Quasisuper - Revision history

ArrowHead294 at 13:07, 19 February 2026

2026-02-19T13:07:31Z

← Older revision		Revision as of 13:07, 19 February 2026
Line 8:		Line 8:
	\| Generators tuning = 708.3		\| Generators tuning = 708.3
	\| Optimization method = CWE		\| Optimization method = CWE
	\| MOS scales = [[5L 2s]], [[5L 7s]], [[5L 12s]], [[17L 5s]]		\| MOS scales = [[5L 2s]], [[5L 7s]], [[5L 12s]], [[17L 5s]]
	\| Pergen = (P8, P5)		\| Pergen = (P8, P5)
	\| Color name = Sasaguti		\| Color name = Sasaguti
Line 14:		Line 14:
	\| Odd limit 2 = 11-limit 15 \| Mistuning 2 = 14.9 \| Complexity 2 = 17		\| Odd limit 2 = 11-limit 15 \| Mistuning 2 = 14.9 \| Complexity 2 = 17
	}}		}}
	'''Quasisuper''' is an alternative [[extension]] of the [[archy]] [[chain of fifths]] to [[superpyth]]. Like superpyth, it is a [[regular temperament\|temperament]] generated by a perfect fifth, where stacking two of them reaches the interval of [[8/7]][[~]][[9/8]], [[tempering out]] [[64/63]]. The difference is that this extension maps [[prime interval\|prime]] [[5/1\|5]] to -13 [[generator]]s, as a double-diminished fifth (C–G𝄫). This extension works in the range [[17edo\|17c-edo]] to [[22edo\|22-edo]]. In contrast, full 7-limit [[superpyth]] does not work in this range, as tunings with a flatter fifth than 22edo swap the sizes of [[7/5]] and [[10/7]]. This extension may be preferred over superpyth due to having a softer [[5L 2s\|diatonic]] scale, with a small step of around 60 [[cent]]s compared to about 50 cents in regular 7-limit superpyth.

	The best extension to the [[11-limit]], '''quasisupra''', maps prime [[11/1\|11]] to -6 generators as a diminished fifth (C–G♭), tempering out [[99/98]] as well as [[121/120]] and [[540/539]]. Removing prime 5 from quasisupra results in a 2.3.7.11-subgroup restriction, called '''supra''', which is notable for its simplicity. Finally, taking every other step of supra gives a 2.9.7.11-subgroup restriction, called [[machine]].		'''Quasisuper''' is an alternative [[extension]] of the [[archy]] [[chain of fifths]] to [[superpyth]]. Like superpyth, it is a [[regular temperament\|temperament]] generated by a perfect fifth, where stacking two of them reaches the interval of [[8/7]][[~]][[9/8]], [[tempering out]] [[64/63]]. The difference is that this extension maps [[prime interval\|prime]] [[5/1\|5]] to −13 [[generator]]s, as a double-diminished fifth (C–G𝄫). This extension works in the range [[17edo\|17c-edo]] to [[22edo\|22-edo]]. In contrast, full 7-limit [[superpyth]] does not work in this range, as tunings with a flatter fifth than 22edo swap the sizes of [[7/5]] and [[10/7]]. This extension may be preferred over superpyth due to having a softer [[5L 2s\|diatonic]] scale, with a small step of around 60 [[cent]]s compared to about 50 cents in regular 7-limit superpyth.

			The best extension to the [[11-limit]], '''quasisupra''', maps prime [[11/1\|11]] to −6 generators as a diminished fifth (C–G♭), tempering out [[99/98]] as well as [[121/120]] and [[540/539]]. Removing prime 5 from quasisupra results in a 2.3.7.11-subgroup restriction, called '''supra''', which is notable for its simplicity. Finally, taking every other step of supra gives a 2.9.7.11-subgroup restriction, called [[machine]].

