Tour of regular temperaments: Difference between revisions

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These are families defined by a ya or 5-limit comma. As we go up in rank two, the various 5-limit temperaments often break up as families of related temperaments, depending on how higher primes are mapped (or equivalently, on which higher limit commas are introduced.) The same comment applies to 7-limit temperaments and rank three, etc. Members of families and their relationships can be classified by the [[Normal lists|normal comma list]] of the various temperaments. Families include weak extensions as well as strong, in other words, the [[pergen]] shown here may change.

; [[Meantone family|Meantone or Gu family]] (P8, P5)

; [[Meantone family|Meantone or Guti family]] (P8, P5)

: The meantone family tempers out [[81/80]], also called the syntonic comma. This comma manifests as the difference between a stack of four 3/2's (81/16, or (3/2)^4) and 5/1 harmonic (5/1, or 80/16). It is so named because it splits the major third into two equal sized tones, signifying that 9/8 and 10/9 are equated, with each tone being sized as a mean of the two tones. It has a flattened fifth or sharpened fourth as generator. Some meantone tunings are [[12edo|12]], [[19edo|19]], [[31edo|31]], [[43edo|43]], [[50edo|50]], [[55edo|55]] and [[81edo|81]] EDOs. Aside from tuning meantone as a subset of some equal division of the octave, some common rank-2 tunings include having a generator of 3/2 flattened by 1/3, 2/7, 1/4, 1/5 or 1/6 of the syntonic comma.

; [[Schismatic family|Schismatic or ~~Layo~~ family]] (P8, P5)

; [[Schismatic family|Schismatic or Layoti family]] (P8, P5)

: The schismatic family tempers out the schisma of {{nowrap|{{Monzo| -15 8 1 }} {{=}} [[32805/32768]]}}, which is the amount by which the Pythagorean comma exceeds the syntonic comma. The 5-limit version of the temperament is a [[microtemperament]] which flattens the fifth by a fraction of a schisma, but other members of the family are less accurate. As a 5-limit system, it is far more accurate than meantone but still with manageable complexity; whereas meantone equates four 3/2's with 5/1, schismatic equates eight 4/3's with 10/1, so that the Pythagorean diminished fourth of 8192/6561 is equated with 5/4. Tunings include [[12edo|12]], [[29edo|29]], [[41edo|41]], [[53edo|53]], and [[118edo|118]] EDOs.

; [[Pelogic family|Pelogic or ~~Layobi~~ family]] (P8, P5)

; [[Pelogic family|Pelogic or Layobiti family]] (P8, P5)

: This tempers out the pelogic comma, {{nowrap|{{Monzo| -7 3 1 }} {{=}} [[135/128]]}}, also known as the major chroma or major limma. These temperaments are notable for having 3/2's tuned so flat that four of them, when stacked together, leads you to 6/5 + 2 octaves instead of 5/4 + 2 octaves, and one consequence of this is that it generates [[2L 5s]] "anti-diatonic" scales. 5/4 is equated to 3 fourths minus 1 octave. Mavila and Armodue are some of the most notable temperaments associated with the pelogic comma. Tunings include [[9edo|9]], [[16edo|16]], [[23edo|23]], and [[25edo|25]] EDOs.

; [[Father family|Father or ~~Gubi~~ family]] (P8, P5)

; [[Father family|Father or Gubiti family]] (P8, P5)

: This tempers out [[16/15]], the just diatonic semitone, and equates 5/4 with 4/3.

; [[Diaschismic family|Diaschismic or ~~Sagugu~~ family]] (P8/2, P5)

; [[Diaschismic family|Diaschismic or Saguguti family]] (P8/2, P5)

: The diaschismic family tempers out the [[diaschisma]], {{nowrap|{{Monzo| 11 -4 -2 }} {{=}} 2048/2025}}, such that two classic major thirds and a [[81/64|Pythagorean major third]] stack to an octave (i.e. {{nowrap|5/4 × 5/4 × 81/64 → 2/1}}). It has a half-octave period of an approximate 45/32 or 64/45, and its generator is an approximate 3/2. 5/4 is equated to 3 periods minus 2 fifths. The major 2nd ~9/8 is divided in half, with each half equated to ~16/15. Diaschismic tunings include [[12edo|12]], [[22edo|22]], [[34edo|34]], [[46edo|46]], [[56edo|56]], [[58edo|58]] and [[80edo|80]] EDOs. An obvious 7-limit interpretation of the period is 7/5, which makes [[pajara]] temperament, where the intervals 50/49 and 64/63 are tempered out. [[22edo|22EDO]] is an excellent pajara tuning.

; [[Bug family|Bug or ~~Gugu~~ family]] (P8, P4/2)

; [[Bug family|Bug or Guguti family]] (P8, P4/2)

: This low-accuracy family of temperaments tempers out [[27/25]], the large limma or bug comma. The generator is an approximate 6/5 or {{nowrap|10/9 {{=}} ~250¢}}, two of which make ~4/3. 5/4 is equated to 1 octave minus 3 generators. An obvious 7-limit interpretation of the generator is 7/6, which makes Slendro aka Semaphore or ~~Zozo~~.

