Xenharmonic Wiki - Recent changes [en]

Enaeikosany

BudjarnLambeth — Fri, 26 Jun 2026 12:12:52 GMT

Created page with "See Combination product set. Category:Smart redirect"

New page

See [[Combination product set]].

[[Category:Smart redirect]]

Pentatriandekany

BudjarnLambeth — Fri, 26 Jun 2026 12:12:48 GMT

Created page with "See Combination product set. Category:Smart redirect"

New page

See [[Combination product set]].

[[Category:Smart redirect]]

Gallery of combination product sets

BudjarnLambeth — Fri, 26 Jun 2026 12:11:47 GMT

Other: Add new

← Older revision		Revision as of 12:11, 26 June 2026
(One intermediate revision by the same user not shown)
Line 646:		Line 646:
	=== Other ===		=== Other ===
	* [[Eikosanyplusop]]		* [[Eikosanyplusop]]

			== Other ==
	* [[1-3-5-7-9-11-13 enaeikosany]]		* [[1-3-5-7-9-11-13 enaeikosany]]
	* [[1-3-5-7-9-11-15 enaeikosany]]		* [[1-3-5-7-9-11-15 enaeikosany]]
	* [[1-3-5-7-9-13-15 enaeikosany]]		* [[1-3-5-7-9-13-15 enaeikosany]]
	* [[1-3-5-7-11-13-15 enaeikosany]]		* [[1-3-5-7-11-13-15 enaeikosany]]
			* [[1-3-5-9-11-13-15 enaeikosany]]
			* [[1-3-7-9-11-13-15 enaeikosany]]
			* [[1-5-7-9-11-13-15 enaeikosany]]
			* [[3-5-7-9-11-13-15 enaeikosany]]
	* [[1-3-5-7-9-11-13 pentatriandekany]]		* [[1-3-5-7-9-11-13 pentatriandekany]]
	* [[1-3-5-7-9-11-15 pentatriandekany]]		* [[1-3-5-7-9-11-15 pentatriandekany]]
	* [[1-3-5-7-9-13-15 pentatriandekany]]		* [[1-3-5-7-9-13-15 pentatriandekany]]
			* [[1-3-5-7-11-13-15 pentatriandekany]]
			* [[1-3-5-9-11-13-15 pentatriandekany]]
			* [[1-3-7-9-11-13-15 pentatriandekany]]
			* [[1-5-7-9-11-13-15 pentatriandekany]]
			* [[3-5-7-9-11-13-15 pentatriandekany]]
			* [[1-3-5-7-9-11-13-15 octaeikosany]]

	{{navbox scale gallery}}		{{navbox scale gallery}}

Well temperament

BudjarnLambeth — Fri, 26 Jun 2026 12:06:35 GMT

← Older revision		Revision as of 12:06, 26 June 2026
Line 1:		Line 1:
	{{Wikipedia\|Well temperament}}		{{Wikipedia\|Well temperament}}
	A '''well temperament''' (or '''circulating temperament''') is a [[tuning system]] which is regarded as an approximation of an [[equal tuning]], has the same [[equave]] as that equal tuning and preserves the transposability of the equal tuning, but is not exactly the equal tuning being approximated. Historical well temperaments were formed by stacking a combination of pure [[3/2]] and flattened fifths (occasionally also sharpened fifths) and had 12 nearly equal steps.		A '''well temperament''' (or '''circulating temperament''') is a [[tuning system]] which is regarded as an approximation of an [[equal tuning]], has the same [[equave]] as that equal tuning and preserves the transposability of the equal tuning (every key is still 'good enough'), but it is not exactly the equal tuning being approximated. Historical well temperaments were formed by stacking a combination of pure [[3/2]] and flattened fifths (occasionally also sharpened fifths) and had 12 nearly equal steps.

	One of the advantages of these tunings is that because they are not quite equal, each chord (or key) has a slightly different character because the interval sizes have changed slightly.		One of the advantages of these tunings is that because they are not quite equal, each chord (or key) has a slightly different character because the interval sizes have changed slightly.

1-3-5-7-9-11-13-15 octaeikosany

Yourmusic Productions — Fri, 26 Jun 2026 09:36:12 GMT

Almost finished the entire 15-odd limit.

New page

[[File:1-3-5-7-9-11-13-15_Octaeikosany.png|thumb|Circle diagram.]] The simplest possible octaeikosany, comprised of two-combination sum products of the first 8 odd numbers. This creates a scale of 1 65/64 33/32 13/12 35/32 9/8 55/48 7/6 39/32 5/4 21/16 65/48 11/8 45/32 35/24 143/96 3/2 25/16 77/48 13/8 5/3 55/32 7/4 11/6 15/8 91/48 2/1, with steps of 65/64 66/65 104/99 105/104 36/35 55/54 56/55 117/112 40/39 21/20 65/63 66/65 45/44 28/27 143/140 144/143 25/24 77/75 78/77 40/39 33/32 56/55 22/21 45/44 91/90 96/91. (5/4 and 15/8 appear twice, reducing it to a 26 note scale.) This contains all the smaller [[15-odd-limit]] [[hexany|hexanies]] and [[dekany|dekanies]], although some will require rotation to see in the mode they originally appear in. It has 14 perfect fifths and covers the whole harmonic sequence from 8-16 above the root, as well as the familiar diatonic scale in the lydian mode, making it more than capable of playing all kinds of music both familiar and xenharmonic.

<pre>
! 1-3-5-7-9-11-13-15_Octaeikosany.scl
!
1 3 5 7 9 11 13 15 2-combination Octaeikosany
26
!
26.841
53.272
138.572
155.139
203.910
235.676
266.871
342.482
386.313
470.781
524.886
551.317
590.223
653.184
689.890
701.955
772.627
818.188
840.527
884.358
937.631
968.825
1049.362
1088.268
1107.398
1200
</pre>

[[Category:Combination product sets]]
[[Category:26-tone scales]]
[[Category:Pages with Scala files]]

File:1-3-5-7-9-11-13-15 Octaeikosany.png

Yourmusic Productions — Fri, 26 Jun 2026 09:15:00 GMT

Yourmusic Productions uploaded File:1-3-5-7-9-11-13-15 Octaeikosany.png Made with [https://nickvuci.github.io/ScaleCircle ''ScaleCircle''] by Nick Vuci.

New page

== Summary ==
Made with [https://nickvuci.github.io/ScaleCircle ''ScaleCircle''] by [[Nick Vuci]].
== Licensing ==
{{self|cc-by-sa-4.0}}