	For technical data see [[Archytas clan #Quasisuper]] and [[Archytas clan #Supra\|#Supra]].		For technical data see [[Archytas clan #Quasisuper]] and [[Archytas clan #Supra\|#Supra]].

FloraC: Cleanup on infobox

2026-02-09T09:36:46Z

Cleanup on infobox

← Older revision		Revision as of 09:36, 9 February 2026
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	{{Infobox ~~Regtemp~~		{{Infobox regtemp
	\| Title = Quasisuper; quasisupra		\| Title = Quasisuper; quasisupra
	\| Subgroups = 2.3.5.7, 2.3.5.7.11		\| Subgroups = 2.3.5.7, 2.3.5.7.11
Line 5:		Line 5:
	\| Edo join 1 = 17c \| Edo join 2 = 22		\| Edo join 1 = 17c \| Edo join 2 = 22
	\| Mapping = 1; 1 -13 -2 -6		\| Mapping = 1; 1 -13 -2 -6
	\| ~~Generator~~ = 3/2		\| Generators = 3/2
	\| ~~Generator~~ tuning = 708.3		\| Generators tuning = 708.3
	\| Optimization method = CWE		\| Optimization method = CWE
	\| MOS scales = [[5L 2s]], [[5L 7s]], [[5L 12s]], [[17L 5s]]		\| MOS scales = [[5L 2s]], [[5L 7s]], [[5L 12s]], [[17L 5s]]

Overthink: expand MOS scales

2026-01-27T23:01:46Z

expand MOS scales

← Older revision		Revision as of 23:01, 27 January 2026
Line 8:		Line 8:
	\| Generator tuning = 708.3		\| Generator tuning = 708.3
	\| Optimization method = CWE		\| Optimization method = CWE
	\| MOS scales = [[5L 2s]], [[5L 7s]], [[5L 12s]]		\| MOS scales = [[5L 2s]], [[5L 7s]], [[5L 12s]], [[17L 5s]]
	\| Pergen = (P8, P5)		\| Pergen = (P8, P5)
	\| Color name = Sasaguti		\| Color name = Sasaguti
	\| Odd limit 1 = 9 \| Mistuning 1 = 13.7 \| Complexity 1 = 17		\| Odd limit 1 = 9 \| Mistuning 1 = 13.7 \| Complexity 1 = 17
	\| Odd limit 2 = (11-limit) 15 \| Mistuning 2 = 14.9 \| Complexity 2 = 17		\| Odd limit 2 = 11-limit 15 \| Mistuning 2 = 14.9 \| Complexity 2 = 17
	}}		}}
	'''Quasisuper''' is an alternative [[extension]] of the [[archy]] [[chain of fifths]] to [[superpyth]]. Like superpyth, it is a [[regular temperament\|temperament]] generated by a perfect fifth, where stacking two of them reaches the interval of [[8/7]][[~]][[9/8]], [[tempering out]] [[64/63]]. The difference is that this extension maps [[prime interval\|prime]] [[5/1\|5]] to -13 [[generator]]s, as a double-diminished fifth (C–G𝄫). This extension works in the range [[17edo\|17c-edo]] to [[22edo\|22-edo]]. In contrast, full 7-limit [[superpyth]] does not work in this range, as tunings with a flatter fifth than 22edo swap the sizes of [[7/5]] and [[10/7]]. This extension may be preferred over superpyth due to having a softer [[5L 2s\|diatonic]] scale, with a small step of around 60 [[cent]]s compared to about 50 cents in regular 7-limit superpyth.		'''Quasisuper''' is an alternative [[extension]] of the [[archy]] [[chain of fifths]] to [[superpyth]]. Like superpyth, it is a [[regular temperament\|temperament]] generated by a perfect fifth, where stacking two of them reaches the interval of [[8/7]][[~]][[9/8]], [[tempering out]] [[64/63]]. The difference is that this extension maps [[prime interval\|prime]] [[5/1\|5]] to -13 [[generator]]s, as a double-diminished fifth (C–G𝄫). This extension works in the range [[17edo\|17c-edo]] to [[22edo\|22-edo]]. In contrast, full 7-limit [[superpyth]] does not work in this range, as tunings with a flatter fifth than 22edo swap the sizes of [[7/5]] and [[10/7]]. This extension may be preferred over superpyth due to having a softer [[5L 2s\|diatonic]] scale, with a small step of around 60 [[cent]]s compared to about 50 cents in regular 7-limit superpyth.

