[15/13]]. In the 11-limit 32edo provides the [[optimal patent val]] for [[kangaroo]] temperament, tempering out [[55/54]], 64/63, and [[245/242]], whereas the 32c val is equally good for [[progress]]. Both temperaments are generated by a flat [[16/11]] such that three of them reduce to [[3/2]] and six of them reduce to [[8/7]]. The 15-note scale could potentially be used as a [[detempering]] of [[15edo]].

	=== Subsets and supersets ===		=== Subsets and supersets ===

CompactStar: /* Intervals */

2026-11-05T22:52:24Z

Intervals

← Older revision		Revision as of 22:52, 5 November 2026
Line 272:		Line 272:
	\| dudmajor 7th		\| dudmajor 7th
	\| vvC#		\| vvC#
	\| [[15/8]], [[28/15]], ''[[24/13]]''		\| [[15/8]], ''[[24/13]]'', [[28/15]]
	\| 92/49		\| 92/49
	\|-		\|-
Line 280:		Line 280:
	\| downmajor 7th		\| downmajor 7th
	\| vC#		\| vC#
	\|		\| [[21/11]], [[25/13]], ''[[64/33]]'', ''[[35/18]]'', ''[[160/81]]''
	\| 23/12, 44/23		\| 23/12, 44/23
	\|-		\|-
Line 288:		Line 288:
	\| major 7th, down 8ve		\| major 7th, down 8ve
	\| C#, vD		\| C#, vD
	\|		\| ''[[48/25]]'', [[88/45]], [[96/49]]
	\| 45/23, 51/26, 100/51		\| 45/23, 51/26, 100/51
	\|-		\|-
Line 296:		Line 296:
	\| 8ve		\| 8ve
	\| D		\| D
	\|		\| [[2/1]]
	\|		\|
	\|}		\|}

CompactStar: /* Intervals */

2026-11-05T22:47:10Z

Intervals

← Older revision		Revision as of 22:47, 5 November 2026
Line 56:		Line 56:
	\| upminor 2nd		\| upminor 2nd
	\| ^Eb		\| ^Eb
	\| [[22/21]], [[26/25]], ''[[33/32]]'', [[36/35]], ''[[81/80]]''		\| [[22/21]], [[26/25]], ''[[33/32]]'', ''[[36/35]]'', ''[[81/80]]''
	\| 24/23, 23/22		\| 24/23, 23/22
	\|-		\|-
Line 272:		Line 272:
	\| dudmajor 7th		\| dudmajor 7th
	\| vvC#		\| vvC#
	\|		\| [[15/8]], [[28/15]], ''[[24/13]]''
	\| 92/49		\| 92/49
	\|-		\|-

CompactStar: /* Intervals */

2026-11-05T22:45:36Z

Intervals

← Older revision		Revision as of 22:45, 5 November 2026
Line 56:		Line 56:
	\| upminor 2nd		\| upminor 2nd
	\| ^Eb		\| ^Eb
	\| [[22/21]], [[26/25]], ''[[33/32]]'', ''[[81/80]]''		\| [[22/21]], [[26/25]], ''[[33/32]]'', [[36/35]], ''[[81/80]]''
	\| 24/23, 23/22		\| 24/23, 23/22
	\|-		\|-

CompactStar: /* Intervals */

2026-11-05T22:45:19Z

Intervals

← Older revision		Revision as of 22:45, 5 November 2026
Line 160:		Line 160:
	\| dup 4th, updim 5th		\| dup 4th, updim 5th
	\| ^^G, ^Ab		\| ^^G, ^Ab
	\| [[11/8]], ''[[27/20]]''		\| [[11/8]], [[48/35]], ''[[27/20]]''
	\|		\|
	\|-		\|-
Line 176:		Line 176:
	\| downaug 4th, dud 5th		\| downaug 4th, dud 5th
	\| vG#, vvA		\| vG#, vvA
	\| [[16/11]],, ''[[40/27]]''		\| [[16/11]], [[35/24]], ''[[40/27]]''
	\|		\|
	\|-		\|-