: This low-accuracy family of temperaments tempers out [[27/25]], the large limma or bug comma. The generator is an approximate 6/5 or {{nowrap|10/9 {{=}} ~250¢}}, two of which make ~4/3. 5/4 is equated to 1 octave minus 3 generators. An obvious 7-limit interpretation of the generator is 7/6, which makes Slendro aka Semaphore or Zozoti.

; [[Immunity family|Immunity or Sasa-~~yoyo~~ family]] (P8, P4/2)

; [[Immunity family|Immunity or Sasa-yoyoti family]] (P8, P4/2)

: This tempers out the immunity comma, {{Monzo| 16 -13 2 }} (1638400/1594323). Its generator is {{nowrap|~729/640 {{=}} ~247¢}}, two of which make ~4/3. 5/4 is equated to 3 octaves minus 13 generators. An obvious 7-limit interpretation of the generator is 7/6, which leads to Slendro aka Semaphore or ~~Zozo~~.

: This tempers out the immunity comma, {{Monzo| 16 -13 2 }} (1638400/1594323). Its generator is {{nowrap|~729/640 {{=}} ~247¢}}, two of which make ~4/3. 5/4 is equated to 3 octaves minus 13 generators. An obvious 7-limit interpretation of the generator is 7/6, which leads to Slendro aka Semaphore or Zozoti.

; [[Dicot family|Dicot or ~~Yoyo~~ family]] (P8, P5/2)

; [[Dicot family|Dicot or Yoyoti family]] (P8, P5/2)

: The dicot family is a low-accuracy family of temperaments which temper out the chromatic semitone, [[25/24]] (the difference between 5/4 and 6/5, or alternatively the difference between two 5/4's and 3/2 OR two 6/5's and 3/2). This temperament hence equates major and minor thirds, evening them out into a neutral-sized 3rd of ~350¢ that is taken to approximate both. [[7edo|7EDO]] makes for a "good" dicot tuning, although it is questionable whether this temperament bears any actual resemblance to 5-limit harmony. Two of the "neutral" dicot 3rds span a 3/2. Tunings include 7EDO, [[10edo|10EDO]], and [[17edo|17EDO]]. An obvious 2.3.11 interpretation of the generator is ~11/9, which leads to Rastmic aka Neutral or ~~Lulu~~.

: The dicot family is a low-accuracy family of temperaments which temper out the chromatic semitone, [[25/24]] (the difference between 5/4 and 6/5, or alternatively the difference between two 5/4's and 3/2 OR two 6/5's and 3/2). This temperament hence equates major and minor thirds, evening them out into a neutral-sized 3rd of ~350¢ that is taken to approximate both. [[7edo|7EDO]] makes for a "good" dicot tuning, although it is questionable whether this temperament bears any actual resemblance to 5-limit harmony. Two of the "neutral" dicot 3rds span a 3/2. Tunings include 7EDO, [[10edo|10EDO]], and [[17edo|17EDO]]. An obvious 2.3.11 interpretation of the generator is ~11/9, which leads to Rastmic aka Neutral or Luluti.

; [[Augmented family|Augmented or ~~Trigu~~ family]] (P8/3, P5)

; [[Augmented family|Augmented or Triguti family]] (P8/3, P5)

: The augmented family tempers out the diesis of {{nowrap|{{Monzo| 7 0 -3 }} {{=}} [[128/125]]}}, the difference between three 5/4 major thirds and a 2/1 octave, and so identifies the major third with the third-octave. Hence it has the same 400-cent 5/4-approximations as [[12edo|12EDO]], which is an excellent tuning for augmented. It is the temperament that results in what is commonly called the "augmented scale" ([[3L 3s]]) in common 12-based music theory, as well as what is commonly called "[http://www.tcherepnin.com/alex/basic_elem1.htm#9step Tcherepnin's scale]" ([[3L 6s]]).

; [[Misty family|Misty or Sasa-~~trigu~~ family]] (P8/3, P5)

; [[Misty family|Misty or Sasa-triguti family]] (P8/3, P5)

: The misty family tempers out the [[misty comma]] of {{monzo| 26 -12 -3 }}, the difference between the [[Pythagorean comma]] and a stack of three [[Schisma|schismas]]. The period is ~512/405 and the generator is ~3/2 (or alternatively ~135/128). 5/4 is equated to 8 periods minus 4 fifths, thus 5/4 is split into 4 equal parts, each 2 periods minus a fifth.

; [[Porcupine family|Porcupine or ~~Triyo~~ family]] (P8, P4/3)

; [[Porcupine family|Porcupine or Triyoti family]] (P8, P4/3)

: The porcupine family tempers out {{nowrap|{{Monzo| 1 -5 3 }} {{=}} [[250/243]]}}, the difference between three 10/9's (1000/729) and 4/3, known as the maximal diesis or porcupine comma. It subdivides the fourth into three equal parts, each taken as an approximated 10/9, of which two approximate 6/5. It also manifests itself as the difference between three 6/5's and 16/9, as the difference between 10/9 and 27/25, and as the difference between 81/80 and 25/24. 5/4 is equated to 1 octave minus 5 generators. Some porcupine temperaments include [[15edo|15]], [[22edo|22]], [[37edo|37]], and [[59edo|59]] EDOs. An important 7-limit extension also tempers out 64/63.

