Tour of regular temperaments - Revision history

FloraC: - alpharabian rank-3 clan (it's cleared)

2026-08-16T11:54:51Z

- alpharabian rank-3 clan (it's cleared)

← Older revision		Revision as of 11:54, 16 August 2026
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	; [[Olympic clan]] (P8, P5, ^1)		; [[Olympic clan]] (P8, P5, ^1)
	: These temper out the [[olympia]], {{monzo\| 17 -5 0 -2 -1 }} (131072/130977). 11/8 is equated with a 2.3.7 interval, and thus every 2.3.7.11 interval is equated with a 2.3.7 interval. In the pergen, {{nowrap\| ^1 {{=}} ~64/63 }}. Its color name is Salururuti.		: These temper out the [[olympia]], {{monzo\| 17 -5 0 -2 -1 }} (131072/130977). 11/8 is equated with a 2.3.7 interval, and thus every 2.3.7.11 interval is equated with a 2.3.7 interval. In the pergen, {{nowrap\| ^1 {{=}} ~64/63 }}. Its color name is Salururuti.

	~~; [[Alphaxenic rank-3 clan]]~~
	: These temper out the [[Alpharabian comma]], {{monzo\| -17 2 0 0 4 }} (131769/131072). In the corresponding [[#Clans defined by a 2.3.11 comma\|2.3.11 rank-2 temperament]], the pergen is (P8/2, M2/4). Its color name is Laquadloti.

	; [[Keenanismic temperaments]]		; [[Keenanismic temperaments]]

FloraC: + parakleismic family & sengic temperaments

2026-08-10T13:54:13Z

+ parakleismic family & sengic temperaments

← Older revision		Revision as of 13:54, 10 August 2026
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	; [[Ditonmic family]] (P8, c4P4/13)		; [[Ditonmic family]] (P8, c4P4/13)
	: This tempers out the [[ditonma]], {{monzo\| -27 -2 13 }} (1220703125/1207959552). Thirteen ~{{monzo\| -12 -1 6 }} generators of about 407{{c}} equals a quadruple-compound fourth. 5/4 is equated to 1 octave minus 2 generators. An obvious 3-limit interpretation of the generator is 81/64, which implies 53edo, which is a good tuning for this high-accuracy family of temperaments. Its color name is Lala-theyoti.		: This tempers out the [[ditonma]], {{monzo\| -27 -2 13 }} (1220703125/1207959552). Thirteen ~{{monzo\| -12 -1 6 }} generators of about 407{{c}} equals a quadruple-compound fourth. 5/4 is equated to 1 octave minus 2 generators. An obvious 3-limit interpretation of the generator is 81/64, which implies 53edo, which is a good tuning for this high-accuracy family of temperaments. Its color name is Lala-theyoti.

			; [[Parakleismic family]] (P8, c3P4/13)
			: This tempers out the [[parakleisma]], {{monzo\| 8 14 -13 }} (1224440064/1220703125). The generator is a slightly sharpened ~5/3 major sixth. Thirteen generators minus three octaves equal ~4/3, and fourteen generators minus three octaves equal ~8/5.

	; [[Luna family]] (P8, ccP4/15)		; [[Luna family]] (P8, ccP4/15)
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	: These temper out the [[avicennma]], {{monzo\| -9 1 2 1 }} (525/512), also known as Avicenna's enharmonic diesis. Its color name is Zoyoyoti.		: These temper out the [[avicennma]], {{monzo\| -9 1 2 1 }} (525/512), also known as Avicenna's enharmonic diesis. Its color name is Zoyoyoti.

	; Sengic temperaments		; [[Sengic temperaments]]
	: Sengic rank-2 temperaments temper out the [[senga]], {{monzo\| 1 -3 -2 3 }} (686/675). Its color name is Trizo-aguguti.		: Sengic rank-2 temperaments temper out the [[senga]], {{monzo\| 1 -3 -2 3 }} (686/675). Its color name is Trizo-aguguti.

