Archytas clan - Revision history

FloraC: /* Archy */ + dichotic

2026-05-29T10:06:04Z

Archy: + dichotic

← Older revision		Revision as of 10:06, 29 May 2026
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	These all use the same generators as archy.		These all use the same generators as archy.

	[[686/675]] gives beatles~~, splitting~~ the fifth in two. [[8748/8575]] gives immunized, splitting the twelfth in two. [[50/49]] gives pajara with a semioctave period. [[392/375]] gives progress, splitting the twelfth in three. [[250/243]] gives porcupine, splitting the fourth in three. [[126/125]] gives augene with a 1/3-octave period. [[4375/4374]] gives modus, splitting the fifth in four. [[3125/3024]] gives brightstone. [[9604/9375]] gives fervor. [[3125/2916]] gives sixix. [[3125/3087]] gives passion. Those split the generator in five in various ways. [[28/27]] gives blackwood with a 1/5-octave period. Finally, [[15625/15552]] gives catalan, splitting the twelfth in six.		[[25/24]] gives dichotic. [[686/675]] gives beatles. Those split the fifth in two. [[8748/8575]] gives immunized, splitting the twelfth in two. [[50/49]] gives pajara with a semioctave period. [[392/375]] gives progress, splitting the twelfth in three. [[250/243]] gives porcupine, splitting the fourth in three. [[126/125]] gives augene with a 1/3-octave period. [[4375/4374]] gives modus, splitting the fifth in four. [[3125/3024]] gives brightstone. [[9604/9375]] gives fervor. [[3125/2916]] gives sixix. [[3125/3087]] gives passion. Those split the generator in five in various ways. [[28/27]] gives blackwood with a 1/5-octave period. Finally, [[15625/15552]] gives catalan, splitting the twelfth in six.

	Temperaments discussed elsewhere are:		Temperaments discussed elsewhere are:
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	* [[Dominant (temperament)\|Dominant]] (+36/35) → [[Meantone family #Dominant\|Meantone family]]		* [[Dominant (temperament)\|Dominant]] (+36/35) → [[Meantone family #Dominant\|Meantone family]]
	* ''[[Medusa]]'' (+15/14) → [[Very low accuracy temperaments #Medusa\|Very low accuracy temperaments]]		* ''[[Medusa]]'' (+15/14) → [[Very low accuracy temperaments #Medusa\|Very low accuracy temperaments]]
			* ''[[Dichotic]]'' (+25/24) → [[Dicot family #Dichotic\|Dicot family]]
	* ''[[Immunized]]'' (+8748/8575) → [[Immunity family #Immunized\|Immunity family]]		* ''[[Immunized]]'' (+8748/8575) → [[Immunity family #Immunized\|Immunity family]]
	* [[Pajara]] (+50/49) → [[Diaschismic family #Pajara\|Diaschismic family]]		* [[Pajara]] (+50/49) → [[Diaschismic family #Pajara\|Diaschismic family]]

FloraC: Modus has an article now. - redundant links

2026-04-15T17:57:11Z

Modus has an article now. - redundant links

FloraC: + link

2026-02-26T11:34:20Z

+ link

← Older revision		Revision as of 11:34, 26 February 2026
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	== Ultrapyth ==		== Ultrapyth ==
	{{Main\| Ultrapyth }}		{{Main\| Ultrapyth }}
			: ''For the 5-limit version, see [[Syntonic–diatonic equivalence continuum #Ultrapyth (5-limit)]].''

	Ultrapyth can be viewed as an extension of the excellent 2.3.7.13/5 [[the Biosphere #Oceanfront\|oceanfront]] temperament, mapping the ~5/4 to +14 fifths as a double-augmented unison (C–C𝄪).		Ultrapyth can be viewed as an extension of the excellent 2.3.7.13/5 [[the Biosphere #Oceanfront\|oceanfront]] temperament, mapping the ~5/4 to +14 fifths as a double-augmented unison (C–C𝄪).