FloraC: Re-introduce supra based on quasisupra. Also note its relation to machine

2026-01-02T14:20:42Z

Re-introduce supra based on quasisupra. Also note its relation to machine

← Older revision		Revision as of 14:20, 2 January 2026
Line 16:		Line 16:
	'''Quasisuper''' is an alternative [[extension]] of the [[archy]] [[chain of fifths]] to [[superpyth]]. Like superpyth, it is a [[regular temperament\|temperament]] generated by a perfect fifth, where stacking two of them reaches the interval of [[8/7]][[~]][[9/8]], [[tempering out]] [[64/63]]. The difference is that this extension maps [[prime interval\|prime]] [[5/1\|5]] to -13 [[generator]]s, as a double-diminished fifth (C–G𝄫). This extension works in the range [[17edo\|17c-edo]] to [[22edo\|22-edo]]. In contrast, full 7-limit [[superpyth]] does not work in this range, as tunings with a flatter fifth than 22edo swap the sizes of [[7/5]] and [[10/7]]. This extension may be preferred over superpyth due to having a softer [[5L 2s\|diatonic]] scale, with a small step of around 60 [[cent]]s compared to about 50 cents in regular 7-limit superpyth.		'''Quasisuper''' is an alternative [[extension]] of the [[archy]] [[chain of fifths]] to [[superpyth]]. Like superpyth, it is a [[regular temperament\|temperament]] generated by a perfect fifth, where stacking two of them reaches the interval of [[8/7]][[~]][[9/8]], [[tempering out]] [[64/63]]. The difference is that this extension maps [[prime interval\|prime]] [[5/1\|5]] to -13 [[generator]]s, as a double-diminished fifth (C–G𝄫). This extension works in the range [[17edo\|17c-edo]] to [[22edo\|22-edo]]. In contrast, full 7-limit [[superpyth]] does not work in this range, as tunings with a flatter fifth than 22edo swap the sizes of [[7/5]] and [[10/7]]. This extension may be preferred over superpyth due to having a softer [[5L 2s\|diatonic]] scale, with a small step of around 60 [[cent]]s compared to about 50 cents in regular 7-limit superpyth.

	The best extension to the [[11-limit]], '''quasisupra''', ~~uses the [[supra]] mapping of~~ prime [[11/1\|11]] to -6 generators, as a diminished fifth (C–G♭)~~. This tempers~~ out [[99/98]] ~~as in supra,~~ as well as [[121/120]] and [[540/539]].		The best extension to the [[11-limit]], '''quasisupra''', maps prime [[11/1\|11]] to -6 generators as a diminished fifth (C–G♭), tempering out [[99/98]] as well as [[121/120]] and [[540/539]]. Removing prime 5 from quasisupra results in a 2.3.7.11-subgroup restriction, called '''supra''', which is notable for its simplicity. Finally, taking every other step of supra gives a 2.9.7.11-subgroup restriction, called [[machine]].

	For technical data see [[Archytas clan #Quasisuper]].		For technical data see [[Archytas clan #Quasisuper]] and [[Archytas clan #Supra\|#Supra]].