User:Thewesterntree

FloraC — Fri, 26 Jun 2026 05:32:43 GMT

User account Thewesterntree was created by FloraC and password was sent by email

Landscape microtemperaments

FloraC — Thu, 25 Jun 2026 12:59:43 GMT

← Older revision		Revision as of 12:59, 25 June 2026
Line 9:		Line 9:
	* ''[[Tritricot]]'' (+{{monzo\| 35 -23 -3 3 }}) → [[Alphatricot family #Tritricot\|Alphatricot family]]		* ''[[Tritricot]]'' (+{{monzo\| 35 -23 -3 3 }}) → [[Alphatricot family #Tritricot\|Alphatricot family]]
	* [[Compton]] (+225/224) → [[Compton family #Compton\|Compton family]]		* [[Compton]] (+225/224) → [[Compton family #Compton\|Compton family]]
	* ''[[Terture]]'' (+359661568/358722675) → [[Vulture family #~~Domain~~\|Vulture family]]		* ''[[Terture]]'' (+359661568/358722675) → [[Vulture family #Terture\|Vulture family]]
	* ''[[Chromat]]'' (10976/10935) → [[~~Hemimage temperaments~~ #Chromat\|~~Hemimage temperaments~~]]		* ''[[Pentadecal]]'' (+875/864) → [[Keemic temperaments #Pentadecal\|Keemic temperaments]]
			* ''[[Chromat]]'' (+10976/10935) → [[Amity family #Chromat\|Amity family]]
	* ''[[Tritikleismic]]'' (+1029/1024) → [[Kleismic family #Tritikleismic\|Kleismic family]]		* ''[[Tritikleismic]]'' (+1029/1024) → [[Kleismic family #Tritikleismic\|Kleismic family]]
	* [[Ennealimmal]] (+2401/2400 or 4375/4374) → [[Septiennealimmal clan #Ennealimmal\|Septiennealimmal clan]]		* [[Ennealimmal]] (+2401/2400 or 4375/4374) → [[Septiennealimmal clan #Ennealimmal\|Septiennealimmal clan]]

Category:Cloudy clan

FloraC — Thu, 25 Jun 2026 12:00:37 GMT

FloraC deleted page Category:Cloudy clan Category for a dissolved temp family

Marvel temperaments

FloraC — Thu, 25 Jun 2026 11:59:11 GMT

Decic: make it explicit that it's a 10th-octave temp

← Older revision		Revision as of 11:59, 25 June 2026
Line 601:		Line 601:
	{{Main\| Decic }}		{{Main\| Decic }}

	Named by [[Xenllium]] in 2021, decic tempers out 16807/16384, the [[cloudy comma]], and {{monzo\| 11 -10 -10 10 }}, the [[linus comma]], in addition to the marvel comma~~, and~~ may be described as the {{nowrap\| 50 & 60 }} temperament, [[support]]ed by [[10edo\|10-]], [[50edo\|50-]], and [[60edo]]. It can be extended ~~naturally~~ to the 11-, 13-, and 17-limit by adding [[385/384]], [[105/104]], and [[170/169]] to the comma list in this order.		Named by [[Xenllium]] in 2021, decic tempers out 16807/16384, the [[cloudy comma]], and {{monzo\| 11 -10 -10 10 }}, the [[linus comma]], in addition to the marvel comma. It may be described as the {{nowrap\| 50 & 60 }} temperament, with a period of 1/10 octave and a [[ploidacot]] signature of decaploid monocot. It is [[support]]ed by [[10edo\|10-]], [[50edo\|50-]], and [[60edo]].

			It can be extended to the 11-, 13-, and 17-limit by adding [[385/384]], [[105/104]], and [[170/169]] to the comma list in this order.

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7

Decic

FloraC — Thu, 25 Jun 2026 11:55:31 GMT

Nothing too interesting here

Show changes

Warlock

FloraC — Thu, 25 Jun 2026 11:40:36 GMT

Recategorize

← Older revision		Revision as of 11:40, 25 June 2026
Line 3:		Line 3:
	[[Category:Rank-2 temperaments]]		[[Category:Rank-2 temperaments]]
	[[Category:Magic family]]		[[Category:Magic family]]
	~~[[Category:Cloudy clan]]~~

Cloudy

FloraC — Thu, 25 Jun 2026 11:39:18 GMT

Update

← Older revision		Revision as of 11:39, 25 June 2026
Line 1:		Line 1:
	#REDIRECT [[~~cloudy clan~~]]		#REDIRECT [[Miscellaneous 7-limit temperaments #Cloudy]]

			[[Category:Cloudy\| ]] <!-- main article -->
			[[Category:Rank-3 temperaments]]

Cloudy comma

FloraC — Thu, 25 Jun 2026 11:38:33 GMT

- temp data (addressed in misc. 7-limit temps), thereby removing the 11-limit extension as there's no justification for it

@@ Line 8: / Line 8: @@
 == Temperaments ==
-[[Tempering out]] this comma splits the octave into 5 equal parts and maps the [[7/4|harmonic seventh]] to [[5edo|4\5]]. For equal divisions ''N'' up to 65, the comma is tempered out if and only if 5 divides ''N''. Examples are [[5edo]], [[10edo]], [[15edo]], [[50edo]], [[55edo]] and [[65edo]]. Rank-2 temperaments tempering it out include [[blackwood]], [[coblack]], [[cloudtone]], [[sengasec]], [[warlock]], [[pentacloud]], [[decic]], [[pentadecal]], and [[quinkee]].
+[[Tempering out]] this comma splits the octave into 5 equal parts and maps the [[7/4|harmonic seventh]] to [[5edo|4\5]]. In the full 7-limit, this leads to the rank-3 [[cloudy]] temperament. For [[edo]]s ''N'' up to 65, the comma is tempered out if and only if 5 divides ''N''. Examples are [[5edo]], [[10edo]], [[15edo]], [[50edo]], [[55edo]] and [[65edo]]. Rank-2 temperaments tempering it out include [[blackwood]], [[coblack]], [[cloudtone]], [[sengasec]], [[warlock]], [[pentacloud]], [[decic]], [[pentadecal]], and [[quinkee]].
 [[Category:Cloudy]]
 [[Category:Commas named for their regular temperament properties]]

Miscellaneous 7-limit temperaments

FloraC — Thu, 25 Jun 2026 11:35:25 GMT

Move cloudy here

← Older revision		Revision as of 11:35, 25 June 2026
Line 500:		Line 500:

	[[Badness]] (Sintel): 13.3		[[Badness]] (Sintel): 13.3

			== Cloudy ==
			Cloudy tempers out the [[cloudy comma]], a.k.a. the 5-7-comma, equating the octave with a stack of five [[8/7]]'s.

			[[Subgroup]]: 2.3.5.7

			[[Comma list]]: 16807/16384

			{{Mapping\|legend=1\| 5 0 0 14 \| 0 1 0 0 \| 0 0 1 0 }}
			: Mapping generators: ~8/7, ~3, ~5

			[[Optimal tuning]]s:
			* [[WE]]: ~8/7 = 240.3136{{c}}, ~3/2 = 700.3807{{c}}, ~5/4 = 383.1686{{c}}
			: [[error map]]: {{val\| +1.568 -0.007 -0.010 -4.436 }}
			* [[CWE]]: ~8/7 = 240.0000{{c}}, ~3/2 = 700.2940{{c}}, ~5/4 = 383.8804{{c}}
			: error map: {{val\| 0.000 -1.661 -2.433 -8.826 }}

			{{Optimal ET sequence\|legend=1\| 5, 10, 15, 35, 40, 45, 50, 60, 110d, 170cdd, 175dd, 235cddd }}

			[[Badness]] (Sintel): 13.9

	== Linus ==		== Linus ==

Miscellaneous 5-limit temperaments

FloraC — Thu, 25 Jun 2026 11:21:41 GMT

Update

← Older revision		Revision as of 11:21, 25 June 2026
Line 723:		Line 723:

	== Pentadecal ==		== Pentadecal ==
	: ''For extensions, see [[~~Cloudy clan~~ #Pentadecal]].''		: ''For extensions, see [[Keemic temperaments #Pentadecal]].''