Lucius Chiaraviglio: /* 7-limit extensions */ Add more links

2026-02-25T11:48:29Z

7-limit extensions: Add more links

Lucius Chiaraviglio: /* 7-limit extensions */ Add links to some commas, even though they do not have articles yet

2026-02-25T11:43:53Z

7-limit extensions: Add links to some commas, even though they do not have articles yet

← Older revision		Revision as of 11:43, 25 February 2026
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	==== 7-limit extensions ====		==== 7-limit extensions ====
	The second comma in the comma list defines which [[7-limit]] family member we are looking at:		The second comma in the comma list defines which [[7-limit]] family member we are looking at:
	* [[#Schism\|Schism]] adds 360/343, for a tuning around [[12edo]];		* [[#Schism\|Schism]] adds [[360/343]], for a tuning around [[12edo]];
	* Dominant adds [[36/35]], for a tuning between [[12edo]] and [[17edo\|17c-edo]];		* Dominant adds [[36/35]], for a tuning between [[12edo]] and [[17edo\|17c-edo]];
	* [[#Quasisuper\|Quasisuper]] adds [[2430/2401]], for a tuning between 17c-edo and [[22edo]];		* [[#Quasisuper\|Quasisuper]] adds [[2430/2401]], for a tuning between 17c-edo and [[22edo]];
	* [[#Superpyth\|Superpyth]] adds [[245/243]], for a tuning between 22edo and [[27edo]];		* [[#Superpyth\|Superpyth]] adds [[245/243]], for a tuning between 22edo and [[27edo]];
	* [[#Quasiultra\|Quasiultra]] adds 33614/32805, for a tuning between 27edo and [[32edo]];		* [[#Quasiultra\|Quasiultra]] adds [[33614/32805]], for a tuning between 27edo and [[32edo]];
	* [[#Ultrapyth\|Ultrapyth]] adds 6860/6561, for a tuning sharp of 32edo;		* [[#Ultrapyth\|Ultrapyth]] adds [[6860/6561]], for a tuning sharp of 32edo;
	* Mother adds [[16/15]], for an exotemperament well tuned around [[5edo]].		* Mother adds [[16/15]], for an exotemperament well tuned around [[5edo]].

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	* ''[[Catalan]]'' (+15625/15552) → [[Kleismic family #Catalan\|Kleismic family]]		* ''[[Catalan]]'' (+15625/15552) → [[Kleismic family #Catalan\|Kleismic family]]

	Considered below are superpyth, quasisuper, ultrapyth, quasiultra, schism, beatles, progress, fervor, and sixix.		Considered below are superpyth, quasisuper, ultrapyth, quasiultra, schism, beatles, progress, fervor, and sixix.

	==== Subgroup extensions ====		==== Subgroup extensions ====

FloraC: Update

2026-01-28T07:45:34Z

Update

← Older revision		Revision as of 07:45, 28 January 2026
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	* ''[[Immunized]]'' (+8748/8575) → [[Immunity family #Immunized\|Immunity family]]		* ''[[Immunized]]'' (+8748/8575) → [[Immunity family #Immunized\|Immunity family]]
	* [[Pajara]] (+50/49) → [[Diaschismic family #Pajara\|Diaschismic family]]		* [[Pajara]] (+50/49) → [[Diaschismic family #Pajara\|Diaschismic family]]
	* [[Augene]] (+126/125) → [[Augmented family #~~Augene~~\|Augmented family]]		* [[Augene]] (+126/125) → [[Augmented family #Septimal augmented (augene)\|Augmented family]]
	* [[Porcupine]] (+250/243) → [[Porcupine family #Septimal porcupine\|Porcupine family]]		* [[Porcupine]] (+250/243) → [[Porcupine family #Septimal porcupine\|Porcupine family]]
	* ''[[Modus]]'' (+4375/4374) → [[Tetracot family #Modus\|Tetracot family]]		* ''[[Modus]]'' (+4375/4374) → [[Tetracot family #Modus\|Tetracot family]]

Overthink: /* Superpyth */ + links

2026-01-05T04:28:30Z

Superpyth: + links

← Older revision		Revision as of 04:28, 5 January 2026
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	: ''For the 5-limit version, see [[Syntonic–diatonic equivalence continuum #Superpyth (5-limit)]].''		: ''For the 5-limit version, see [[Syntonic–diatonic equivalence continuum #Superpyth (5-limit)]].''