FloraC: Update

2026-08-10T13:41:19Z

Update

← Older revision		Revision as of 13:41, 10 August 2026
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	; [[Garischismic clan]] (P8, P5)		; [[Garischismic clan]] (P8, P5)
	: This clan tempers out the [[garischisma]], {{monzo\| 25 -14 0 -1 }} (33554432/33480783). It equates 8/7 to two apotomes ({{monzo\| -~~11 7~~ }}, 2187/2048) and 7/4 to a double-diminished octave {{monzo\| 23 -14 }}. This clan includes [[~~vulture~~ family #~~Vulture~~\|~~vulture~~]], [[~~breedsmic temperaments~~ #Newt\|newt]], [[~~schismatic family~~ #~~Garibaldi~~\|~~garibaldi~~]], [[~~landscape microtemperaments~~ #~~Sextile~~\|~~sextile~~]], and [[~~canousmic temperaments~~ #~~Satin~~\|~~satin~~]]. Its color name is Sasaruti.		: This clan tempers out the [[garischisma]], {{monzo\| 25 -14 0 -1 }} (33554432/33480783). It equates 8/7 to two apotomes ({{monzo\| -22 14 }}, (2187/2048)<sup>2</sup>) and 7/4 to a double-diminished octave {{monzo\| 23 -14 }}. This clan includes [[schismatic family #Garibaldi\|garibaldi]], [[garischismic clan #Newt\|newt]], [[garischismic clan #Satin\|satin]], [[vulture family #Vulture\|vulture]], and [[garischismic clan #Sextile\|sextile]]. Its color name is Sasaruti.

	; Sasazoti clan (P8, P5)		; Sasazoti clan (P8, P5)
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	: Cataharry rank-2 temperaments temper out the [[cataharry comma]], {{monzo\| -4 9 -2 -2 }} (19683/19600). Its color name is Labiruguti.		: Cataharry rank-2 temperaments temper out the [[cataharry comma]], {{monzo\| -4 9 -2 -2 }} (19683/19600). Its color name is Labiruguti.

	; [[~~Canousmic~~ temperaments]]		; [[Cathartic temperaments]]
	: ~~Canousmic~~ rank-2 temperaments temper out the [[~~canousma~~]], {{monzo\| 4 -14 3 4 }} (4802000/4782969). Its color name is Saquadzo-atriyoti.		: Cathartic rank-2 temperaments temper out the [[cathartic comma]], {{monzo\| 4 -14 3 4 }} (4802000/4782969). Its color name is Saquadzo-atriyoti.

	; [[Triwellismic temperaments]]		; [[Triwellismic temperaments]]
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	: The gariboh family of rank-3 temperaments tempers out the gariboh comma, {{monzo\| 0 -2 5 -3 }} (3125/3087). Three ~25/21 generators equal the pergen's downmajor sixth of ~5/3. Its color name is Triru-aquinyoti.		: The gariboh family of rank-3 temperaments tempers out the gariboh comma, {{monzo\| 0 -2 5 -3 }} (3125/3087). Three ~25/21 generators equal the pergen's downmajor sixth of ~5/3. Its color name is Triru-aquinyoti.

	; [[~~Canou~~ family]] (P8, P5, vm6/3)		; [[Cathartic family]] (P8, P5, vm6/3)
	: The ~~canou~~ family of rank-3 temperaments tempers out the ~~canousma~~, {{monzo\| 4 -14 3 4 }} (4802000/4782969). Three ~81/70 generators equal the pergen's downminor sixth of ~14/9. Its color name is Saquadzo-atriyoti.		: The cathartic family of rank-3 temperaments tempers out the cathartic comma, {{monzo\| 4 -14 3 4 }} (4802000/4782969). Three ~81/70 generators equal the pergen's downminor sixth of ~14/9. Its color name is Saquadzo-atriyoti.