; [[Tricot family|Tricot or Quadsa-~~triyo~~ family]] (P8, P11/3)

; [[Tricot family|Tricot or Quadsa-triyoti family]] (P8, P11/3)

: The tricot family tempers out the [[Tricot|tricot comma]], {{Monzo| 39 -29 3 }}. The generator is {{nowrap|~59049/40960 {{=}} {{monzo| -13 10 -1 }} {{=}} 633¢}}, or its octave inverse {{nowrap|~81920/59049 {{=}} 567¢}}. Three of the latter generators equals a compound 4th of ~8/3. 5/4 is equated to 14 octaves minus 29 of these generators. An obvious 7-limit interpretation of the generator is {{nowrap|81/56 {{=}} 639¢}}, a much simpler ratio which leads to the [[Tour of Regular Temperaments#~~Latriru~~ clan (P8, P11/3)|~~Latriru~~ clan]]. An obvious 13-limit interpretation is {{nowrap|13/9 {{=}} 637¢}}, an even simpler ratio implying the [[Tour of Regular Temperaments #~~Satritho~~ clan (P8, P11/3)|~~Satritho~~ clan]].

: The tricot family tempers out the [[Tricot|tricot comma]], {{Monzo| 39 -29 3 }}. The generator is {{nowrap|~59049/40960 {{=}} {{monzo| -13 10 -1 }} {{=}} 633¢}}, or its octave inverse {{nowrap|~81920/59049 {{=}} 567¢}}. Three of the latter generators equals a compound 4th of ~8/3. 5/4 is equated to 14 octaves minus 29 of these generators. An obvious 7-limit interpretation of the generator is {{nowrap|81/56 {{=}} 639¢}}, a much simpler ratio which leads to the [[Tour of Regular Temperaments#Latriruti clan (P8, P11/3)|Latriruti clan]]. An obvious 13-limit interpretation is {{nowrap|13/9 {{=}} 637¢}}, an even simpler ratio implying the [[Tour of Regular Temperaments #Satrithoti clan (P8, P11/3)|Satrithoti clan]].

; [[Dimipent family|Dimipent or ~~Quadgu~~ family]] (P8/4, P5)

; [[Dimipent family|Dimipent or Quadguti family]] (P8/4, P5)

: The dimipent (or diminished) family tempers out the major diesis or diminished comma, {{Monzo| 3 4 -4 }} or [[648/625]], the amount by which four 6/5 minor thirds exceed an octave, and so identifies the minor third with the quarter-octave. Hence it has the same 300-cent 6/5-approximations as [[12edo|12EDO]]. 5/4 is equated to 1 fifth minus 1 period.

; [[Undim family|Undim or Trisa-~~quadgu~~ family]] (P8/4, P5)

; [[Undim family|Undim or Trisa-quadguti family]] (P8/4, P5)

: The undim family tempers out the [[undim comma]] of {{monzo| 41 -20 -4 }}, the difference between the Pythagorean comma and a stack of four schismas.

; [[Negri|Negri or ~~Laquadyo~~ family]] (P8, P4/4)

; [[Negri|Negri or Laquadyoti family]] (P8, P4/4)

: This tempers out the [[negri comma]], {{Monzo| -14 3 4 }}. Its generator is ~16/15, four of which make ~4/3. 5/4 is equated to 3 generators.

; [[Tetracot family|Tetracot or ~~Saquadyo~~ family]] (P8, P5/4)

; [[Tetracot family|Tetracot or Saquadyoti family]] (P8, P5/4)

: The tetracot family is a much higher accuracy affair than the dicot family. Instead of taking two neutral thirds to reach 3/2, it takes four minor (10/9) whole tones. Four of these exceed 3/2 by {{Monzo| 5 -9 4 }} (20000/19683), the minimal diesis or [[tetracot comma]]. 5/4 is equated to 9 generators minus an octave. [[7edo|7EDO]] can also be considered a tetracot tuning, as can [[20edo|20EDO]], [[27edo|27EDO]], [[34edo|34EDO]], and [[41edo|41EDO]].

; [[Smate family|Smate or ~~Saquadgu~~ family]] (P8, P11/4)

; [[Smate family|Smate or Saquadguti family]] (P8, P11/4)

: This tempers out the symbolic comma, {{nowrap|{{Monzo| 11 -1 -4 }} {{=}} 2048/1875}}. Its generator is {{nowrap|~5/4 {{=}} ~421¢}}, four of which make ~8/3.

; [[Vulture family|Vulture or Sasa-~~quadyo~~ family]] (P8, P12/4)

; [[Vulture family|Vulture or Sasa-quadyoti family]] (P8, P12/4)

: This tempers out the [[vulture comma]], {{Monzo| 24 -21 4 }}. Its generator is {{nowrap|~320/243 {{=}} ~475¢}}, four of which make ~3/1. 5/4 is equated to 21 generators minus 8 octaves. An obvious 7-limit interpretation of the generator is 21/16, which makes ~~Saquadru~~.

: This tempers out the [[vulture comma]], {{Monzo| 24 -21 4 }}. Its generator is {{nowrap|~320/243 {{=}} ~475¢}}, four of which make ~3/1. 5/4 is equated to 21 generators minus 8 octaves. An obvious 7-limit interpretation of the generator is 21/16, which makes Saquadruti.