	Superpyth, virtually the canonical extension, adds [[245/243]] and [[1728/1715]] to the comma list and can be described as {{nowrap\| 22 & 27 }}. ~5/4 is found at +9 generator steps, as an augmented second (C–D♯). In the 11-limit it finds the ~11/8 at +16 generator steps, as a double-augmented second (C–D𝄪). 49edo remains an obvious tuning choice in either case.		Superpyth, virtually the canonical extension, adds [[245/243]] and [[1728/1715]] to the comma list and can be described as {{nowrap\| [[22edo\|22]] [[&]] [[27edo\|27]] }}. ~[[5/4]] is found at +9 generator steps, as an augmented second (C–D♯). In the [[11-limit]] it finds the ~[[11/8]] at +16 generator steps, as a double-augmented second (C–D𝄪). [[49edo]] remains an obvious tuning choice in either case.

	Extending superpyth to the 13-limit is more diffcult. Tridecimal superpyth finds the ~13/8 at +13 generator steps, as a double-augmented fourth (C–F𝄪), for which 27edo can be recommended as a tuning since it is the only 13-odd-limit diamond monotone tuning. The other extension, called uberpyth, is more flexible with its tunings, but unfortunately tends to tune the 13 very sharp.		Extending superpyth to the [[13-limit]] is more diffcult. Tridecimal superpyth finds the ~[[13/8]] at +13 generator steps, as a double-augmented fourth (C–F𝄪), for which 27edo can be recommended as a tuning since it is the only [[13-odd-limit]] [[diamond monotone]] tuning. The other extension, called uberpyth, is more flexible with its tunings, but unfortunately tends to tune the 13 very sharp.

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

FloraC: Improve descriptions to reflect recent research results

2026-01-02T14:49:09Z

Improve descriptions to reflect recent research results

← Older revision		Revision as of 14:49, 2 January 2026
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	: ''For the 5-limit version, see [[Syntonic–diatonic equivalence continuum #Superpyth (5-limit)]].''		: ''For the 5-limit version, see [[Syntonic–diatonic equivalence continuum #Superpyth (5-limit)]].''

	Superpyth, virtually the canonical extension, adds [[245/243]] and [[1728/1715]] to the comma list and can be described as {{nowrap\| 22 & 27 }}. ~5/4 is found at +9 generator steps, as an augmented second (C–D♯). 49edo remains an obvious tuning choice.		Superpyth, virtually the canonical extension, adds [[245/243]] and [[1728/1715]] to the comma list and can be described as {{nowrap\| 22 & 27 }}. ~5/4 is found at +9 generator steps, as an augmented second (C–D♯). In the 11-limit it finds the ~11/8 at +16 generator steps, as a double-augmented second (C–D𝄪). 49edo remains an obvious tuning choice in either case.

			Extending superpyth to the 13-limit is more diffcult. Tridecimal superpyth finds the ~13/8 at +13 generator steps, as a double-augmented fourth (C–F𝄪), for which 27edo can be recommended as a tuning since it is the only 13-odd-limit diamond monotone tuning. The other extension, called uberpyth, is more flexible with its tunings, but unfortunately tends to tune the 13 very sharp.

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7
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	=== 11-limit ===		=== 11-limit ===
	The canonical extension to the 13-limit finds the ~11/8 at +16 generator steps, as a double-augmented second (C–D𝄪) and finds the ~13/8 at +13 generator steps, as a double-augmented fourth (C–F𝄪).

	Subgroup: 2.3.5.7.11		Subgroup: 2.3.5.7.11

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	== Quasisuper ==		== Quasisuper ==
	{{Main\|Quasisuper}}		{{Main\|Quasisuper}}
	Quasisuper can be described as {{nowrap\| 17c & 22 }}, with the ~5/4 mapped to -13 generator steps, as a double-diminished fifth (C–G𝄫).
			Quasisuper can be described as {{nowrap\| 17c & 22 }}, with the ~5/4 mapped to -13 generator steps, as a double-diminished fifth (C–G𝄫). The 11-limit version, quasisupra, can be viewed as an extension of the excellent 2.3.7.11-subgroup temperament [[supra]], with the quasisuper mapping of 5 thrown in, rather than the superpyth mapping of 5 (which results in suprapyth).