	[[Subgroup]]: 2.3.5		[[Subgroup]]: 2.3.5

Talk:Keemic temperaments

FloraC — Thu, 25 Jun 2026 11:20:00 GMT

Created page with "== Pentadecal == The 11-limit extension is problematic and as we can see the other extension has much lower badness. This is becuz pentadecal tempers out 64827/64000 and suggests using the identity 64827/64000 = (121/120)⋅(441/440)<sup>2</sup>, which competes with the keemic path of extension using the identity 875/864 = (100/99)⋅(385/384), and is evidenced by the fact that both 45 and 60 are kinda dual-11 systems. Another problem is the extension of the other 11-l..."

New page

== Pentadecal ==
The 11-limit extension is problematic and as we can see the other extension has much lower badness. This is becuz pentadecal tempers out 64827/64000 and suggests using the identity 64827/64000 = (121/120)⋅(441/440)<sup>2</sup>, which competes with the keemic path of extension using the identity 875/864 = (100/99)⋅(385/384), and is evidenced by the fact that both 45 and 60 are kinda dual-11 systems.

Another problem is the extension of the other 11-limit extension to the 13-limit. It should be 15 & 45f. The 45f val should be used as it's significantly better, and of course 15 is better than 15f. This is the same mapping of 13 as the above 11-limit extension. Therefore only these two mappings are worth documenting: 15 & 45f and 15 & 45ef.

If we can't come up with appropriate names for them right now, I think both 11-limit extensions should be deleted and it should be presented as 2.3.5.7.13.

—[[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 11:19, 25 June 2026 (UTC)

Starling temperaments

FloraC — Thu, 25 Jun 2026 11:01:21 GMT

Update

← Older revision		Revision as of 11:01, 25 June 2026
Line 17:		Line 17:
	* [[Wollemia]] (+2240/2187) → [[Tetracot family #Wollemia\|Tetracot family]]		* [[Wollemia]] (+2240/2187) → [[Tetracot family #Wollemia\|Tetracot family]]
	* ''[[Unicorn]]'' (+10976/10935) → [[Unicorn family #Unicorn\|Unicorn family]]		* ''[[Unicorn]]'' (+10976/10935) → [[Unicorn family #Unicorn\|Unicorn family]]
	* ''[[Coblack]]'' (+16807/16384) → [[Trisedodge family #Coblack\|Trisedodge family~~]] / [[Cloudy clan #Coblack\|cloudy clan~~]]		* ''[[Coblack]]'' (+16807/16384) → [[Trisedodge family #Coblack\|Trisedodge family]]
	* ''[[Grackle]]'' (+32805/32768) → [[Schismatic family #Grackle\|Schismatic family]]		* ''[[Grackle]]'' (+32805/32768) → [[Schismatic family #Grackle\|Schismatic family]]
	* ''[[Worschmidt]]'' (+33075/32768) → [[Würschmidt family #Worschmidt\|Würschmidt family]]		* ''[[Worschmidt]]'' (+33075/32768) → [[Würschmidt family #Worschmidt\|Würschmidt family]]

Coblack

FloraC — Thu, 25 Jun 2026 10:59:35 GMT

Update

← Older revision		Revision as of 10:59, 25 June 2026
Line 1:		Line 1:
	#redirect [[~~Cloudy clan~~ #Coblack]]		#redirect [[Trisedodge family #Coblack]]

	[[Category:~~Temperaments~~]]		[[Category:Rank-2 temperaments]]
	[[Category:Trisedodge family]]		[[Category:Trisedodge family]]
	~~[[Category:Cloudy clan]]~~
	[[Category:Starling temperaments]]		[[Category:Starling temperaments]]

Talk:Marvel temperaments

FloraC — Thu, 25 Jun 2026 10:58:06 GMT

← Older revision		Revision as of 10:58, 25 June 2026
Line 79:		Line 79:
	== Links to other marvel temperaments ==		== Links to other marvel temperaments ==
	I was the one who added these details in the first place so I know what I'm doing by undoing them. All these details don't inform much yet they take an enormous amount of space, making these links difficult to use. If you want to know about one of these temps, click the link and you'll likely find a description on what it does. —[[User:FloraC\|FloraC]] ([[User talk:FloraC\|talk]]) 10:19, 2 May 2026 (UTC)		I was the one who added these details in the first place so I know what I'm doing by undoing them. All these details don't inform much yet they take an enormous amount of space, making these links difficult to use. If you want to know about one of these temps, click the link and you'll likely find a description on what it does. —[[User:FloraC\|FloraC]] ([[User talk:FloraC\|talk]]) 10:19, 2 May 2026 (UTC)

			== Decic ==
			Uses the same mapping for 13 in all its extensions, so the 11-limit extension may be decanonicalized in favor of the 2.3.5.7.13 subgroup interpretation. —[[User:FloraC\|FloraC]] ([[User talk:FloraC\|talk]]) 10:58, 25 June 2026 (UTC)

5-7-comma

FloraC — Thu, 25 Jun 2026 10:54:07 GMT

Redirected page to Cloudy comma

New page

#redirect [[Cloudy comma]]

Cloudy comma

FloraC — Thu, 25 Jun 2026 10:53:44 GMT

Rework

← Older revision		Revision as of 10:53, 25 June 2026
Line 5:		Line 5:
	\| Comma = yes		\| Comma = yes
	}}		}}
			'''16807/16384''', the '''cloudy comma''', or systematically the '''5-7-comma''', is a [[medium comma]] in the [[7-limit]] with a size of about 44.1 [[cent]]s. It is the amount by which five [[8/7]]'s fall short of an octave. In the [[2.5.7 subgroup]], it exceeds [[128/125]] by the [[rainy comma]].
	'''16807/16384''', the '''cloudy comma''', is a 7-limit ~~medium comma~~. It is the amount by which five [[8/7]]s fall short of ~~one~~ octave ~~and exceeds [[128/125]] by~~ the [[~~rainy comma]]~~. ~~For equal divisions ''N'' up to 65, the comma is tempered out if and only if~~ 5 ~~divides ''N''~~. ~~Examples are [[5edo~~]], [[~~10edo~~]], [[~~15edo]], [[50edo]], [[55edo]] and [[65edo~~]].

	== Temperaments ==		== Temperaments ==
	Tempering out ~~the cloudy~~ comma splits the octave into 5 equal parts and maps the harmonic 7 to 4\5. ~~It leads~~ to ~~a number of regular~~ temperaments ~~in the~~ [[~~cloudy clan~~]].		[[Tempering out]] this comma splits the octave into 5 equal parts and maps the [[7/4\|harmonic seventh]] to [[5edo\|4\5]]. For equal divisions ''N'' up to 65, the comma is tempered out if and only if 5 divides ''N''. Examples are [[5edo]], [[10edo]], [[15edo]], [[50edo]], [[55edo]] and [[65edo]]. Rank-2 temperaments tempering it out include [[blackwood]], [[coblack]], [[cloudtone]], [[sengasec]], [[warlock]], [[pentacloud]], [[decic]], [[pentadecal]], and [[quinkee]].

	~~Cloudy~~ rank-3 temperament can be described as the 10&~~amp;~~15&~~amp;~~50 temperament, which ~~tempers~~ out 385/384 and 3087/3025 in the 11-limit; 105/104, 144/143, and 4459/4400 ~~in the 13-limit~~.		The cloudy rank-3 temperament can be described as the 10 & 15 & 50 temperament, which can be extended to the 11-limit by tempering out 385/384 and 3087/3025, and the 13-limit by tempering out 105/104, 144/143, and 4459/4400.

