Tour of regular temperaments - Revision history

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

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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

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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

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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

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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)

Xenllium: /* Temperaments defined by a 2.3.5.7 comma */

2026-01-31T14:33:20Z

Temperaments defined by a 2.3.5.7 comma

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	; Compass temperaments		; Compass temperaments
	: Compass rank-2 temperaments temper out the [[compass comma]], {{monzo\| -6 -2 10 -5 }} (9765625/9680832). Its color name is Quinruyoyoti.		: Compass rank-2 temperaments temper out the [[compass comma]], {{monzo\| -6 -2 10 -5 }} (9765625/9680832). Its color name is Quinruyoyoti.

			; [[Sensibeta temperaments]]
			: Sensibeta rank-2 temperaments temper out the [[sensibeta comma]], {{monzo\| -1 -12 5 3 }} (1071875/1062882). Its color name is Satrizo-aquinyoti.

	; Trimyna temperaments		; Trimyna temperaments
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	; [[Mistismic temperaments]]		; [[Mistismic temperaments]]
	: Mistismic rank-2 temperaments temper out the [[mistisma]], {{monzo\| 16 -6 -4 1 }} (458752/455625). Its color name is Sazoquadguti.		: Mistismic rank-2 temperaments temper out the [[mistisma]], {{monzo\| 16 -6 -4 1 }} (458752/455625). Its color name is Sazoquadguti.

			; [[Bronzismic temperaments]]
			: Bronzismic rank-2 temperaments temper out the [[bronzisma]], {{monzo\| 21 -5 -2 -3 }} (2097152/2083725). Its color name is Satriru-aguguti.

	; [[Varunismic temperaments]]		; [[Varunismic temperaments]]

Xenllium: /* Rank-2 temperaments */

2026-01-18T02:13:19Z

Rank-2 temperaments

← Older revision		Revision as of 02:13, 18 January 2026
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	: This clan tempers out the [[bleu comma]], {{monzo\| 3 7 0 -5 }} (17496/16807). The ~54/49 generator is about 139{{c}}. Two of them equal ~7/6, three equal ~9/7, five equal ~3/2, and seven equal ~7/4.		: This clan tempers out the [[bleu comma]], {{monzo\| 3 7 0 -5 }} (17496/16807). The ~54/49 generator is about 139{{c}}. Two of them equal ~7/6, three equal ~9/7, five equal ~3/2, and seven equal ~7/4.

	; Septimagic clan (P8, P12/5)		; [[Septimagic clan]] (P8, P12/5)
	: This clan tempers out the [[septimagic comma]], {{monzo\| 5 -12 0 5 }} (537824/531441). Its generator is {{nowrap\| ~243/196 {{=}} ~380{{c}} }}. Five generators makes ~3/1. 7/4 is equated to 12 generators minus 3 octaves. An obvious 5-limit interpretation of the generator is 5/4, leading to the [[magic]] temperament, which is in the magic family. Its color name is Saquinzoti.		: This clan tempers out the [[septimagic comma]], {{monzo\| 5 -12 0 5 }} (537824/531441). Its generator is {{nowrap\| ~243/196 {{=}} ~380{{c}} }}. Five generators makes ~3/1. 7/4 is equated to 12 generators minus 3 octaves. An obvious 5-limit interpretation of the generator is 5/4, leading to the [[magic]] temperament, which is in the magic family. Its color name is Saquinzoti.

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	: This 2.3.11 clan tempers out the [[nexus comma]] {{monzo\| -16 -3 0 0 6 }}. Its 1/3-octave period is ~121/96 and its least-cents generator is ~12/11. A period plus a generator equals ~11/8. Six of these generators equals ~27/16. A period minus a generator equals ~1331/1152 or ~1536/1331. Two of these alternative generators equals ~4/3. Its color name is Tribiloti.		: This 2.3.11 clan tempers out the [[nexus comma]] {{monzo\| -16 -3 0 0 6 }}. Its 1/3-octave period is ~121/96 and its least-cents generator is ~12/11. A period plus a generator equals ~11/8. Six of these generators equals ~27/16. A period minus a generator equals ~1331/1152 or ~1536/1331. Two of these alternative generators equals ~4/3. Its color name is Tribiloti.