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7
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	=== Quasisupra ===		=== Quasisupra ===
	Quasisupra can be viewed as an extension of the excellent 2.3.7.11 temperament [[supra]], with the quasisuper mapping of 5 thrown in, rather than the superpyth mapping of 5 (which results in suprapyth).

	Subgroup: 2.3.5.7.11		Subgroup: 2.3.5.7.11

Overthink: /* Quasisuper */ + main

2025-12-30T12:26:22Z

Quasisuper: + main

← Older revision		Revision as of 12:26, 30 December 2025
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	== Quasisuper ==		== Quasisuper ==
			{{Main\|Quasisuper}}
	Quasisuper can be described as {{nowrap\| 17c & 22 }}, with the ~5/4 mapped to -13 generator steps, as a double-diminished fifth (C–G𝄫).		Quasisuper can be described as {{nowrap\| 17c & 22 }}, with the ~5/4 mapped to -13 generator steps, as a double-diminished fifth (C–G𝄫).

Overthink: /* Supraphon */ Better explanation of mapping

2025-12-29T08:27:30Z

Supraphon: Better explanation of mapping

← Older revision		Revision as of 08:27, 29 December 2025
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	==== Supraphon ====		==== Supraphon ====
	This extension maps [[12/11]][[~]][[14/13]] to ~~+7 generators~~ (C–C♯), and [[13/12]] to ~~-10 generators~~ (C–E𝄫)~~; [[17edo]] is the tuning equating all of them~~.		This extension maps [[13/11]] to the minor third (C–E♭), [[12/11]][[~]][[14/13]] to the augmented unison (C–C♯), and [[13/12]] to the diminished third (C–E𝄫).

	Subgroup: 2.3.7.11.13		Subgroup: 2.3.7.11.13

← Older revision		Revision as of 07:45, 28 January 2026
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	* ''[[Immunized]]'' (+8748/8575) → [[Immunity family #Immunized\|Immunity family]]		* ''[[Immunized]]'' (+8748/8575) → [[Immunity family #Immunized\|Immunity family]]
	* [[Pajara]] (+50/49) → [[Diaschismic family #Pajara\|Diaschismic family]]		* [[Pajara]] (+50/49) → [[Diaschismic family #Pajara\|Diaschismic family]]
	* [[Augene]] (+126/125) → [[Augmented family #~~Augene~~\|Augmented family]]		* [[Augene]] (+126/125) → [[Augmented family #Septimal augmented (augene)\|Augmented family]]
	* [[Porcupine]] (+250/243) → [[Porcupine family #Septimal porcupine\|Porcupine family]]		* [[Porcupine]] (+250/243) → [[Porcupine family #Septimal porcupine\|Porcupine family]]
	* ''[[Modus]]'' (+4375/4374) → [[Tetracot family #Modus\|Tetracot family]]		* ''[[Modus]]'' (+4375/4374) → [[Tetracot family #Modus\|Tetracot family]]