	; [[Dimcomp family]] (P8/4, P5, ^1)		; [[Dimcomp family]] (P8/4, P5, ^1)
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	: These temper out the [[4000/3993\|wizardharry comma]], {{monzo\| 5 -1 3 0 -3 }} (4000/3993), and split the fourth in three. In the pergen, ^1 is either ~33/32 or ~729/704. Its color name is Triluyoti.		: These temper out the [[4000/3993\|wizardharry comma]], {{monzo\| 5 -1 3 0 -3 }} (4000/3993), and split the fourth in three. In the pergen, ^1 is either ~33/32 or ~729/704. Its color name is Triluyoti.

	; [[~~Semicanousmic~~ clan]] (P8, P5, ^1)		; [[Semicathartismic clan]] (P8, P5, ^1)
	: These temper out the [[~~semicanousma~~]], {{monzo\| -2 -6 -1 0 4 }} (14641/14580). 5/4 is equated to a 2.3.11 (color name: ila) interval, thus every 2.3.5.11 interval is equated to a 2.3.11 interval, and both the pergen and the lattice are identical to that of 2.3.11-subgroup JI. In the pergen, ^1 is either ~33/32 or ~729/704. Its color name is Quadlo-aguti.		: These temper out the [[semicathartisma]], {{monzo\| -2 -6 -1 0 4 }} (14641/14580). 5/4 is equated to a 2.3.11 (color name: ila) interval, thus every 2.3.5.11 interval is equated to a 2.3.11 interval, and both the pergen and the lattice are identical to that of 2.3.11-subgroup JI. In the pergen, ^1 is either ~33/32 or ~729/704. Its color name is Quadlo-aguti.

	; [[Semiporwellismic clan]] (P8, P5, ^1)		; [[Semiporwellismic clan]] (P8, P5, ^1)

Fredg999: Update link

2026-07-08T04:05:54Z

Update link

← Older revision		Revision as of 04:05, 8 July 2026
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	; [[Gammic family]] (P8, P5/20)		; [[Gammic family]] (P8, P5/20)
	: The gammic family tempers out the [[gammic comma]], {{monzo\| -29 -11 20 }}. Nine generators of about 35{{c}} equals ~6/5, eleven equals ~5/4 and twenty equals ~3/2. 34edo is an obvious tuning. The head of the family is 5-limit gammic, whose generator chain is [[Carlos Gamma]]. Another member is the [[neptune]] temperament. Its color name is Laquinquadyoti.		: The gammic family tempers out the [[gammic comma]], {{monzo\| -29 -11 20 }}. Nine generators of about 35{{c}} equals ~6/5, eleven equals ~5/4 and twenty equals ~3/2. 34edo is an obvious tuning. The head of the family is 5-limit gammic, whose generator chain is [[Carlos Gamma]]. Another member is the [[Neptune (temperament)\|neptune]] temperament. Its color name is Laquinquadyoti.

	=== Clans defined by a 2.3.7 comma ===		=== Clans defined by a 2.3.7 comma ===

FloraC at 11:25, 28 June 2026

2026-06-28T11:25:18Z

← Older revision		Revision as of 11:25, 28 June 2026
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	== Miscellaneous other temperaments ==		== Miscellaneous other temperaments ==
	~~; [[Limmic temperaments]]~~
	~~: Various subgroup temperaments all tempering out the limma, 256/243.~~

	; [[Fractional-octave temperaments]]		; [[Fractional-octave temperaments]]
	: These temperaments all have a fractional-octave period.		: These temperaments all have a fractional-octave period.

FloraC: - non-existent "cloudy clan". Update on blackwood family

2026-06-28T11:24:28Z

- non-existent "cloudy clan". Update on blackwood family

← Older revision		Revision as of 11:24, 28 June 2026
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	These are families defined by a 3-limit (color name: wa) comma. If only primes 2 and 3 are part of the [[subgroup]], the comma creates a rank-1 temperament, an [[edo]]. But if another prime such as 5 is present, the comma creates a rank-2 temperament. Since edos are discussed elsewhere, this section assumes the presence of at least one additional prime. The rank-2 temperament created consists of multiple "copies" of an edo. The edo copies can be thought of as being offset from one another by a small comma. This small comma is represented in the [[pergen]] by ^1.		These are families defined by a 3-limit (color name: wa) comma. If only primes 2 and 3 are part of the [[subgroup]], the comma creates a rank-1 temperament, an [[edo]]. But if another prime such as 5 is present, the comma creates a rank-2 temperament. Since edos are discussed elsewhere, this section assumes the presence of at least one additional prime. The rank-2 temperament created consists of multiple "copies" of an edo. The edo copies can be thought of as being offset from one another by a small comma. This small comma is represented in the [[pergen]] by ^1.