CompactStar: /* Intervals */

2026-11-05T22:44:42Z

Intervals

← Older revision		Revision as of 22:44, 5 November 2026
Line 48:		Line 48:
	\| up unison, minor 2nd		\| up unison, minor 2nd
	\| ^D, Eb		\| ^D, Eb
	\| ''[[25/24]]'', [[45/44]], [[49/48~~]], [[50/49~~]]		\| ''[[25/24]]'', [[45/44]], [[49/48]]
	\| 46/45, 52/51, 51/50		\| 46/45, 52/51, 51/50
	\|-		\|-
Line 56:		Line 56:
	\| upminor 2nd		\| upminor 2nd
	\| ^Eb		\| ^Eb
	\| [[22/21]], [[26/25]], ''[[33/32]]''		\| [[22/21]], [[26/25]], ''[[33/32]]'', ''[[81/80]]''
	\| 24/23, 23/22		\| 24/23, 23/22
	\|-		\|-
Line 64:		Line 64:
	\| dupminor 2nd		\| dupminor 2nd
	\| ^^Eb		\| ^^Eb
	\| [[15/14]], [[16/15]]		\| ''[[13/12]]'', [[15/14]], [[16/15]]
	\| 49/46		\| 49/46
	\|-		\|-
Line 72:		Line 72:
	\| dudmajor 2nd		\| dudmajor 2nd
	\| vvE		\| vvE
	\| [[12/11]]		\| ''[[10/9]]'', [[12/11]], ''[[14/13]]'', [[35/32]]
	\| 25/23		\| 25/23
	\|-		\|-
Line 80:		Line 80:
	\| aug 1sn, downmajor 2nd		\| aug 1sn, downmajor 2nd
	\| D#, vE		\| D#, vE
	\| [[19/17]]		\| ''[[11/10]]''
	\| 19/17		\| 19/17
	\|-		\|-
Line 96:		Line 96:
	\| minor 3rd		\| minor 3rd
	\| F		\| F
	\| [[7/6]], [[15/13]]		\| [[7/6]], ''[[13/11]]'', [[15/13]]
	\| 57/49		\| 57/49
	\|-		\|-
Line 136:		Line 136:
	\| major 3rd		\| major 3rd
	\| F#		\| F#
	\| [[9/7]], [[13/10]]		\| [[9/7]], [[13/10]], ''[[32/25]]'', [[64/49]]
	\| 22/17, 57/44		\| 22/17, 57/44
	\|-		\|-
Line 152:		Line 152:
	\| up 4th		\| up 4th
	\| ^G		\| ^G
	\|		\| [[15/11]]
	\| 19/14, 23/17		\| 19/14, 23/17
	\|-		\|-
Line 160:		Line 160:
	\| dup 4th, updim 5th		\| dup 4th, updim 5th
	\| ^^G, ^Ab		\| ^^G, ^Ab
	\| [[11/8]]		\| [[11/8]], ''[[27/20]]''
	\|		\|
	\|-		\|-
	\| 16		\| 16
Line 168:		Line 168:
	\| dudaug 4th, dupdim 5th		\| dudaug 4th, dupdim 5th
	\| vvG#, ^^Ab		\| vvG#, ^^Ab
	\|		\| [[7/5]], [[10/7]], [[45/32]], [[64/45]]
	\| 17/12, 12/17		\| 17/12, 12/17
	\|-		\|-
Line 176:		Line 176:
	\| downaug 4th, dud 5th		\| downaug 4th, dud 5th
	\| vG#, vvA		\| vG#, vvA
	\|		\| [[16/11]],, ''[[40/27]]''
	\|		\|
	\|-		\|-
Line 184:		Line 184:
	\| down 5th		\| down 5th
	\| vA		\| vA
	\|		\| [[22/15]]
	\| 28/19, 34/23		\| 28/19, 34/23
	\|-		\|-
Line 192:		Line 192:
	\| perfect 5th		\| perfect 5th
	\| A		\| A
	\|		\| [[3/2]], [[32/21]]
	\| 68/45, 128/85		\| 68/45, 128/85
	\|-		\|-
Line 200:		Line 200:
	\| minor 6th		\| minor 6th
	\| Bb		\| Bb
	\|		\| [[14/9]], [[20/13]], ''[[25/16]]'', [[49/32]]
	\| 17/11, 88/57		\| 17/11, 88/57
	\|-		\|-
Line 208:		Line 208:
	\| upminor 6th		\| upminor 6th
	\| ^Bb		\| ^Bb
	\|		\| [[11/7]]
	\| 30/19		\| 30/19
	\|-		\|-
Line 216:		Line 216:
	\| dupminor 6th		\| dupminor 6th
	\| ^^Bb		\| ^^Bb
	\|		\| [[8/5]], [[13/8]], [[44/27]]
	\| 29/18		\| 29/18
	\|-		\|-
Line 224:		Line 224:
	\| dudmajor 6th		\| dudmajor 6th
	\| vvB		\| vvB
	\|		\| ''[[5/3]]'', [[18/11]], [[64/39]]
	\| 28/17, 23/14		\| 28/17, 23/14
	\|-		\|-
Line 232:		Line 232:
	\| downmajor 6th		\| downmajor 6th
	\| vB		\| vB
	\|		\| [[56/33]]
	\| 32/19		\| 32/19
	\|-		\|-
Line 240:		Line 240:
	\| major 6th		\| major 6th
	\| B		\| B
	\|		\| [[12/7]], ''[[22/13]]'', [[26/15]]
	\| 98/57		\| 98/57
	\|-		\|-
Line 248:		Line 248:
	\| minor 7th		\| minor 7th
	\| C		\| C
	\|		\| [[7/4]], ''[[16/9]]''
	\| 100/57		\| 100/57
	\|-		\|-
Line 256:		Line 256:
	\| upminor 7th		\| upminor 7th
	\| ^C		\| ^C
	\|		\| [[20/11]]
	\| 34/19		\| 34/19
	\|-		\|-
Line 264:		Line 264:
	\| dupminor 7th		\| dupminor 7th
	\| ^^C		\| ^^C
	\|		\| ''[[9/5]]'', [[11/6]], ''[[13/7]]'', [[64/35]]
	\| 46/25		\| 46/25
	\|-		\|-