← Older revision		Revision as of 17:57, 15 April 2026
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	The second comma in the comma list defines which [[7-limit]] family member we are looking at:		The second comma in the comma list defines which [[7-limit]] family member we are looking at:
	* [[#Schism\|Schism]] adds [[360/343]], for a tuning around [[12edo]];		* [[#Schism\|Schism]] adds [[360/343]], for a tuning around [[12edo]];
	* [[Dominant ~~(temperament)~~\|Dominant]] adds [[36/35]], for a tuning between [[12edo]] and [[17edo\|17c-edo]];		* [[Meantone family #Dominant\|Dominant]] adds [[36/35]], for a tuning between [[12edo]] and [[17edo\|17c-edo]];
	* [[#Quasisuper\|Quasisuper]] adds [[2430/2401]], for a tuning between 17c-edo and [[22edo]];		* [[#Quasisuper\|Quasisuper]] adds [[2430/2401]], for a tuning between 17c-edo and [[22edo]];
	* [[#Superpyth\|Superpyth]] adds [[245/243]], for a tuning between 22edo and [[27edo]];		* [[#Superpyth\|Superpyth]] adds [[245/243]], for a tuning between 22edo and [[27edo]];
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	Temperaments discussed elsewhere are:		Temperaments discussed elsewhere are:
	* ''[[Mother]]'' (+[[16/15]]) → [[Father family #Mother\|Father family]]		* ''[[Mother]]'' (+16/15) → [[Father family #Mother\|Father family]]
	* [[Dominant (temperament)\|Dominant]] (+[[36/35]]) → [[Meantone family #Dominant\|Meantone family]]		* [[Dominant (temperament)\|Dominant]] (+36/35) → [[Meantone family #Dominant\|Meantone family]]
	* ''[[Medusa]]'' (+[[15/14]]) → [[Very low accuracy temperaments #Medusa\|Very low accuracy temperaments]]		* ''[[Medusa]]'' (+15/14) → [[Very low accuracy temperaments #Medusa\|Very low accuracy temperaments]]
	* ''[[Immunized]]'' (+[[8748/8575]]) → [[Immunity family #Immunized\|Immunity family]]		* ''[[Immunized]]'' (+8748/8575) → [[Immunity family #Immunized\|Immunity family]]
	* [[Pajara]] (+[[50/49]]) → [[Diaschismic family #Pajara\|Diaschismic family]]		* [[Pajara]] (+50/49) → [[Diaschismic family #Pajara\|Diaschismic family]]
	* [[Augene]] (+[[126/125]]) → [[Augmented family #Septimal augmented (augene)\|Augmented family]]		* [[Augene]] (+126/125) → [[Augmented family #Septimal augmented (augene)\|Augmented family]]
	* [[Porcupine]] (+[[250/243]]) → [[Porcupine family #Septimal porcupine\|Porcupine family]]		* [[Porcupine]] (+250/243) → [[Porcupine family #Septimal porcupine\|Porcupine family]]
	* ''[[Modus]]'' (+[[4375/4374]]) → [[Tetracot family #Modus\|Tetracot family]]		* [[Modus]] (+4375/4374) → [[Tetracot family #Modus\|Tetracot family]]
	* ''[[Brightstone]]'' (+[[3125/3024]]) → [[Magic family #Brightstone\|Magic family]]		* ''[[Brightstone]]'' (+3125/3024) → [[Magic family #Brightstone\|Magic family]]
	* ''[[Passion]]'' (+[[3125/3087]]) → [[Passion family #Septimal passion\|Passion family]]		* ''[[Passion]]'' (+3125/3087) → [[Passion family #Septimal passion\|Passion family]]
	* [[Blackwood]] (+[[28/27]]) → [[Limmic temperaments #Blackwood\|Limmic temperaments]]		* [[Blackwood]] (+28/27) → [[Limmic temperaments #Blackwood\|Limmic temperaments]]
	* ''[[Catalan]]'' (+[[15625/15552]]) → [[Kleismic family #Catalan\|Kleismic family]]		* ''[[Catalan]]'' (+15625/15552) → [[Kleismic family #Catalan\|Kleismic family]]

	Considered below are superpyth, quasisuper, ultrapyth, quasiultra, schism, beatles, progress, fervor, and sixix.		Considered below are superpyth, quasisuper, ultrapyth, quasiultra, schism, beatles, progress, fervor, and sixix.

	==== Subgroup extensions ====		==== Subgroup extensions ====
	Omitting prime 5, archy can be extended to the 2.3.7.11 subgroup by identifying 11/8 as a diminished fourth (C–G♭). This is called supra, given right below. Discussed elsewhere is [[suhajira]] of the [[~~neutral~~ clan #Suhajira\|~~neutral~~ clan]].		Omitting prime 5, archy can be extended to the 2.3.7.11 subgroup by identifying 11/8 as a diminished fourth (C–G♭). This is called supra, given right below. Discussed elsewhere is [[suhajira]] of the [[rastmic clan #Suhajira\|rastmic clan]].