	; [[~~Limmic temperaments\|~~Blackwood family]] (P8/5, ^1)		; [[Blackwood family]] (P8/5, ^1)
	: This family tempers out the [[limma]], {{monzo\| 8 -5 }} (256/243). It equates 5 fifths with 3 octaves, which creates multiple copies of [[5edo]]. The fifth is ~~~720¢~~, quite sharp. The only member of this family is the [[blackwood]] temperament, which is 5-limit. Blackwood's edo copies are offset from one another by 5/4, or alternatively by 81/80. 5/4 is usually tempered sharp, perhaps ~~~400¢~~, to match the sharp fifth. Its color name is Sawati.		: This family tempers out the [[Pythagorean limma]], {{monzo\| 8 -5 }} (256/243). It equates 5 fifths with 3 octaves, which creates multiple copies of [[5edo]]. The fifth is ~720{{c}}, quite sharp. The only notable member of this family is the [[blackwood]] temperament, which is 5-limit. Blackwood's edo copies are offset from one another by 5/4, or alternatively by 81/80. 5/4 is usually tempered sharp, perhaps ~400{{c}}, to match the sharp fifth. Its color name is Sawati.

	; [[Whitewood family]] (P8/7, ^1)		; [[Whitewood family]] (P8/7, ^1)
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	; [[Buzzardsmic clan]] (P8, P12/4)		; [[Buzzardsmic clan]] (P8, P12/4)
	: This clan tempers out the [[buzzardsma]], {{monzo\| 16 -3 0 -4 }} (65536/64827). Its generator is ~21/16. Four generators makes ~3/1. 7/4 is equated to 2 octaves minus 3 generators. Its color name is Saquadruti. This clan includes as a strong extension the [[Vulture family #Septimal vulture\|vulture]] temperament, which is in the vulture family.		: This clan tempers out the [[buzzardsma]], {{monzo\| 16 -3 0 -4 }} (65536/64827). Its generator is ~21/16. Four generators makes ~3/1. 7/4 is equated to 2 octaves minus 3 generators. Its color name is Saquadruti. This clan includes as a strong extension the [[Vulture family #Septimal vulture\|vulture]] temperament, which is in the vulture family.

	~~; [[Cloudy clan]] (P8/5, P5)~~
	: This clan tempers out the [[cloudy comma]], {{monzo\| -14 0 0 5 }} (16807/16384). It has a period of 1/5 octave, which represents ~8/7. The generator is ~3/2. Unlike the blackwood or Sawati family, ~3/2 is not equated with three-fifths of an octave, resulting in very small intervals. Its color name is Laquinzoti.

	; Quinruti clan (P8, P5/5)		; Quinruti clan (P8, P5/5)

FloraC: Update

2026-06-18T08:19:22Z

Update

← Older revision		Revision as of 08:19, 18 June 2026
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	: The sensipent family tempers out the [[sensipent comma]], 78732/78125 ({{monzo\| 2 9 -7 }}), also known as the medium semicomma. Its generator is {{nowrap\| ~162/125 {{=}} ~443{{c}} }}. Seven generators equals a double-compound fifth of ~6/1. 5/4 is equated to 9 generators minus 3 octaves. Tunings include [[8edo]], [[19edo]], [[46edo]], and [[65edo]]. Its color name is Sepguti. An obvious 7-limit interpretation of the generator is 9/7, leading to the Sasepzoti temperament.		: The sensipent family tempers out the [[sensipent comma]], 78732/78125 ({{monzo\| 2 9 -7 }}), also known as the medium semicomma. Its generator is {{nowrap\| ~162/125 {{=}} ~443{{c}} }}. Seven generators equals a double-compound fifth of ~6/1. 5/4 is equated to 9 generators minus 3 octaves. Tunings include [[8edo]], [[19edo]], [[46edo]], and [[65edo]]. Its color name is Sepguti. An obvious 7-limit interpretation of the generator is 9/7, leading to the Sasepzoti temperament.