; [[Pental family|Pental or Trila-~~quingu~~ family]] (P8/5, P5)

; [[Pental family|Pental or Trila-quinguti family]] (P8/5, P5)

: This tempers out the pental comma, {{nowrap|847288609443/838860800000 {{=}} {{Monzo| -28 25 -5 }}}}. The period is ~59049/51200, and 5 periods make an octave. The generator is a 5th, or equivalently, 3/5 of an 8ve minus a 5th. This alternate generator is only about 18¢, thus the scales have a very lopsided L/s ratio. 5/4 is equated to 2/5 of an octave minus 5 of these 18¢ generators. An obvious 7-limit interpretation of the generator is 8/7, which leads to ~~Laquinzo~~.

: This tempers out the pental comma, {{nowrap|847288609443/838860800000 {{=}} {{Monzo| -28 25 -5 }}}}. The period is ~59049/51200, and 5 periods make an octave. The generator is a 5th, or equivalently, 3/5 of an 8ve minus a 5th. This alternate generator is only about 18¢, thus the scales have a very lopsided L/s ratio. 5/4 is equated to 2/5 of an octave minus 5 of these 18¢ generators. An obvious 7-limit interpretation of the generator is 8/7, which leads to Laquinzoti.

; [[Ripple family|Ripple or ~~Quingu~~ family]] (P8, P4/5)

; [[Ripple family|Ripple or Quinguti family]] (P8, P4/5)

: This tempers out the ripple comma, {{nowrap|6561/6250 {{=}} {{monzo| -1 8 -5 }}}}, which equates a stack of four [[10/9]]'s with [[8/5]], and five of them with [[16/9]]. The generator is [[27/25]], two of which equals 10/9, three of which equals [[6/5]], and five of which equals [[4/3]]. 5/4 is equated to an octave minus 8 generators. As one might expect, [[12edo|12EDO]] is about as accurate as it can be.

; [[Passion family|Passion or ~~Saquingu~~ family]] (P8, P4/5)

; [[Passion family|Passion or Saquinguti family]] (P8, P4/5)

: This tempers out the passion comma, {{nowrap|262144/253125 {{=}} {{monzo| 18 -4 -5 }}}}, which equates a stack of four [[16/15]]'s with [[5/4]], and five of them with [[4/3]].

; [[Quintaleap family|Quintaleap or Trisa-~~quingu~~ family]] (P8, P4/5)

; [[Quintaleap family|Quintaleap or Trisa-quinguti family]] (P8, P4/5)

: This tempers out the ''quintaleap'' comma, {{monzo| 37 -16 -5 }}. The generator is ~135/128, five of them gives ~4/3, and sixteen of them gives [[5/2]]. An obvious 17-limit interpretation of the generator is ~18/17, which makes ~~saquinso~~.

: This tempers out the ''quintaleap'' comma, {{monzo| 37 -16 -5 }}. The generator is ~135/128, five of them gives ~4/3, and sixteen of them gives [[5/2]]. An obvious 17-limit interpretation of the generator is ~18/17, which makes Saquinsoti.

; [[Quindromeda family|Quindromeda or Quinsa-~~quingu~~ family]] (P8, P4/5)

; [[Quindromeda family|Quindromeda or Quinsa-quinguti family]] (P8, P4/5)

: This tempers out the ''quindromeda'' comma, {{monzo| 56 -28 -5 }}. The generator is ~4428675/4194304, five of them gives ~4/3, and 28 of them gives the fifth harmonic, [[5/1]]. An obvious 17-limit interpretation of the generator is ~18/17, which makes ~~saquinso~~.

: This tempers out the ''quindromeda'' comma, {{monzo| 56 -28 -5 }}. The generator is ~4428675/4194304, five of them gives ~4/3, and 28 of them gives the fifth harmonic, [[5/1]]. An obvious 17-limit interpretation of the generator is ~18/17, which makes Saquinsoti.

; [[Amity family|Amity or ~~Saquinyo~~ family]] (P8, P11/5)

; [[Amity family|Amity or Saquinyoti family]] (P8, P11/5)

: This tempers out the [[amity comma]], {{nowrap|1600000/1594323 {{=}} {{monzo| 9 -13 5 }}}}. The generator is {{nowrap|243/200 {{=}} ~339.5¢}}, five of which make ~8/3. 5/4 is equated to 4 octaves minus 13 generators, or 2 fifths minus 3 generators. An obvious 11-limit interpretation of the generator is 11/9, which makes ~~Saquinlo~~. An obvious 13-limit interpretation of the generator is 39/32, which makes Lala-~~quintho~~.

: This tempers out the [[amity comma]], {{nowrap|1600000/1594323 {{=}} {{monzo| 9 -13 5 }}}}. The generator is {{nowrap|243/200 {{=}} ~339.5¢}}, five of which make ~8/3. 5/4 is equated to 4 octaves minus 13 generators, or 2 fifths minus 3 generators. An obvious 11-limit interpretation of the generator is 11/9, which makes Saquinloti. An obvious 13-limit interpretation of the generator is 39/32, which makes Lala-quinthoti.

; [[Magic family|Magic or ~~Laquinyo~~ family]] (P8, P12/5)

; [[Magic family|Magic or Laquinyoti family]] (P8, P12/5)

: The magic family tempers out {{Monzo| -10 -1 5 }} (3125/3072), known as the [[magic comma]] or small diesis, which is the difference between five 5/4's (3125/2048) and a 3/1. The generator is itself an approximate 5/4. The magic family includes [[16edo|16]], [[19edo|19]], [[22edo|22]], [[25edo|25]], and [[41edo|41]] EDOs among its possible tunings, with the latter being near-optimal.