CompactStar: /* Music */

2026-11-05T22:28:21Z

Music

← Older revision		Revision as of 22:28, 5 November 2026
Line 1,344:		Line 1,344:
	* [https://www.youtube.com/watch?v=LI-lMuAYws8 ''Revelation''] (2026)		* [https://www.youtube.com/watch?v=LI-lMuAYws8 ''Revelation''] (2026)

			== Notes ==
			<references group="note"/>
	[[Category:Listen]]		[[Category:Listen]]
	[[Category:Sixix]]		[[Category:Sixix]]
	{{Todo\|add scales list}}		{{Todo\|add scales list}}

CompactStar: /* Intervals */

2026-11-05T22:23:06Z

Intervals

← Older revision		Revision as of 22:23, 5 November 2026
Line 144:		Line 144:
	\| perfect 4th		\| perfect 4th
	\| G		\| G
	\| [[4/3]], [[32/21]]~~, [[~~		\| [[4/3]], [[21/16]]
	\| 45/34, 85/64		\| 45/34, 85/64
	\|-		\|-
Line 152:		Line 152:
	\| up 4th		\| up 4th
	\| ^G		\| ^G
	\|		\|
	\| 19/14, 23/17		\| 19/14, 23/17
	\|-		\|-
Line 160:		Line 160:
	\| dup 4th, updim 5th		\| dup 4th, updim 5th
	\| ^^G, ^Ab		\| ^^G, ^Ab
	\|		\| [[11/8]]
	\|		\|
	\|-		\|-