	; [[~~Vishnuzmic~~ family]] (P8/2, P4/7)		; [[Vishnu family]] (P8/2, P4/7)
	: This tempers out the [[~~vishnuzma~~]], {{monzo\| 23 6 -14 }}, or the amount by which seven chromatic semitones (25/24) fall short of a perfect fourth (4/3), or (4/3)/(25/24)<sup>7</sup>. The period is ~{{monzo\| -11 -3 7 }} and the generator is ~25/24. 5/4 is equated to 1 period minus 3 generators. Its color name is Sasepbiguti.		: This tempers out the [[vishnu comma]], {{monzo\| 23 6 -14 }}, or the amount by which seven chromatic semitones (25/24) fall short of a perfect fourth (4/3), or (4/3)/(25/24)<sup>7</sup>. The period is ~{{monzo\| -11 -3 7 }} and the generator is ~25/24. 5/4 is equated to 1 period minus 3 generators. Its color name is Sasepbiguti.

	; [[Unicorn family]] (P8, P4/8)		; [[Unicorn family]] (P8, P4/8)
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	: This tempers out the [[vavoom comma]], {{monzo\| -68 18 17 }}. The generator is {{nowrap\| ~16/15 {{=}} ~111.9{{c}} }}. Seventeen generators equals a twelfth (~3/1). 5/4 is equated to two octaves minus 18 generators. Its color name is Quinla-seyoti.		: This tempers out the [[vavoom comma]], {{monzo\| -68 18 17 }}. The generator is {{nowrap\| ~16/15 {{=}} ~111.9{{c}} }}. Seventeen generators equals a twelfth (~3/1). 5/4 is equated to two octaves minus 18 generators. Its color name is Quinla-seyoti.

	; [[~~Minortonic~~ family]] (P8, ccP5/17)		; [[Minortone family]] (P8, ccP5/17)
	: This tempers out the [[minortone comma]], {{monzo\| -16 35 -17 }}. The head of the family is ~~minortonic temperament~~, with a generator of a minor tone (~10/9). Seventeen generators equals a double-compound fifth (~6/1). 5/4 is equated to 35 generators minus 5 octaves. Its color name is Trila-seguti.		: This tempers out the [[minortone comma]], {{monzo\| -16 35 -17 }}. The head of the family is minortone, with a generator of a minor tone (~10/9). Seventeen generators equals a double-compound fifth (~6/1). 5/4 is equated to 35 generators minus 5 octaves. Its color name is Trila-seguti.

	; [[Maja family]] (P8, c<sup>6</sup>P4/17)		; [[Maja family]] (P8, c<sup>6</sup>P4/17)

FloraC: Update

2026-06-06T12:57:45Z

Update

← Older revision		Revision as of 12:57, 6 June 2026
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	; Sasazoti clan (P8, P5)		; Sasazoti clan (P8, P5)
	: This clan tempers out the [[leapfrog comma]], {{monzo\| 21 -15 0 1 }} (14680064/14348907). It equates 7/6 to two apotomes and 7/4 to double augmented fifth. This clan includes [[~~hemifamity~~ temperaments #Leapday\|leapday]], [[sensamagic clan #Leapweek\|leapweek]] and [[diaschismic family #Srutal\|srutal]].		: This clan tempers out the [[leapfrog comma]], {{monzo\| 21 -15 0 1 }} (14680064/14348907). It equates 7/6 to two apotomes and 7/4 to double augmented fifth. This clan includes [[aberschismic temperaments #Leapday\|leapday]], [[sensamagic clan #Leapweek\|leapweek]] and [[diaschismic family #Srutal\|srutal]].