	=== Cloudy (10&~~amp;~~15&~~amp;~~50) ===		=== Cloudy (10 & 15 & 50) ===
	Subgroup: 2.3.5.7		Subgroup: 2.3.5.7

Line 26:		Line 25:
	{{Optimal ET sequence\|legend=1\| 5, 10, 15, 25, 35, 45, 50, 55, 60, 65 }}		{{Optimal ET sequence\|legend=1\| 5, 10, 15, 25, 35, 45, 50, 55, 60, 65 }}

	=== 11-limit cloudy (10&~~amp;~~15&~~amp;~~50) ===		=== 11-limit cloudy (10 & 15 & 50) ===
	Subgroup: 2.3.5.7.11		Subgroup: 2.3.5.7.11

Line 37:		Line 36:
	{{Optimal ET sequence\|legend=1\| 5, 10, 15, 35, 40, 50, 55, 60, 65 }}		{{Optimal ET sequence\|legend=1\| 5, 10, 15, 35, 40, 50, 55, 60, 65 }}

	=== 13-limit cloudy (10&~~amp;~~15&~~amp;~~50) ===		=== 13-limit cloudy (10 & 15 & 50) ===
	Subgroup: 2.3.5.7.11.13		Subgroup: 2.3.5.7.11.13

Cloudy clan

FloraC — Thu, 25 Jun 2026 10:45:17 GMT

Dissolved

Show changes

Pentadecal

FloraC — Thu, 25 Jun 2026 10:26:07 GMT

Update & recategorize

← Older revision		Revision as of 10:26, 25 June 2026
Line 1:		Line 1:
	#REDIRECT [[~~Cloudy clan~~#Pentadecal]]		#REDIRECT [[Keemic temperaments #Pentadecal]]

			[[Category:Rank-2 temperaments]]
			[[Category:Keemic temperaments]]

Porwell temperaments

FloraC — Thu, 25 Jun 2026 10:24:28 GMT

Update

← Older revision		Revision as of 10:24, 25 June 2026
Line 17:		Line 17:
	* ''[[Hemikleismic]]'' (+4000/3969) → [[Kleismic family #Hemikleismic\|Kleismic family]]		* ''[[Hemikleismic]]'' (+4000/3969) → [[Kleismic family #Hemikleismic\|Kleismic family]]
	* ''[[Bison]]'' (+78732/78125) → [[Sensipent family #Bison\|Sensipent family]]		* ''[[Bison]]'' (+78732/78125) → [[Sensipent family #Bison\|Sensipent family]]
	* ''[[Quinkee]]'' (+1029/1000) → [[~~Cloudy clan~~ #Quinkee\|~~Cloudy clan~~]]		* ''[[Quinkee]]'' (+1029/1000) → [[Keegic temperaments #Quinkee\|Keegic temperaments]]
	* ''[[Hemiwürschmidt]]'' (+2401/2400 or 3136/3125) → [[Hemimean clan #Hemiwürschmidt\|Hemimean clan]]		* ''[[Hemiwürschmidt]]'' (+2401/2400 or 3136/3125) → [[Hemimean clan #Hemiwürschmidt\|Hemimean clan]]
	* ''[[Septisuperfourth]]'' (+118098/117649) → [[Escapade family #Septisuperfourth\|Escapade family]]		* ''[[Septisuperfourth]]'' (+118098/117649) → [[Escapade family #Septisuperfourth\|Escapade family]]

Quinkee

FloraC — Thu, 25 Jun 2026 10:23:26 GMT

Update & recategorize

← Older revision		Revision as of 10:23, 25 June 2026
Line 1:		Line 1:
	#REDIRECT [[~~Cloudy clan~~#Quinkee]]		#REDIRECT [[Keegic temperaments #Quinkee]]

	[[Category:~~Quinkee~~]]		[[Category:Rank-2 temperaments]]
	[[Category:~~Cloudy clan~~]]		[[Category:Keegic temperaments]]
	[[Category:Porwell temperaments]]		[[Category:Porwell temperaments]]
	~~[[Category:Temperaments]]~~

Keegic temperaments

FloraC — Thu, 25 Jun 2026 10:22:32 GMT

Move quinkee here

← Older revision		Revision as of 10:22, 25 June 2026
Line 3:		Line 3:

	Temperaments discussed elsewhere include [[Very low accuracy temperaments\|antitonic]], [[Trienstonic clan\|kangaroo]], [[Kleismic family\|keemun]], [[Meantone family\|liese]], [[Archytas clan\|progress]], [[Mint temperaments\|subklei]], [[Marvel temperaments\|triton]], [[Augmented family\|trisected]], and [[Sensamagic clan\|xenia]].		Temperaments discussed elsewhere include [[Very low accuracy temperaments\|antitonic]], [[Trienstonic clan\|kangaroo]], [[Kleismic family\|keemun]], [[Meantone family\|liese]], [[Archytas clan\|progress]], [[Mint temperaments\|subklei]], [[Marvel temperaments\|triton]], [[Augmented family\|trisected]], and [[Sensamagic clan\|xenia]].

			== Quinkee ==
			Quinkee has a period of 1/5 octave and tempers out the [[keega]] (1029/1000), from which it derives its name. It may be described as the {{nowrap\| 15 & 55 }} temperament. It was named by [[Xenllium]] in 2021.

			[[Subgroup]]: 2.3.5.7

			[[Comma list]]: 1029/1000, 6144/6125

			{{Mapping\|legend=1\| 5 0 9 14 \| 0 3 1 0 }}
			: mapping generators: ~8/7, ~10/7

			[[Optimal tuning]]s:
			* [[WE]]: ~8/7 = 240.0512{{c}}, ~10/7 = 633.5744{{c}} (~25/24 = 86.5794{{c}})
			: [[error map]]: {{val\| +0.256 -1.232 +7.722 -8.108 }}
			* [[CWE]]: ~8/7 = 240.0000{{c}}, ~10/7 = 633.4834{{c}} (~25/24 = 86.5160{{c}})
			: error map: {{val\| 0.000 -1.505 +7.170 -8.826 }}

			{{Optimal ET sequence\|legend=1\| 15, 40, 55 }}

			[[Badness]] (Sintel): 4.66

			=== 11-limit ===
			Subgroup: 2.3.5.7.11

			Comma list: 121/120, 176/175, 1029/1000

			Mapping: {{mapping\| 5 0 9 14 12 \| 0 3 1 0 2 }}

			Optimal tunings:
			* WE: ~8/7 = 240.0916{{c}}, ~10/7 = 633.6802{{c}} (~22/21 = 86.5947{{c}})
			* CWE: ~8/7 = 240.0000{{c}}, ~10/7 = 633.5204{{c}} (~22/21 = 86.4796{{c}})

			{{Optimal ET sequence\|legend=0\| 15, 40, 55 }}

			Badness (Sintel): 2.16

			=== 13-limit ===
			Subgroup: 2.3.5.7.11.13

			Comma list: 66/65, 105/104, 121/120, 637/625

			Mapping: {{mapping\| 5 9 12 14 18 20 \| 0 3 1 0 2 4 }}

			Optimal tunings:
			* WE: ~8/7 = 240.0392{{c}}, ~10/7 = 632.9013{{c}} (~22/21 = 87.2162{{c}})
			* CWE: ~8/7 = 240.0000{{c}}, ~10/7 = 632.8351{{c}} (~22/21 = 87.1649{{c}})