	; Alphaxenic ~~or Laquadloti~~ clan (P8/2, M2/4)		; Alphaxenic clan (P8/2, M2/4)
	: This 2.3.11 clan tempers out the [[Alpharabian comma]] {{monzo\| -17 2 0 0 4 }}. Its half-octave period is ~363/256, and its generator is ~33/32. Four generators equals ~9/8. 3/2 is equated to a period plus 2 generators, and 11/8 is equated to a period minus a generator. This clan includes a strong extension to the comic or Saquadyobiti temperament, which is in the jubilismic clan. Its color name is Laquadloti.		: This 2.3.11 clan tempers out the [[Alpharabian comma]] {{monzo\| -17 2 0 0 4 }}. Its half-octave period is ~363/256, and its generator is ~33/32. Four generators equals ~9/8. 3/2 is equated to a period plus 2 generators, and 11/8 is equated to a period minus a generator. This clan includes a strong extension to the comic or Saquadyobiti temperament, which is in the jubilismic clan. Its color name is Laquadloti.

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	: This clan tempers out the [[vorwell comma]] (named for being tempered in [[septimal vulture]] and [[orwell]]), {{monzo\| 27 0 -8 -3 }} (134217728/133984375). The generator is {{nowrap\| ~1024/875 {{=}} ~272{{c}} }}. Three generators equals ~8/5 and eight of them equals ~7/2. Its color name is Sasatriru-aquadbiguti Nowa.		: This clan tempers out the [[vorwell comma]] (named for being tempered in [[septimal vulture]] and [[orwell]]), {{monzo\| 27 0 -8 -3 }} (134217728/133984375). The generator is {{nowrap\| ~1024/875 {{=}} ~272{{c}} }}. Three generators equals ~8/5 and eight of them equals ~7/2. Its color name is Sasatriru-aquadbiguti Nowa.

	; ~~Quinzo-atriyoti Nowa~~ clan (P8, M3/5)		; Rainy clan (P8, M3/5)
	: This clan tempers out the [[rainy comma]], {{monzo\| -21 0 3 5 }} (2100875/2097152). The generator is {{nowrap\| ~256/245 {{=}} ~77{{c}} }}. Three generators equals ~8/7 and five of them equals the classic major third (~5/4).		: This clan tempers out the [[rainy comma]], {{monzo\| -21 0 3 5 }} (2100875/2097152). The generator is {{nowrap\| ~256/245 {{=}} ~77{{c}} }}. Three generators equals ~8/7 and five of them equals the classic major third (~5/4). Its color name is Quinzo-atriyoti Nowa.

	; [[Llywelynsmic clan]] (P8, cM3/7)		; [[Llywelynsmic clan]] (P8, cM3/7)
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	; [[Quince clan]] (P8, m6/7)		; [[Quince clan]] (P8, m6/7)
	: This clan tempers out the [[quince comma]], {{monzo\| -15 0 -2 7 }} (823543/819200). The generator is {{nowrap\| ~343/320 {{=}} ~116{{c}} }}. Two generators equals ~8/7, five generators equals ~7/5, and seven generators equals the classical minor sixth ~8/5. An obvious 5-limit interpretation of the generator is ~16/15, leading to the [[miracle]] temperament, which is in the gamelismic clan. Its color name is Lasepzo-aguguti Nowa.		: This clan tempers out the [[quince comma]], {{monzo\| -15 0 -2 7 }} (823543/819200). The generator is {{nowrap\| ~343/320 {{=}} ~116{{c}} }}. Two generators equals ~8/7, five generators equals ~7/5, and seven generators equals the classical minor sixth ~8/5. An obvious 5-limit interpretation of the generator is ~16/15, leading to the [[miracle]] temperament, which is in the gamelismic clan. Its color name is Lasepzo-aguguti Nowa.

			; Exodia clan (P8, ccM3/8)
			: This clan tempers out the [[exodia comma]], {{monzo\| -48 0 11 8 }}. The generator is {{nowrap\| ~262144/214375 {{=}} ~348{{c}} }}. Eight generators equals ~5/1, 11 of them equals ~64/7, and 19 of them equals ~320/7 (five octaves above ~10/7). Its color name is Trila-quadbizo-aleyoti Nowa.