	; Laruruti clan (P8/2, P5)		; Laruruti clan (P8/2, P5)
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	: This 3.5.7 clan tempers out the [[gariboh comma]] {{monzo\| 0 -2 5 -3 }} (3125/3087). The generator is ~25/21, two generators equals ~7/5, and three generators equals the classical major sixth (~5/3). Its color name is Triru-aquinyoti Noca.		: This 3.5.7 clan tempers out the [[gariboh comma]] {{monzo\| 0 -2 5 -3 }} (3125/3087). The generator is ~25/21, two generators equals ~7/5, and three generators equals the classical major sixth (~5/3). Its color name is Triru-aquinyoti Noca.

	; [[~~Mirkwai~~ clan]] (P12, cm7/5)		; [[Canopic clan]] (P12, cm7/5)
	: This 3.5.7 clan tempers out the [[~~mirkwai~~ comma]], {{monzo\| 0 3 4 -5 }} (16875/16807). The generator is ~7/5, four generators equals ~27/7, and five generators equals the classical compound minor seventh (~27/5). Its color name is Quinru-aquadyoti Noca.		: This 3.5.7 clan tempers out the [[canopic comma]], {{monzo\| 0 3 4 -5 }} (16875/16807). The generator is ~7/5, four generators equals ~27/7, and five generators equals the classical compound minor seventh (~27/5). Its color name is Quinru-aquadyoti Noca.

	; Sasepzo-atriguti Noca clan (P12, m7/7)		; Sasepzo-atriguti Noca clan (P12, m7/7)
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	: Hemimage rank-2 temperaments temper out the [[hemimage comma]], {{monzo\| 5 -7 -1 3 }} (10976/10935). Its color name is Satrizo-aguti.		: Hemimage rank-2 temperaments temper out the [[hemimage comma]], {{monzo\| 5 -7 -1 3 }} (10976/10935). Its color name is Satrizo-aguti.

	; [[~~Hemifamity~~ temperaments]]		; [[Aberschismic temperaments]]
	: ~~Hemifamity~~ rank-2 temperaments temper out the [[~~hemifamity comma~~]], {{monzo\| 10 -6 1 -1 }} (5120/5103). Its color name is Saruyoti.		: Aberschismic rank-2 temperaments temper out the [[aberschisma]], {{monzo\| 10 -6 1 -1 }} (5120/5103). Its color name is Saruyoti.

	; [[Parkleiness temperaments]]		; [[Parkleiness temperaments]]
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	: These temper out the nuwell comma, {{monzo\| 1 5 1 -4 }} (2430/2401). In the pergen, {{nowrap\| ^1 {{=}} ~64/63 }}. Its color name is Quadru-ayoti.		: These temper out the nuwell comma, {{monzo\| 1 5 1 -4 }} (2430/2401). In the pergen, {{nowrap\| ^1 {{=}} ~64/63 }}. Its color name is Quadru-ayoti.

	; [[~~Ragisma~~ family]] (P8, P5, ^1)		; [[Ragismic family]] (P8, P5, ^1)
	: The 7-limit rank-3 microtemperament which tempers out the ragisma, {{monzo\| -1 -7 4 1 }} (4375/4374), extends to various higher-limit rank-3 temperaments such as thor. These are not by any means all microtemperaments, but those which are not highly accurate are probably best discussed under another heading. In the pergen, {{nowrap\| ^1 {{=}} ~81/80 }}. Its color name is Zoquadyoti.		: The 7-limit rank-3 microtemperament which tempers out the ragisma, {{monzo\| -1 -7 4 1 }} (4375/4374), extends to various higher-limit rank-3 temperaments such as thor. These are not by any means all microtemperaments, but those which are not highly accurate are probably best discussed under another heading. In the pergen, {{nowrap\| ^1 {{=}} ~81/80 }}. Its color name is Zoquadyoti.