			{{Optimal ET sequence\|legend=0\| 15, 40, 55 }}

			Badness (Sintel): 2.00

	== Aurora ==		== Aurora ==

Keemic temperaments

FloraC — Thu, 25 Jun 2026 10:21:38 GMT

Move pentadecal here

@@ Line 14: / Line 14: @@
 * ''[[Undeka]]'' (+3200/3087) → [[11th-octave temperaments #Undeka|11th-octave temperaments]]
-Discussed below are quasitemp, chromo, barbad, hyperkleismic, and sevond, in the order of increasing [[TE logflat badness]].
+Discussed below are quasitemp, chromo, barbad, pentadecal, hyperkleismic, and sevond, in the order of increasing [[TE logflat badness]].
 == Quasitemp ==
@@ Line 173: / Line 173: @@
 Badness (Sintel): 1.62
 == Hyperkleismic ==

Marvel temperaments

FloraC — Thu, 25 Jun 2026 10:15:11 GMT

Move decic here

Show changes

Cloudy clan

FloraC — Thu, 25 Jun 2026 10:11:00 GMT

Switch to Sintel's badness, WE & CWE tunings (2/2)

Show changes

User:FloraC/Temperament extension issues

FloraC — Thu, 25 Jun 2026 08:08:03 GMT

+ gammic, lunatic, neptune

@@ Line 13: / Line 13: @@
 : 7-limit → 11-limit
 : 11-limit diminished should be decanonicalized. It flips the optimal tuning from flat to sharp of just.
 : Proposed solution:
@@ Line 23: / Line 28: @@
 : 11-limit → 13-limit
 : 13-limit keemun should be decanonicalized. Kema, which maps prime 13 to +14 steps, is the right extension to use, as in all kleismic temperaments.
 : Proposed solution:

4000/3993

FloraC — Thu, 25 Jun 2026 07:44:29 GMT

Undo. It's backwards

← Older revision		Revision as of 07:44, 25 June 2026
Line 14:		Line 14:
	On the low-accuracy end, this may be reminiscent of how the [[250/243\|porcupine comma]] splits 4/3 into three 10/9's instead. In fact, 2.3.5.11-subgroup [[porcupine]] equates 10/9 with 11/10 and 12/11 so that the equally-split fourth represents 9:10:11:12, making porcupine as efficient and elegant as it can reasonably be. (As a [[rank-3]] detemperament of porcupine, one way to extend it to include prime 7 is by tempering out [[385/384]], which septimal porcupine also tempers out.)		On the low-accuracy end, this may be reminiscent of how the [[250/243\|porcupine comma]] splits 4/3 into three 10/9's instead. In fact, 2.3.5.11-subgroup [[porcupine]] equates 10/9 with 11/10 and 12/11 so that the equally-split fourth represents 9:10:11:12, making porcupine as efficient and elegant as it can reasonably be. (As a [[rank-3]] detemperament of porcupine, one way to extend it to include prime 7 is by tempering out [[385/384]], which septimal porcupine also tempers out.)

	Tempering it out along with the [[schisma]] results in the rank-2 [[tertiaschis]] temperament. Tempering it out with the trimitone comma [[8019/8000]] ([[S-expression\|S9/S10]], so that three [[10/9]]'s are also an [[11/8]]) implies also tempering out the [[semiparticular]] [[243/242]] ([[S-expression\|S9/S11]]) = ([[3/2]])/([[11/9]])<sup>2</sup> leading to [[~~Gravity_family#2.3.5.11_subgroup_(larry)\|~~larry]] in the [[~~Gravity\|~~gravity family]]. Tempering it out with both the schisma and trimitone comma gives a description of [[65edo]] in the no-7's 11-limit, making it an excellent way to extend schismic to include prime 11.		Tempering it out along with the [[schisma]] results in the rank-2 [[tertiaschis]] temperament. Tempering it out with the trimitone comma [[8019/8000]] ([[S-expression\|S9/S10]], so that three [[10/9]]'s are also an [[11/8]]) implies also tempering out the [[semiparticular]] [[243/242]] ([[S-expression\|S9/S11]]) = ([[3/2]])/([[11/9]])<sup>2</sup> leading to [[larry]] in the [[gravity family]]. Tempering it out with both the schisma and trimitone comma gives a description of [[65edo]] in the no-7's 11-limit, making it an excellent way to extend schismic to include prime 11.

	Another strategy is to take advantage of the size of 121/120 (S11) so as to equate it with [[144/143]] ({{S\|12}}) = ([[16/13]])/(11/9), for those seeking to keep the undecimal and tridecimal neutral thirds distinct, thus tempering out the marveltwin comma, [[325/324]] ([[S-expression\|S10/S12]]), a comma with various advantages.		Another strategy is to take advantage of the size of 121/120 (S11) so as to equate it with [[144/143]] ({{S\|12}}) = ([[16/13]])/(11/9), for those seeking to keep the undecimal and tridecimal neutral thirds distinct, thus tempering out the marveltwin comma, [[325/324]] ([[S-expression\|S10/S12]]), a comma with various advantages.

Unnoticeable comma

FilterNashi — Thu, 25 Jun 2026 06:21:38 GMT

13-limit commas: +1 comma (Tendoartisma)

← Older revision		Revision as of 06:21, 25 June 2026
Line 1,247:		Line 1,247:
	\| 0.14765		\| 0.14765
	\| [[User:Xenllium\|Xenllium]] (2022)		\| [[User:Xenllium\|Xenllium]] (2022)
			\|-
			\| [[Tendoartisma]]
			\| sasa-sethoguma
			\| ss17(3o)17gM
			\| <abbr title="8650415919381337933 / 8649755859375000000">(38 digits)</abbr>
			\| {{Monzo\| -6 -11 -17 0 0 17 }}
			\| 0.13210
			\| [[User:FilterNashi\|FilterNashi]] (2026)
	\|-		\|-
	\| [[Pontigailimma]]		\| [[Pontigailimma]]

Tendoartisma

FilterNashi — Thu, 25 Jun 2026 06:15:33 GMT

Etymology

← Older revision		Revision as of 06:15, 25 June 2026
Line 12:		Line 12:
	==Etymology==		==Etymology==
	Named by [[User:FilterNashi\|FilterNashi]] in 2026 after the '''[[arto and tendo theory]]''' aka '''extraclassical tonality''' theory.		Named by [[User:FilterNashi\|FilterNashi]] in 2026 after the '''[[arto and tendo theory]]''' aka '''extraclassical tonality''' theory.

			==See also==
			* [[Unnoticeable comma]]

User:Tyler Henthorn

Tyler Henthorn — Thu, 25 Jun 2026 05:48:25 GMT

← Older revision		Revision as of 05:48, 25 June 2026
Line 1:		Line 1:
	Sysadmin.		Sysadmin.

	Agonanist.		Agonanist.

	You can contact me by [https://en.xen.wiki/w/Special:EmailUser?target=Tyler_Henthorn email]		You can contact me by [https://en.xen.wiki/w/Special:EmailUser?target=Tyler_Henthorn email]

7:9:11

Pailiaq — Thu, 25 Jun 2026 05:17:48 GMT

← Older revision		Revision as of 05:17, 25 June 2026
Line 1:		Line 1:
	{{Infobox chord\|ColorName = ru loru 5, r(1or5)}}		{{Infobox chord\|ColorName = ru loru 5, r(1or5)}}
	'''7:9:11''' is a chord. It sort of sounds like an augmented fifth chord, including two types of third, a [[9/7]] supermajor third, and a [[11/9]] neutral third.		'''7:9:11''' is the Greeley Major chord. It sort of sounds like an augmented fifth chord, including two types of third, a [[9/7]] supermajor third, and a [[11/9]] neutral third.