; [[Fifive family|Fifive or ~~Saquinbiyo~~ family]] (P8/2, P5/5)

; [[Fifive family|Fifive or Saquinbiyoti family]] (P8/2, P5/5)

: This tempers out the fifive comma, {{nowrap|{{Monzo| -1 -14 10 }} {{=}} 9765625/9565938}}. The period is ~{{nowrap|4374/3125 {{=}} {{monzo| 1 7 -5 }}}}, two of which make an octave. The generator is ~27/25, five of which make ~3/2. 5/4 is equated to 7 generators minus 1 period.

; [[Quintosec family|Quintosec or Quadsa-~~quinbigu~~ family]] (P8/5, P5/2)

; [[Quintosec family|Quintosec or Quadsa-quinbiguti family]] (P8/5, P5/2)

: This tempers out the quintosec comma, {{nowrap|140737488355328/140126044921875 {{=}} {{monzo| 47 -15 -10 }}}}. The period is ~{{nowrap|524288/455625 {{=}} {{monzo| 19 -6 -4 }}}}, five of which equals an octave. The generator is ~16/15. A period plus a generator makes half a fifth. 5/4 is equated to 3 periods minus 3 generators. An obvious 7-limit interpretation of the period is 8/7.

; [[Trisedodge family|Trisedodge or ~~Saquintrigu~~ family]] (P8/5, P4/3)

; [[Trisedodge family|Trisedodge or Saquintriguti family]] (P8/5, P4/3)

: This tempers out the trisedodge comma, {{nowrap|30958682112/30517578125 {{=}} {{monzo| 19 10 -15 }}}}. The period is {{nowrap|~144/125 {{=}} 240¢}}. The generator is ~6/5. Six periods minus three generators equals ~4/3. 5/4 is equated to 2 generators minus 1 period. An obvious 7-limit interpretation of the period is 8/7.

; [[Ampersand|Ampersand or Lala-~~tribiyo~~ family]] (P8, P5/6)

; [[Ampersand|Ampersand or Lala-tribiyoti family]] (P8, P5/6)

: This tempers out Ampersand's comma, {{nowrap|34171875/33554432 {{=}} {{monzo| -25 7 6 }}}}. The generator is ~16/15, of which six make ~3/2. 5/4 is equated to 1 octave minus 7 generators. If the generator is also equated to ~15/14, and three generators to ~11/9, one gets the [[Miracle]] temperament.

; [[Kleismic family|Kleismic or ~~Tribiyo~~ family]] (P8, P12/6)

; [[Kleismic family|Kleismic or Tribiyoti family]] (P8, P12/6)

: The kleismic family of temperaments tempers out the [[kleisma]] {{nowrap|{{Monzo| -6 -5 6 }} {{=}} 15625/15552}}, which is the difference between six 6/5's and 3/1. It takes a slightly sharpened minor third as a generator, optimally tuned about 1.4 cents sharp. 5/4 is equated to 5 generators minus 1 octave. The kleismic family includes [[15edo|15]], [[19edo|19]], [[34edo|34]], [[49edo|49]], [[53edo|53]], [[72edo|72]], [[87edo|87]] and [[140edo|140]] EDOs among its possible tunings.

; [[Semicomma family|Orson, semicomma or ~~Lasepyo~~ family]] (P8, P12/7)

; [[Semicomma family|Orson, semicomma or Lasepyoti family]] (P8, P12/7)

: The [[semicomma]] (also known as Fokker's comma), {{nowrap|2109375/2097152 {{=}} {{monzo| -21 3 7 }}}}, is tempered out by the members of the semicomma family. Its generator is ~75/64, seven of which equals ~3/1. 5/4 is equated to 1 octave minus 3 generators. This temperament doesn't have much independent existence as a 5-limit temperament, since its generator has a natural interpretation as ~7/6, leading to [[orwell|Orwell or Sepru]] temperament.

; [[Wesley family|Wesley or ~~Lasepyobi~~ family]] (P8, ccP4/7)

; [[Wesley family|Wesley or Lasepyobiti family]] (P8, ccP4/7)

: This tempers out the wesley comma, {{nowrap|{{Monzo| -13 -2 7 }} {{=}} 78125/73728}}. The generator is {{nowrap|~125/96 {{=}} ~412¢}}. Seven generators equals a double-compound 4th of ~16/3. 5/4 is equated to 1 octave minus 2 generators. An obvious 7-limit interpretation of the generator is 9/7, leading to the ~~Lasepru~~ temperament. An obvious 3-limit interpretation of the generator is 81/64, implying [[29edo|29EDO]].

: This tempers out the wesley comma, {{nowrap|{{Monzo| -13 -2 7 }} {{=}} 78125/73728}}. The generator is {{nowrap|~125/96 {{=}} ~412¢}}. Seven generators equals a double-compound 4th of ~16/3. 5/4 is equated to 1 octave minus 2 generators. An obvious 7-limit interpretation of the generator is 9/7, leading to the Lasepruti temperament. An obvious 3-limit interpretation of the generator is 81/64, implying [[29edo|29EDO]].