	== Interval chain ==		== Interval chain ==

FloraC: /* Interval chain */ move supra here

2026-01-02T14:10:44Z

Interval chain: move supra here

@@ Line 21: / Line 21: @@
 == Interval chain ==
-In the following table, odd harmonics and subharmonics 1–11 are in '''bold'''.
+In the following tables, odd harmonics and subharmonics 1–11 are in '''bold'''.
 {| class="wikitable center-1 right-2"
 ! #
 ! Cents*
@@ Line 100: / Line 127: @@
 | 81/80, 56/55
 |}
-<nowiki/>* in 11-limit [[CWE]] tuning, octave reduced
+<nowiki/>* in 11-limit CWE tuning, octave reduced
 == Scales ==

FloraC: + link to Scala files

2026-01-01T15:29:24Z

+ link to Scala files

← Older revision		Revision as of 15:29, 1 January 2026
Line 101:		Line 101:
	\|}		\|}
	<nowiki/>* in 11-limit [[CWE]] tuning, octave reduced		<nowiki/>* in 11-limit [[CWE]] tuning, octave reduced

			== Scales ==
			=== Scala files ===
			* [[Supra7]] – in 56edo tuning
			* [[Supra12]] – in 56edo tuning
			* [[12-22a]] – in 22edo tuning

	== Tunings ==		== Tunings ==

FloraC: + categories

2026-01-01T15:20:14Z

+ categories

← Older revision		Revision as of 15:20, 1 January 2026
Line 280:		Line 280:
	<nowiki/>* Besides the octave		<nowiki/>* Besides the octave

			[[Category:Quasisuper\| ]] <!-- main article -->
	[[Category:Rank-2 temperaments]]		[[Category:Rank-2 temperaments]]
	[[Category:Archytas clan]]		[[Category:Archytas clan]]
	[[Category:Nuwell temperaments]]		[[Category:Nuwell temperaments]]
			[[Category:Hemimage temperaments]]

FloraC: /* Tunings */ + tuning spectrum

2026-01-01T15:06:39Z

Tunings: + tuning spectrum

Show changes

FloraC: /* Tunings */ + basic norm-based tunings

2025-12-31T11:42:22Z

Tunings: + basic norm-based tunings

← Older revision		Revision as of 11:42, 31 December 2025
Line 103:		Line 103:

	== Tunings ==		== Tunings ==
			{\| class="wikitable mw-collapsible mw-collapsed"
			\|+ style="font-size: 105%; white-space: nowrap;" \| 7-limit norm-based tunings
			\|-
			! rowspan="2" \|
			! colspan="3" \| Euclidean
			\|-
			! Constrained
			! Constrained & skewed
			! Destretched
			\|-
			! Tenney
			\| CTE: ~3/2 = 708.7690{{c}}
			\| CWE: ~3/2 = 708.3716{{c}}
			\| POTE: ~3/2 = 708.2385{{c}}
			\|}

			{\| class="wikitable mw-collapsible mw-collapsed"
			\|+ style="font-size: 105%; white-space: nowrap;" \| 11-limit norm-based tunings
			\|-
			! rowspan="2" \|
			! colspan="3" \| Euclidean
			\|-
			! Constrained
			! Constrained & skewed
			! Destretched
			\|-
			! Tenney
			\| CTE: ~3/2 = 708.7131{{c}}
			\| CWE: ~3/2 = 708.3200{{c}}
			\| POTE: ~3/2 = 708.2046{{c}}
			\|}