	It is one of the simplest chords that truly sounds xenharmonic. [[6:7:9:11]] and variants are another such simple xen chords.		It is one of the simplest chords that truly sounds xenharmonic. [[6:7:9:11]] and variants are another such simple xen chords.

Tendoartisma

FilterNashi — Thu, 25 Jun 2026 04:51:34 GMT

Etymology

← Older revision		Revision as of 04:51, 25 June 2026
(One intermediate revision by the same user not shown)
Line 9:		Line 9:
	==Temperaments==		==Temperaments==
	[[Tempering]] it out in 2.3.5.13 subgroup leads to the '''tendoartic''' temperament, and '''tendoartismic''' in full 13-limit. Further [[retraction]] to the 2.3.13/5 [[fractional subgroup]] leads to the '''[[subgroup temperaments#Seventeen-cot\|seventeen-cot]]''' temperament. Both tendoartic and seventeen-cot can [[extension\|extend]] by tempering out [[225000/224939]] or [[43940/43923]] in larger subgroups.		[[Tempering]] it out in 2.3.5.13 subgroup leads to the '''tendoartic''' temperament, and '''tendoartismic''' in full 13-limit. Further [[retraction]] to the 2.3.13/5 [[fractional subgroup]] leads to the '''[[subgroup temperaments#Seventeen-cot\|seventeen-cot]]''' temperament. Both tendoartic and seventeen-cot can [[extension\|extend]] by tempering out [[225000/224939]] or [[43940/43923]] in larger subgroups.

			==Etymology==
			Named by [[User:FilterNashi\|FilterNashi]] in 2026 after the '''[[arto and tendo theory]]''' aka '''extraclassical tonality''' theory.

189/187

FilterNashi — Thu, 25 Jun 2026 04:45:10 GMT

Temperament

← Older revision		Revision as of 04:45, 25 June 2026
Line 27:		Line 27:
	189/187 is a 1/4-square particulars which is S18S19S20*S21.		189/187 is a 1/4-square particulars which is S18S19S20*S21.

	==~~Temperament~~==		==Temperaments==
	Tempering out this comma in the 3.7.11.17 [[subgroup]] leads to the rank-3 '''chouten temperament'''.		Tempering out this comma in the 3.7.11.17 [[subgroup]] leads to the rank-3 '''chouten temperament'''.
	===Chouten===		===Chouten===

Tendoartisma

FilterNashi — Thu, 25 Jun 2026 04:41:09 GMT

Created page with "{{Infobox Interval | Monzo = -6 -11 -17 0 0 17 | Name = Tendoartisma | Color name = sasa-sethogu 8ve, ss17(3o)17gM | Comma = yes }} '''Tendoartisma''' is a 13-limit or 2.3.5.13 subgroup comma. It's the difference between a stack of six 3/2 pure fifths and a stack of seventeen 15/13<nowiki>s</nowiki>. ==Temperaments== Tempering it out in 2.3.5.13 subgroup leads to the '''tendoartic''' temperament, and '''tendoartismic''' in full 13-limit...."

New page

{{Infobox Interval
| Monzo = -6 -11 -17 0 0 17
| Name = Tendoartisma
| Color name = sasa-sethogu 8ve, ss17(3o)17gM
| Comma = yes
}}
'''Tendoartisma''' is a [[13-limit]] or [[subgroup|2.3.5.13 subgroup]] [[comma]]. It's the difference between a stack of six [[3/2]] pure fifths and a stack of seventeen [[15/13]]<nowiki>s</nowiki>.

==Temperaments==
[[Tempering]] it out in 2.3.5.13 subgroup leads to the '''tendoartic''' temperament, and '''tendoartismic''' in full 13-limit. Further [[retraction]] to the 2.3.13/5 [[fractional subgroup]] leads to the '''[[subgroup temperaments#Seventeen-cot|seventeen-cot]]''' temperament. Both tendoartic and seventeen-cot can [[extension|extend]] by tempering out [[225000/224939]] or [[43940/43923]] in larger subgroups.

Gamelan

Lucius Chiaraviglio — Thu, 25 Jun 2026 04:17:26 GMT

Further reading: Gamelan Music of Java: an Introduction — add dates

← Older revision		Revision as of 04:17, 25 June 2026
Line 9:		Line 9:
	* [https://www.youtube.com/watch?v=gM3yodZbRok Alunan gamelan mana paling bagus? (Which gamelan game is the best?)] - A comparison of audio-video recordings of gamelan orchestras from different regions of Indonesia		* [https://www.youtube.com/watch?v=gM3yodZbRok Alunan gamelan mana paling bagus? (Which gamelan game is the best?)] - A comparison of audio-video recordings of gamelan orchestras from different regions of Indonesia
	* [https://www.reddit.com/r/GlobalMusicTheory/wiki/indonesianmusictheory/ r/GlobalMusicTheory's list] of sources about gamelan theory; many academic papers		* [https://www.reddit.com/r/GlobalMusicTheory/wiki/indonesianmusictheory/ r/GlobalMusicTheory's list] of sources about gamelan theory; many academic papers
	* [https://www.youtube.com/watch?v=dmwqIv8rVrE Gamelan Music of Java: an Introduction] - Video introduction, with Hardja Susilo		* [https://www.youtube.com/watch?v=dmwqIv8rVrE Gamelan Music of Java: an Introduction] (1983, uploaded 2025) - Video introduction, with Hardja Susilo
	* [https://gamelan.org/wp-content/uploads/2025/09/Sorrell01_guide_gamelan.pdf A Guide to the Gamelan], Neil Sorrell - Book		* [https://gamelan.org/wp-content/uploads/2025/09/Sorrell01_guide_gamelan.pdf A Guide to the Gamelan], Neil Sorrell - Book
	* [https://gamelan.org American Gamelan Institute] - Including the Balungan journal and a library of further resources		* [https://gamelan.org American Gamelan Institute] - Including the Balungan journal and a library of further resources

4000/3993

Lucius Chiaraviglio — Thu, 25 Jun 2026 03:30:31 GMT

Temperaments: Fix links to Larry and Gravity

← Older revision		Revision as of 03:30, 25 June 2026
Line 14:		Line 14:
	On the low-accuracy end, this may be reminiscent of how the [[250/243\|porcupine comma]] splits 4/3 into three 10/9's instead. In fact, 2.3.5.11-subgroup [[porcupine]] equates 10/9 with 11/10 and 12/11 so that the equally-split fourth represents 9:10:11:12, making porcupine as efficient and elegant as it can reasonably be. (As a [[rank-3]] detemperament of porcupine, one way to extend it to include prime 7 is by tempering out [[385/384]], which septimal porcupine also tempers out.)		On the low-accuracy end, this may be reminiscent of how the [[250/243\|porcupine comma]] splits 4/3 into three 10/9's instead. In fact, 2.3.5.11-subgroup [[porcupine]] equates 10/9 with 11/10 and 12/11 so that the equally-split fourth represents 9:10:11:12, making porcupine as efficient and elegant as it can reasonably be. (As a [[rank-3]] detemperament of porcupine, one way to extend it to include prime 7 is by tempering out [[385/384]], which septimal porcupine also tempers out.)