	; [[~~Hemifamity~~ family]] (P8, P5, ^1)		; [[Aberschismic family]] (P8, P5, ^1)
	: The ~~hemifamity~~ family of rank-3 temperaments tempers out the ~~hemifamity comma~~, {{monzo\| 10 -6 1 -1 }} (5120/5103), which divides 10/7 into three 9/8's. In the pergen, {{nowrap\| ^1 {{=}} ~81/80 }}. Its color name is Saruyoti.		: The aberschismic family of rank-3 temperaments tempers out the aberschisma, {{monzo\| 10 -6 1 -1 }} (5120/5103), which divides 10/7 into three 9/8's. In the pergen, {{nowrap\| ^1 {{=}} ~81/80 }}. Its color name is Saruyoti.

	; [[Horwell family]] (P8, P5, ^1)		; [[Horwell family]] (P8, P5, ^1)
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	: The dimcomp family of rank-3 temperaments tempers out the dimcomp comma, {{monzo\| -1 -4 8 -4 }} (390625/388962). In the pergen, the 1/4-octave period is ~25/21, and {{nowrap\| ^1 {{=}} ~81/80 }}. Its color name is Quadruyoyoti.		: The dimcomp family of rank-3 temperaments tempers out the dimcomp comma, {{monzo\| -1 -4 8 -4 }} (390625/388962). In the pergen, the 1/4-octave period is ~25/21, and {{nowrap\| ^1 {{=}} ~81/80 }}. Its color name is Quadruyoyoti.

	; [[~~Mirkwai~~ family]] (P8, P5, c^M7/4)		; [[Canopic family]] (P8, P5, c^M7/4)
	: The ~~mirkwai~~ family of rank-3 temperaments tempers out the ~~mirkwai~~ comma, {{monzo\| 0 3 4 -5 }} (16875/16807). Four ~7/5 generators equal the pergen's compound upmajor seventh of ~27/7. Its color name is Quinru-aquadyoti.		: The canopic family of rank-3 temperaments tempers out the canopic comma, {{monzo\| 0 3 4 -5 }} (16875/16807). Four ~7/5 generators equal the pergen's compound upmajor seventh of ~27/7. Its color name is Quinru-aquadyoti.

	=== Temperaments defined by an 11-limit comma ===		=== Temperaments defined by an 11-limit comma ===

Xenllium: /* Miscellaneous other temperaments */

2026-01-31T16:14:26Z

Miscellaneous other temperaments

← Older revision		Revision as of 16:14, 31 January 2026
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	; [[Miscellaneous 5-limit temperaments]]		; [[Miscellaneous 5-limit temperaments]]
	: High in badness, but worth cataloging for one reason or another.		: High in badness, but worth cataloging for one reason or another.

			; [[Miscellaneous 7-limit temperaments]]
			: Various rank-3 temperaments which are high in badness.

	; [[Low harmonic entropy linear temperaments]]		; [[Low harmonic entropy linear temperaments]]

Xenllium: /* Temperaments defined by an 11-limit comma */

2026-01-31T14:44:35Z

Temperaments defined by an 11-limit comma

← Older revision		Revision as of 14:44, 31 January 2026
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	; [[Moctdelismic clan]]		; [[Moctdelismic clan]]
	: These temper out the [[moctdelisma]], {{monzo\| -2 0 3 -3 1 }} (1375/1372). To be a rank-3 temperament, either an additional comma must vanish or the prime subgroup must omit prime 3. Thus no assumptions can be made about the pergen. Its color name is Lotriruyoti.		: These temper out the [[moctdelisma]], {{monzo\| -2 0 3 -3 1 }} (1375/1372). To be a rank-3 temperament, either an additional comma must vanish or the prime subgroup must omit prime 3. Thus no assumptions can be made about the pergen. Its color name is Lotriruyoti.

			; [[Wizardharry clan]] (P8, P4/3, ^1)
			: These temper out the [[4000/3993\|wizardharry comma]], {{monzo\| 5 -1 3 0 -3 }} (4000/3993), and split the fourth in three. In the pergen, ^1 is either ~33/32 or ~729/704. Its color name is Triluyoti.

	; [[Semicanousmic clan]] (P8, P5, ^1)		; [[Semicanousmic clan]] (P8, P5, ^1)