; [[Sensipent family|Sensipent or ~~Sepgu~~ family]] (P8, ccP5/7)

; [[Sensipent family|Sensipent or Sepguti family]] (P8, ccP5/7)

: The sensipent (sensi) family tempers out the [[sensipent comma]], {{Monzo| 2 9 -7 }} (78732/78125), also known as the medium semicomma. Its generator is {{nowrap|~162/125 {{=}} ~443¢}}. Seven generators equals a double-compound 5th of ~6/1. 5/4 is equated to 9 generators minus 3 octaves. Tunings include [[8edo|8EDO]], [[19edo|19EDO]], [[46edo|46EDO]], and [[65edo|65EDO]]. An obvious 7-limit interpretation of the generator is 9/7, leading to the ~~Sasepzo~~ temperament.

: The sensipent (sensi) family tempers out the [[sensipent comma]], {{Monzo| 2 9 -7 }} (78732/78125), also known as the medium semicomma. Its generator is {{nowrap|~162/125 {{=}} ~443¢}}. Seven generators equals a double-compound 5th of ~6/1. 5/4 is equated to 9 generators minus 3 octaves. Tunings include [[8edo|8EDO]], [[19edo|19EDO]], [[46edo|46EDO]], and [[65edo|65EDO]]. An obvious 7-limit interpretation of the generator is 9/7, leading to the Sasepzoti temperament.

; [[Vishnuzmic family|Vishnuzmic or ~~Sasepbigu~~ family]] (P8/2, P4/7)

; [[Vishnuzmic family|Vishnuzmic or Sasepbiguti 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)^7. The period is ~{{Monzo| -11 -3 7 }} and the generator is ~25/24. 5/4 is equated to 1 period minus 3 generators.

; [[Unicorn family|Unicorn or ~~Laquadbigu~~ family]] (P8, P4/8)

; [[Unicorn family|Unicorn or Laquadbiguti family]] (P8, P4/8)

: This tempers out the unicorn comma, {{nowrap|1594323/1562500 {{=}} {{monzo| -2 13 -8 }}}}. The generator is {{nowrap|~250/243 {{=}} ~62¢}} and eight of them equal ~4/3.

; [[Würschmidt family|Würschmidt or ~~Saquadbigu~~ family]] (P8, ccP5/8)

; [[Würschmidt family|Würschmidt or Saquadbiguti family]] (P8, ccP5/8)

: The würschmidt (or wuerschmidt) family tempers out the {{monzo|[Würschmidt comma]], {{nowrap|393216/390625 {{=}} {{monzo| 17 1 -8 }}}}. Würschmidt itself has a generator of a major third, eight of which give a 6/1 (the 6th harmonic, or a double-compound perfect 5th); that is, {{nowrap|(5/4)<sup}}8 * (393216/390625) {{=}} 6}}. It tends to generate the same MOSs as [[Magic_family|magic temperament]], but is tuned slightly more accurately. Both [[31edo|31EDO]] and [[34edo|34EDO]] can be used as würschmidt tunings, as can [[65edo|65EDO]], which is quite accurate.

; [[Escapade family|Escapade or Sasa-~~tritrigu~~ family]] (P8, P4/9)

; [[Escapade family|Escapade or Sasa-tritriguti family]] (P8, P4/9)

: This tempers out the [[escapade comma]], {{Monzo| 32 -7 -9 }}, which is the difference between nine just major thirds and seven just fourths. The generator is {{nowrap|{{Monzo| -14 3 4 }} {{=}} ~55¢}} and nine of them equal ~4/3. Seven of them equal ~5/4, thus two of them equal ~16/15. An obvious 11-limit interpretation of the generator is 33/32, leading to the Trisa-~~tritrilu~~ temperament.

: This tempers out the [[escapade comma]], {{Monzo| 32 -7 -9 }}, which is the difference between nine just major thirds and seven just fourths. The generator is {{nowrap|{{Monzo| -14 3 4 }} {{=}} ~55¢}} and nine of them equal ~4/3. Seven of them equal ~5/4, thus two of them equal ~16/15. An obvious 11-limit interpretation of the generator is 33/32, leading to the Trisa-tritriluti temperament.

; [[Shibboleth family|Shibboleth or ~~Tritriyo~~ family]] (P8, ccP4/9)

; [[Shibboleth family|Shibboleth or Tritriyoti family]] (P8, ccP4/9)

: This tempers out the shibboleth comma, {{nowrap|{{Monzo| -5 -10 9 }} {{=}} 1953125/1889568}}. Nine generators of ~6/5 equal a double compound 4th of ~16/3. 5/4 is equated to 3 octaves minus 10 generators.

; [[Mabila family|Mabila or Sasa-~~quinbigu~~ family]] (P8, c4P4/10)

; [[Mabila family|Mabila or Sasa-quinbiguti family]] (P8, c4P4/10)

: The mabila family tempers out the mabila comma, {{nowrap|{{Monzo| 28 -3 -10 }} {{=}} 268435456/263671875}}. The generator is {{nowrap|~512/375 {{=}} ~530¢}}, three generators equals ~5/2 and ten of them equals a quadruple-compound 4th of ~64/3. An obvious 11-limit interpretation of the generator is ~15/11.