	Tempering it out along with the [[schisma]] results in the rank-2 [[tertiaschis]] temperament. Tempering it out with the trimitone comma [[8019/8000]] ([[S-expression\|S9/S10]], so that three [[10/9]]'s are also an [[11/8]]) implies also tempering out the [[semiparticular]] [[243/242]] ([[S-expression\|S9/S11]]) = ([[3/2]])/([[11/9]])<sup>2</sup> leading to [[larry]] in the [[gravity family]]. Tempering it out with both the schisma and trimitone comma gives a description of [[65edo]] in the no-7's 11-limit, making it an excellent way to extend schismic to include prime 11.		Tempering it out along with the [[schisma]] results in the rank-2 [[tertiaschis]] temperament. Tempering it out with the trimitone comma [[8019/8000]] ([[S-expression\|S9/S10]], so that three [[10/9]]'s are also an [[11/8]]) implies also tempering out the [[semiparticular]] [[243/242]] ([[S-expression\|S9/S11]]) = ([[3/2]])/([[11/9]])<sup>2</sup> leading to [[Gravity_family#2.3.5.11_subgroup_(larry)\|larry]] in the [[Gravity\|gravity family]]. Tempering it out with both the schisma and trimitone comma gives a description of [[65edo]] in the no-7's 11-limit, making it an excellent way to extend schismic to include prime 11.

	Another strategy is to take advantage of the size of 121/120 (S11) so as to equate it with [[144/143]] ({{S\|12}}) = ([[16/13]])/(11/9), for those seeking to keep the undecimal and tridecimal neutral thirds distinct, thus tempering out the marveltwin comma, [[325/324]] ([[S-expression\|S10/S12]]), a comma with various advantages.		Another strategy is to take advantage of the size of 121/120 (S11) so as to equate it with [[144/143]] ({{S\|12}}) = ([[16/13]])/(11/9), for those seeking to keep the undecimal and tridecimal neutral thirds distinct, thus tempering out the marveltwin comma, [[325/324]] ([[S-expression\|S10/S12]]), a comma with various advantages.

User:Fredg999/Sandbox

Fredg999 — Wed, 24 Jun 2026 21:22:21 GMT

Undo revision 232660 by Fredg999 (talk) - Bug fixed

← Older revision		Revision as of 21:22, 24 June 2026
Line 1:		Line 1:
	~~<!-- temp storage for plugins page edit while it's bugged~~
	~~\| ash taylor?!~~
	~~\| [https://estrobiologist.gumroad.com/l/sflt SFLT]~~
	~~\| Soundfont player~~
	~~\| Windows, macOS~~
	~~\| VST3, CLAP, AU, native FL Studio plugin~~
	~~\| style="color: #007f00;" \| '''Full-keyboard microtuning'''~~
	~~\| MPE, scl/kbm file import~~
	~~\| style="color: #007f00;" \| '''Freeware'''~~
	\|-
	~~-->~~
	== Perfect fourth ==		== Perfect fourth ==
	{{Wikipedia\|Perfect fourth}}		{{Wikipedia\|Perfect fourth}}

List of microtonal software plugins

Fredg999 — Wed, 24 Jun 2026 21:21:39 GMT

Add SFLT

← Older revision		Revision as of 21:21, 24 June 2026
Line 273:		Line 273:
	\| MPE, MTS-ESP client		\| MPE, MTS-ESP client
	\| €149/$149		\| €149/$149
			\|-
			\| ash taylor?!
			\| [https://estrobiologist.gumroad.com/l/sflt SFLT]
			\| Soundfont player
			\| Windows, macOS
			\| VST3, CLAP, AU, native FL Studio plugin
			\| style="color: #007f00;" \| '''Full-keyboard microtuning'''
			\| MPE, scl/kbm file import
			\| style="color: #007f00;" \| '''Freeware'''
	\|-		\|-
	\| Audio Damage		\| Audio Damage

New Tuning Method

Fredg999 category edits — Wed, 24 Jun 2026 21:19:24 GMT

Moving from Category:Midi to Category:MIDI using Cat-a-lot

← Older revision		Revision as of 21:19, 24 June 2026
Line 200:		Line 200:

	RPN LSB: Bc 64 nn (note to reset)		RPN LSB: Bc 64 nn (note to reset)
	[[Category:~~midi~~]]		[[Category:MIDI]]
	[[Category:tuning]]		[[Category:tuning]]

← Older revision		Revision as of 12:59, 25 June 2026
Line 9:		Line 9:
	* ''[[Tritricot]]'' (+{{monzo\| 35 -23 -3 3 }}) → [[Alphatricot family #Tritricot\|Alphatricot family]]		* ''[[Tritricot]]'' (+{{monzo\| 35 -23 -3 3 }}) → [[Alphatricot family #Tritricot\|Alphatricot family]]
	* [[Compton]] (+225/224) → [[Compton family #Compton\|Compton family]]		* [[Compton]] (+225/224) → [[Compton family #Compton\|Compton family]]
	* ''[[Terture]]'' (+359661568/358722675) → [[Vulture family #~~Domain~~\|Vulture family]]		* ''[[Terture]]'' (+359661568/358722675) → [[Vulture family #Terture\|Vulture family]]
	* ''[[Chromat]]'' (10976/10935) → [[~~Hemimage temperaments~~ #Chromat\|~~Hemimage temperaments~~]]		* ''[[Pentadecal]]'' (+875/864) → [[Keemic temperaments #Pentadecal\|Keemic temperaments]]
			* ''[[Chromat]]'' (+10976/10935) → [[Amity family #Chromat\|Amity family]]
	* ''[[Tritikleismic]]'' (+1029/1024) → [[Kleismic family #Tritikleismic\|Kleismic family]]		* ''[[Tritikleismic]]'' (+1029/1024) → [[Kleismic family #Tritikleismic\|Kleismic family]]
	* [[Ennealimmal]] (+2401/2400 or 4375/4374) → [[Septiennealimmal clan #Ennealimmal\|Septiennealimmal clan]]		* [[Ennealimmal]] (+2401/2400 or 4375/4374) → [[Septiennealimmal clan #Ennealimmal\|Septiennealimmal clan]]

← Older revision		Revision as of 11:01, 25 June 2026
Line 17:		Line 17:
	* [[Wollemia]] (+2240/2187) → [[Tetracot family #Wollemia\|Tetracot family]]		* [[Wollemia]] (+2240/2187) → [[Tetracot family #Wollemia\|Tetracot family]]
	* ''[[Unicorn]]'' (+10976/10935) → [[Unicorn family #Unicorn\|Unicorn family]]		* ''[[Unicorn]]'' (+10976/10935) → [[Unicorn family #Unicorn\|Unicorn family]]
	* ''[[Coblack]]'' (+16807/16384) → [[Trisedodge family #Coblack\|Trisedodge family~~]] / [[Cloudy clan #Coblack\|cloudy clan~~]]		* ''[[Coblack]]'' (+16807/16384) → [[Trisedodge family #Coblack\|Trisedodge family]]
	* ''[[Grackle]]'' (+32805/32768) → [[Schismatic family #Grackle\|Schismatic family]]		* ''[[Grackle]]'' (+32805/32768) → [[Schismatic family #Grackle\|Schismatic family]]
	* ''[[Worschmidt]]'' (+33075/32768) → [[Würschmidt family #Worschmidt\|Würschmidt family]]		* ''[[Worschmidt]]'' (+33075/32768) → [[Würschmidt family #Worschmidt\|Würschmidt family]]