	; Slither clan (P8, ccm6/9)		; Slither clan (P8, ccm6/9)

FloraC at 10:50, 10 January 2026

2026-01-10T10:50:47Z

← Older revision		Revision as of 10:50, 10 January 2026
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	: These temper out the [[pentacircle comma]], {{monzo\| 7 -4 0 1 -1 }} (896/891). The interval between 11/8 and 7/4 is equated to 81/64. Since that is a 3-limit interval, every 2.3.11 interval is equated to a 2.3.7 interval and vice versa, and both the pergen and the lattice are identical to that of either 2.3.7 JI or 2.3.11 JI. In the pergen, ^1 is either ~64/63 or ~33/32 or ~729/704. Its color name is Saluzoti.		: These temper out the [[pentacircle comma]], {{monzo\| 7 -4 0 1 -1 }} (896/891). The interval between 11/8 and 7/4 is equated to 81/64. Since that is a 3-limit interval, every 2.3.11 interval is equated to a 2.3.7 interval and vice versa, and both the pergen and the lattice are identical to that of either 2.3.7 JI or 2.3.11 JI. In the pergen, ^1 is either ~64/63 or ~33/32 or ~729/704. Its color name is Saluzoti.

	; [[~~Moctdel~~ clan]]		; [[Moctdelismic clan]]
	: These temper out the [[~~moctdel comma~~]], {{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.

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

Xenllium at 23:24, 9 January 2026

2026-01-09T23:24:26Z

← Older revision		Revision as of 23:24, 9 January 2026
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	: This clan tempers out the [[bleu comma]], {{monzo\| 3 7 0 -5 }} (17496/16807). The ~54/49 generator is about 139{{c}}. Two of them equal ~7/6, three equal ~9/7, five equal ~3/2, and seven equal ~7/4.		: This clan tempers out the [[bleu comma]], {{monzo\| 3 7 0 -5 }} (17496/16807). The ~54/49 generator is about 139{{c}}. Two of them equal ~7/6, three equal ~9/7, five equal ~3/2, and seven equal ~7/4.

	; ~~Saquinzoti~~ clan (P8, P12/5)		; Septimagic clan (P8, P12/5)
	: This clan tempers out the ~~Saquinzo~~ comma, {{monzo\| 5 -12 0 5 }} (537824/531441). Its generator is {{nowrap\| ~243/196 {{=}} ~380{{c}} }}. Five generators makes ~3/1. 7/4 is equated to 12 generators minus 3 octaves. An obvious 5-limit interpretation of the generator is 5/4, leading to the [[magic]] temperament, which is in the magic family.		: This clan tempers out the [[septimagic comma]], {{monzo\| 5 -12 0 5 }} (537824/531441). Its generator is {{nowrap\| ~243/196 {{=}} ~380{{c}} }}. Five generators makes ~3/1. 7/4 is equated to 12 generators minus 3 octaves. An obvious 5-limit interpretation of the generator is 5/4, leading to the [[magic]] temperament, which is in the magic family. Its color name is Saquinzoti.

	; Lasepzoti clan (P8, P11/7)		; Lasepzoti clan (P8, P11/7)
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	; [[Pentacircle clan]] (P8, P5, ^1)		; [[Pentacircle clan]] (P8, P5, ^1)
	: These temper out the [[pentacircle comma]], {{monzo\| 7 -4 0 1 -1 }} (896/891). The interval between 11/8 and 7/4 is equated to 81/64. Since that is a 3-limit interval, every 2.3.11 interval is equated to a 2.3.7 interval and vice versa, and both the pergen and the lattice are identical to that of either 2.3.7 JI or 2.3.11 JI. In the pergen, ^1 is either ~64/63 or ~33/32 or ~729/704. Its color name is Saluzoti.		: These temper out the [[pentacircle comma]], {{monzo\| 7 -4 0 1 -1 }} (896/891). The interval between 11/8 and 7/4 is equated to 81/64. Since that is a 3-limit interval, every 2.3.11 interval is equated to a 2.3.7 interval and vice versa, and both the pergen and the lattice are identical to that of either 2.3.7 JI or 2.3.11 JI. In the pergen, ^1 is either ~64/63 or ~33/32 or ~729/704. Its color name is Saluzoti.

			; [[Moctdel clan]]
			: These temper out the [[moctdel comma]], {{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.

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