; [[Sycamore family|Sycamore or ~~Laleyo~~ family]] (P8, P5/11)

; [[Sycamore family|Sycamore or Laleyoti family]] (P8, P5/11)

: The sycamore family tempers out the sycamore comma, {{nowrap|{{Monzo| -16 -6 11 }} {{=}} 48828125/47775744}}, which is the amount by which five stacked chromatic semitones, 25/24, exceed 6/5, and hence also the amount six exceeds 5/4. Eleven of these generators equals ~3/2.

; [[Quartonic family|Quartonic or ~~Saleyo~~ family]] (P8, P4/11)

; [[Quartonic family|Quartonic or Saleyoti family]] (P8, P4/11)

: The quartonic family tempers out the quartonic comma, {{nowrap|{{Monzo| 3 -18 11 }} {{=}} 390625000/387420489}}. The generator is {{nowrap|~250/243 {{=}} ~45¢}}, seven generators equals ~6/5, and eleven generators equals ~4/3. An obvious 7-limit interpretation of the generator is ~36/35.

; [[Lafa family|Lafa or Tribisa-~~quadtrigu~~ family]] (P8, P12/12)

; [[Lafa family|Lafa or Tribisa-quadtriguti family]] (P8, P12/12)

: This tempers out the lafa comma, {{Monzo| 77 -31 -12 }}. The generator is {{nowrap|~4982259375/4294967296 {{=}} ~258.6¢}}. Twelve generators equals a twelfth (~3/1). 5/4 is equated to 7 octaves minus 31 generators.

; [[Ditonmic family|Ditonmic or Lala-~~theyo~~ family]] (P8, c4P4/13)

; [[Ditonmic family|Ditonmic or Lala-theyoti family]] (P8, c4P4/13)

: This tempers out the ditonma, {{nowrap|{{Monzo| -27 -2 13 }} {{=}} 1220703125/1207959552}}. Thirteen ~{{Monzo| -12 -1 6 }} generators of about 407¢ equals a quadruple-compound 4th. 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.

; [[Luna family|Luna or Sasa-~~quintrigu~~ family]] (P8, ccP4/15)

; [[Luna family|Luna or Sasa-quintriguti family]] (P8, ccP4/15)

: This tempers out the luna comma, {{nowrap|{{Monzo| 38 -2 -15 }} {{=}} 274877906944/274658203125}}. The generator is {{nowrap|~{{Monzo| 18 -1 -7 }} {{=}} ~193¢}}. Two generators equals ~5/4, and fifteen generators equals a double-compound 4th of ~16/3.

; [[Vavoom family|Vavoom or Quinla-~~seyo~~ family]] (P8, P12/17)

; [[Vavoom family|Vavoom or Quinla-seyoti family]] (P8, P12/17)

: This tempers out the vavoom comma, {{Monzo| -68 18 17 }}. The generator is {{nowrap|~16/15 {{=}} ~111.9¢}}. Seventeen generators equals a twelfth (~3/1). 5/4 is equated to two octaves minus 18 generators.

; [[Minortonic family|Minortonic or Trila-~~segu~~ family]] (P8, ccP5/17)

; [[Minortonic family|Minortonic or Trila-seguti 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 5th (~6/1). 5/4 is equated to 35 generators minus 5 octaves.

; [[Maja family|Maja or ~~Saseyo~~ family]] (P8, ~~c6P4~~/17)

; [[Maja family|Maja or Saseyoti family]] (P8, c6P4/17)

: This tempers out the maja comma, {{nowrap|{{Monzo| -3 -23 17 }} {{=}} 762939453125/753145430616}}. The generator is {{nowrap|~162/125 {{=}} ~453¢}}. Seventeen generators equals a sextuple-compound 4th. 5/4 is equated to 9 octaves minus 23 generators.

; [[Maquila family|Maquila or Trisa-~~segu~~ family]] (P8, ~~c7P5~~/17)

; [[Maquila family|Maquila or Trisa-seguti family]] (P8, c7P5/17)

: This tempers out the maquila comma, {{nowrap|562949953421312/556182861328125 {{=}} {{monzo| 49 -6 -17 }}}}. The generator is {{nowrap|~512/375 {{=}} ~535¢}}. Seventeen generators equals a septuple-compound 5th. 5/4 is equated to 3 octaves minus 6 generators. An obvious 11-limit interpretation of the generator is 11/8, leading to the Lala-~~selo~~ temperament. However, Lala-~~selo~~ isn't nearly as accurate as Trisa-~~segu~~.

: This tempers out the maquila comma, {{nowrap|562949953421312/556182861328125 {{=}} {{monzo| 49 -6 -17 }}}}. The generator is {{nowrap|~512/375 {{=}} ~535¢}}. Seventeen generators equals a septuple-compound 5th. 5/4 is equated to 3 octaves minus 6 generators. An obvious 11-limit interpretation of the generator is 11/8, leading to the Lala-seloti temperament. However, Lala-seloti isn't nearly as accurate as Trisa-seguti.

; [[Gammic family|Gammic or ~~Laquinquadyo~~ family]] (P8, P5/20)

; [[Gammic family|Gammic or Laquinquadyoti family]] (P8, P5/20)

: The gammic family tempers out the gammic comma, {{Monzo| -29 -11 20 }}. Nine generators of about 35¢ 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 Neptune temperament.