	{{Todo\|inline=1\|complete section}}		{{Todo\|inline=1\|complete section}}

FloraC: I'm just copypasting ultrapyth for the opening

2025-12-31T11:38:43Z

I'm just copypasting ultrapyth for the opening

← Older revision		Revision as of 11:38, 31 December 2025
Line 14:		Line 14:
	\| Odd limit 2 = (11-limit) 15 \| Mistuning 2 = 14.9 \| Complexity 2 = 17		\| Odd limit 2 = (11-limit) 15 \| Mistuning 2 = 14.9 \| Complexity 2 = 17
	}}		}}
	'''Quasisuper''' is an alternative extension of [[2.~~3.7 subgroup~~\|~~2.3.~~7]] [[~~archy~~]] to prime [[5/1\|5]]~~. This extension maps prime 5~~ to -13 [[generator]]s, as a double-diminished fifth (C–G𝄫). This extension works in the range [[17edo\|17c-edo]] to [[22edo\|22-edo]]. In contrast, full 7-limit [[superpyth]] does not work in this range, as tunings with a flatter fifth than 22edo swap the sizes of [[7/5]] and [[10/7]]. This extension may be preferred over superpyth due to having a softer [[5L 2s\|diatonic]] scale, with a small step of around 60 [[cent]]s compared to about 50 cents in regular 7-limit superpyth. The best extension to the [[11-limit]], '''quasisupra''', uses the [[supra]] mapping of prime [[11/1\|11]] to -6 generators, as a diminished fifth (C–G♭). This tempers out [[99/98]] as in supra, as well as [[121/120]] and [[540/539]].		'''Quasisuper''' is an alternative [[extension]] of the [[archy]] [[chain of fifths]] to [[superpyth]]. Like superpyth, it is a [[regular temperament\|temperament]] generated by a perfect fifth, where stacking two of them reaches the interval of [[8/7]][[~]][[9/8]], [[tempering out]] [[64/63]]. The difference is that this extension maps [[prime interval\|prime]] [[5/1\|5]] to -13 [[generator]]s, as a double-diminished fifth (C–G𝄫). This extension works in the range [[17edo\|17c-edo]] to [[22edo\|22-edo]]. In contrast, full 7-limit [[superpyth]] does not work in this range, as tunings with a flatter fifth than 22edo swap the sizes of [[7/5]] and [[10/7]]. This extension may be preferred over superpyth due to having a softer [[5L 2s\|diatonic]] scale, with a small step of around 60 [[cent]]s compared to about 50 cents in regular 7-limit superpyth.

			The best extension to the [[11-limit]], '''quasisupra''', uses the [[supra]] mapping of prime [[11/1\|11]] to -6 generators, as a diminished fifth (C–G♭). This tempers out [[99/98]] as in supra, as well as [[121/120]] and [[540/539]].

			For technical data see [[Archytas clan #Quasisuper]].

	~~For technical data see [[Archytas clan#Quasisuper]].~~
	~~{{todo\|expand\|review\|cleanup\|improve synopsis\|improve readability}}~~
	~~{{Clear}}~~
	== Interval chain ==		== Interval chain ==
	In the following table, odd harmonics and subharmonics ~~1–15~~ are in '''bold'''.		In the following table, odd harmonics and subharmonics 1–11 are in '''bold'''.

	{\| class="wikitable"		{\| class="wikitable center-1 right-2"
	~~\|+ style="font~~-~~size: 105%~~" ~~\| Intervals of quasisupra (11-limit)~~		! #
	! ~~Generators~~
	! Cents*		! Cents*
	! ~~Intervals~~		! Approximate ratios
	\|-		\|-
	\| 0		\| 0
Line 50:		Line 50:
	\| 5		\| 5
	\| 1141.6		\| 1141.6
	\| 27/14~~, 21/11~~		\| 21/11, 27/14
	\|-		\|-
	\| 6		\| 6
Line 58:		Line 58:
	\| 7		\| 7
	\| 158.2		\| 158.2
	\| 12/11~~, 11/10~~		\| 11/10, 12/11
	\|-		\|-
	\| 8		\| 8
Line 78:		Line 78:
	\| 12		\| 12
	\| 99.8		\| 99.8
	\| ~~'''~~16/15~~'''~~		\| 16/15
	\|-		\|-
	\| 13		\| 13
Line 103:		Line 103:

	== Tunings ==		== Tunings ==
	{{~~todo\|complete section~~\|inline=1}}		{{Todo\|inline=1\|complete section}}

	[[Category:Rank-2 temperaments]]		[[Category:Rank-2 temperaments]]
	[[Category:Archytas clan]]		[[Category:Archytas clan]]
	[[Category:Nuwell temperaments]]		[[Category:Nuwell temperaments]]