← Older revision		Revision as of 10:24, 25 June 2026
Line 17:		Line 17:
	* ''[[Hemikleismic]]'' (+4000/3969) → [[Kleismic family #Hemikleismic\|Kleismic family]]		* ''[[Hemikleismic]]'' (+4000/3969) → [[Kleismic family #Hemikleismic\|Kleismic family]]
	* ''[[Bison]]'' (+78732/78125) → [[Sensipent family #Bison\|Sensipent family]]		* ''[[Bison]]'' (+78732/78125) → [[Sensipent family #Bison\|Sensipent family]]
	* ''[[Quinkee]]'' (+1029/1000) → [[~~Cloudy clan~~ #Quinkee\|~~Cloudy clan~~]]		* ''[[Quinkee]]'' (+1029/1000) → [[Keegic temperaments #Quinkee\|Keegic temperaments]]
	* ''[[Hemiwürschmidt]]'' (+2401/2400 or 3136/3125) → [[Hemimean clan #Hemiwürschmidt\|Hemimean clan]]		* ''[[Hemiwürschmidt]]'' (+2401/2400 or 3136/3125) → [[Hemimean clan #Hemiwürschmidt\|Hemimean clan]]
	* ''[[Septisuperfourth]]'' (+118098/117649) → [[Escapade family #Septisuperfourth\|Escapade family]]		* ''[[Septisuperfourth]]'' (+118098/117649) → [[Escapade family #Septisuperfourth\|Escapade family]]

← Older revision		Revision as of 07:44, 25 June 2026
Line 14:		Line 14:
	On the low-accuracy end, this may be reminiscent of how the [[250/243\|porcupine comma]] splits 4/3 into three 10/9's instead. In fact, 2.3.5.11-subgroup [[porcupine]] equates 10/9 with 11/10 and 12/11 so that the equally-split fourth represents 9:10:11:12, making porcupine as efficient and elegant as it can reasonably be. (As a [[rank-3]] detemperament of porcupine, one way to extend it to include prime 7 is by tempering out [[385/384]], which septimal porcupine also tempers out.)		On the low-accuracy end, this may be reminiscent of how the [[250/243\|porcupine comma]] splits 4/3 into three 10/9's instead. In fact, 2.3.5.11-subgroup [[porcupine]] equates 10/9 with 11/10 and 12/11 so that the equally-split fourth represents 9:10:11:12, making porcupine as efficient and elegant as it can reasonably be. (As a [[rank-3]] detemperament of porcupine, one way to extend it to include prime 7 is by tempering out [[385/384]], which septimal porcupine also tempers out.)

	Tempering it out along with the [[schisma]] results in the rank-2 [[tertiaschis]] temperament. Tempering it out with the trimitone comma [[8019/8000]] ([[S-expression\|S9/S10]], so that three [[10/9]]'s are also an [[11/8]]) implies also tempering out the [[semiparticular]] [[243/242]] ([[S-expression\|S9/S11]]) = ([[3/2]])/([[11/9]])<sup>2</sup> leading to [[~~Gravity_family#2.3.5.11_subgroup_(larry)\|~~larry]] in the [[~~Gravity\|~~gravity family]]. Tempering it out with both the schisma and trimitone comma gives a description of [[65edo]] in the no-7's 11-limit, making it an excellent way to extend schismic to include prime 11.		Tempering it out along with the [[schisma]] results in the rank-2 [[tertiaschis]] temperament. Tempering it out with the trimitone comma [[8019/8000]] ([[S-expression\|S9/S10]], so that three [[10/9]]'s are also an [[11/8]]) implies also tempering out the [[semiparticular]] [[243/242]] ([[S-expression\|S9/S11]]) = ([[3/2]])/([[11/9]])<sup>2</sup> leading to [[larry]] in the [[gravity family]]. Tempering it out with both the schisma and trimitone comma gives a description of [[65edo]] in the no-7's 11-limit, making it an excellent way to extend schismic to include prime 11.

	Another strategy is to take advantage of the size of 121/120 (S11) so as to equate it with [[144/143]] ({{S\|12}}) = ([[16/13]])/(11/9), for those seeking to keep the undecimal and tridecimal neutral thirds distinct, thus tempering out the marveltwin comma, [[325/324]] ([[S-expression\|S10/S12]]), a comma with various advantages.		Another strategy is to take advantage of the size of 121/120 (S11) so as to equate it with [[144/143]] ({{S\|12}}) = ([[16/13]])/(11/9), for those seeking to keep the undecimal and tridecimal neutral thirds distinct, thus tempering out the marveltwin comma, [[325/324]] ([[S-expression\|S10/S12]]), a comma with various advantages.

← Older revision		Revision as of 03:30, 25 June 2026
Line 14:		Line 14:
	On the low-accuracy end, this may be reminiscent of how the [[250/243\|porcupine comma]] splits 4/3 into three 10/9's instead. In fact, 2.3.5.11-subgroup [[porcupine]] equates 10/9 with 11/10 and 12/11 so that the equally-split fourth represents 9:10:11:12, making porcupine as efficient and elegant as it can reasonably be. (As a [[rank-3]] detemperament of porcupine, one way to extend it to include prime 7 is by tempering out [[385/384]], which septimal porcupine also tempers out.)		On the low-accuracy end, this may be reminiscent of how the [[250/243\|porcupine comma]] splits 4/3 into three 10/9's instead. In fact, 2.3.5.11-subgroup [[porcupine]] equates 10/9 with 11/10 and 12/11 so that the equally-split fourth represents 9:10:11:12, making porcupine as efficient and elegant as it can reasonably be. (As a [[rank-3]] detemperament of porcupine, one way to extend it to include prime 7 is by tempering out [[385/384]], which septimal porcupine also tempers out.)

	Tempering it out along with the [[schisma]] results in the rank-2 [[tertiaschis]] temperament. Tempering it out with the trimitone comma [[8019/8000]] ([[S-expression\|S9/S10]], so that three [[10/9]]'s are also an [[11/8]]) implies also tempering out the [[semiparticular]] [[243/242]] ([[S-expression\|S9/S11]]) = ([[3/2]])/([[11/9]])<sup>2</sup> leading to [[larry]] in the [[gravity family]]. Tempering it out with both the schisma and trimitone comma gives a description of [[65edo]] in the no-7's 11-limit, making it an excellent way to extend schismic to include prime 11.		Tempering it out along with the [[schisma]] results in the rank-2 [[tertiaschis]] temperament. Tempering it out with the trimitone comma [[8019/8000]] ([[S-expression\|S9/S10]], so that three [[10/9]]'s are also an [[11/8]]) implies also tempering out the [[semiparticular]] [[243/242]] ([[S-expression\|S9/S11]]) = ([[3/2]])/([[11/9]])<sup>2</sup> leading to [[Gravity_family#2.3.5.11_subgroup_(larry)\|larry]] in the [[Gravity\|gravity family]]. Tempering it out with both the schisma and trimitone comma gives a description of [[65edo]] in the no-7's 11-limit, making it an excellent way to extend schismic to include prime 11.

	Another strategy is to take advantage of the size of 121/120 (S11) so as to equate it with [[144/143]] ({{S\|12}}) = ([[16/13]])/(11/9), for those seeking to keep the undecimal and tridecimal neutral thirds distinct, thus tempering out the marveltwin comma, [[325/324]] ([[S-expression\|S10/S12]]), a comma with various advantages.		Another strategy is to take advantage of the size of 121/120 (S11) so as to equate it with [[144/143]] ({{S\|12}}) = ([[16/13]])/(11/9), for those seeking to keep the undecimal and tridecimal neutral thirds distinct, thus tempering out the marveltwin comma, [[325/324]] ([[S-expression\|S10/S12]]), a comma with various advantages.