	=== Supra ===		=== Supra ===

← Older revision		Revision as of 11:48, 25 February 2026
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	The second comma in the comma list defines which [[7-limit]] family member we are looking at:		The second comma in the comma list defines which [[7-limit]] family member we are looking at:
	* [[#Schism\|Schism]] adds [[360/343]], for a tuning around [[12edo]];		* [[#Schism\|Schism]] adds [[360/343]], for a tuning around [[12edo]];
	* Dominant adds [[36/35]], for a tuning between [[12edo]] and [[17edo\|17c-edo]];		* [[Dominant (temperament)\|Dominant]] adds [[36/35]], for a tuning between [[12edo]] and [[17edo\|17c-edo]];
	* [[#Quasisuper\|Quasisuper]] adds [[2430/2401]], for a tuning between 17c-edo and [[22edo]];		* [[#Quasisuper\|Quasisuper]] adds [[2430/2401]], for a tuning between 17c-edo and [[22edo]];
	* [[#Superpyth\|Superpyth]] adds [[245/243]], for a tuning between 22edo and [[27edo]];		* [[#Superpyth\|Superpyth]] adds [[245/243]], for a tuning between 22edo and [[27edo]];
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	Temperaments discussed elsewhere are:		Temperaments discussed elsewhere are:
	* ''[[Mother]]'' (+16/15) → [[Father family #Mother\|Father family]]		* ''[[Mother]]'' (+[[16/15]]) → [[Father family #Mother\|Father family]]
	* [[Dominant (temperament)\|Dominant]] (+36/35) → [[Meantone family #Dominant\|Meantone family]]		* [[Dominant (temperament)\|Dominant]] (+[[36/35]]) → [[Meantone family #Dominant\|Meantone family]]
	* ''[[Medusa]]'' (+15/14) → [[Very low accuracy temperaments #Medusa\|Very low accuracy temperaments]]		* ''[[Medusa]]'' (+[[15/14]]) → [[Very low accuracy temperaments #Medusa\|Very low accuracy temperaments]]
	* ''[[Immunized]]'' (+8748/8575) → [[Immunity family #Immunized\|Immunity family]]		* ''[[Immunized]]'' (+[[8748/8575]]) → [[Immunity family #Immunized\|Immunity family]]
	* [[Pajara]] (+50/49) → [[Diaschismic family #Pajara\|Diaschismic family]]		* [[Pajara]] (+[[50/49]]) → [[Diaschismic family #Pajara\|Diaschismic family]]
	* [[Augene]] (+126/125) → [[Augmented family #Septimal augmented (augene)\|Augmented family]]		* [[Augene]] (+[[126/125]]) → [[Augmented family #Septimal augmented (augene)\|Augmented family]]
	* [[Porcupine]] (+250/243) → [[Porcupine family #Septimal porcupine\|Porcupine family]]		* [[Porcupine]] (+[[250/243]]) → [[Porcupine family #Septimal porcupine\|Porcupine family]]
	* ''[[Modus]]'' (+4375/4374) → [[Tetracot family #Modus\|Tetracot family]]		* ''[[Modus]]'' (+[[4375/4374]]) → [[Tetracot family #Modus\|Tetracot family]]
	* ''[[Brightstone]]'' (+3125/3024) → [[Magic family #Brightstone\|Magic family]]		* ''[[Brightstone]]'' (+[[3125/3024]]) → [[Magic family #Brightstone\|Magic family]]
	* ''[[Passion]]'' (+3125/3087) → [[Passion family #Septimal passion\|Passion family]]		* ''[[Passion]]'' (+[[3125/3087]]) → [[Passion family #Septimal passion\|Passion family]]
	* [[Blackwood]] (+28/27) → [[Limmic temperaments #Blackwood\|Limmic temperaments]]		* [[Blackwood]] (+[[28/27]]) → [[Limmic temperaments #Blackwood\|Limmic temperaments]]
	* ''[[Catalan]]'' (+15625/15552) → [[Kleismic family #Catalan\|Kleismic family]]		* ''[[Catalan]]'' (+[[15625/15552]]) → [[Kleismic family #Catalan\|Kleismic family]]

	Considered below are superpyth, quasisuper, ultrapyth, quasiultra, schism, beatles, progress, fervor, and sixix.		Considered below are superpyth, quasisuper, ultrapyth, quasiultra, schism, beatles, progress, fervor, and sixix.