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If a 5-limit comma defines a family of rank two temperaments, then we might say a comma belonging to another [[Just_intonation_subgroups|subgroup]] of the 7-limit can define a clan. In particular we might say a triprime comma (one with exactly three primes in the factorization) can define a clan. We can modify the definition of [[Normal_lists|normal comma list]] for clans by changing the ordering of prime numbers, and using this to sort out clan relationships.

; [[Archytas clan|Archytas or Ru clan]] (P8, P5)

; [[Archytas clan|Archytas or Ruti clan]] (P8, P5)

: This clan tempers out the Archytas comma, [[64/63]]. It equates 7/4 with 16/9. The clan consists of rank two temperaments, and should not be confused with the [[archytas family]] of rank three temperaments. Its best downward extension is [[superpyth]].

; [[Trienstonic clan|Trienstonic or Zo clan]] (P8, P5)

; [[Trienstonic clan|Trienstonic or Zoti clan]] (P8, P5)

: This clan tempers out the septimal third-tone [[28/27]], a low-accuracy temperament that equates 7/6 with 9/8, and 7/4 with 27/16.

; [[Harrison's comma|Harrison or ~~Laru~~ clan]] (P8, P5)

; [[Harrison's comma|Harrison or Laruti clan]] (P8, P5)

: This clan tempers out the Laru comma, {{nowrap|{{Monzo| -13 10 0 -1 }} {{=}} 59049/57344}}. It equates 7/4 to an augmented 6th. Its best downward extension is [[Meantone family|septimal meantone]].

; [[Garischismic clan|Garischismic or ~~Sasaru~~ clan]] (P8, P5)

; [[Garischismic clan|Garischismic or Sasaruti clan]] (P8, P5)

: This clan tempers out the [[garischisma]], {{nowrap|{{Monzo| 25 -14 0 -1 }} {{=}} 33554432/33480783}}. It equates 8/7 to two apotomes ({{nowrap|{{Monzo| -11 7 }} {{=}} 2187/2048}}) and 7/4 to a double-diminished 8ve {{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]].

; Leapfrog or ~~Sasazo~~ clan (P8, P5)

; Leapfrog or Sasazoti clan (P8, P5)

: This clan tempers out the Sasazo comma, {{nowrap|{{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]].

; [[Slendro clan|Slendro (Semaphore) or ~~Zozo~~ clan]] (P8, P4/2)

; Laruruti clan (P8/2, P5)

: This clan tempers out the Laruru comma, {{nowrap|{{Monzo| -7 8 0 -2 }} {{=}} 6561/6272}}. Two ~81/56 periods equal an 8ve. The generator is ~3/2, and four generators minus three periods equals ~7/4. The major 2nd ~9/8 is divided in half, with each half equated to ~28/27. See also the Diaschismic or Saguguti temperament and the Jubilismic or Biruyoti temperament.

; [[Slendro clan|Slendro (Semaphore) or Zozoti clan]] (P8, P4/2)

: This clan tempers out the slendro diesis, [[49/48]]. Its generator is ~8/7 or ~7/6. Its best downward extension is [[godzilla]]. See also [[Semaphore]].

; ~~Laruru~~ clan (P8/2~~, P5~~)

; Parahemif or Sasa-zozoti clan (P8, P5/2)

: This clan tempers out the ~~Laruru~~ comma, {{nowrap|{{Monzo| -~~7 8~~ 0 -2 }} {{=}} ~~6561~~/~~6272~~}}. ~~Two ~81~~/~~56 periods equal an 8ve. The generator~~ is ~~~3/2, and four~~ generators minus ~~three periods equals~~ ~7/~~4. The major 2nd ~~~9~~/8 is divided in half~~, ~~with each half equated~~ to ~~~28/27. See also~~ the ~~Diaschismic or Sagugu temperament and the Jubilismic or Biruyo~~ temperament.

: This clan tempers out the parahemif comma, {{nowrap|{{Monzo| 15 -13 0 2 }} {{=}} 1605632/1594323}}, and includes the [[hemif]] temperament and its strong extension [[hemififths]]. 7/4 is equated to 13 generators minus 3 octaves. An obvious 11-limit interpretation of the ~351¢ generator is 11/9, leading to the Luluti temperament.

; ~~Parahemif or Sasa-zozo~~ clan (P8, P5/2)

; Triruti clan (P8/3, P5)

: This clan tempers out the ~~parahemif~~ comma, {{nowrap|{{Monzo| 15 -13 0 2 }} {{=}} ~~1605632~~/~~1594323~~}}, ~~and includes the [[hemif]]~~ temperament ~~and its strong extension [[hemififths]]~~. 7/~~4 is equated to 13~~ generators minus ~~3 octaves~~. An obvious 11-limit interpretation of the ~~~351¢ generator~~ is 11/9, leading to the ~~Lulu~~ temperament.

: This clan tempers out the Triru comma, {{nowrap|{{Monzo| -1 6 0 -3 }} {{=}} 729/686}}, a low-accuracy temperament. Three ~9/7 periods equals an 8ve. The generator is ~3/2, and two generators minus a period equals ~7/4. An obvious 5-limit interpretation of the ~400¢ period is 5/4, leading to the [[augmented]] temperament.

; [[Gamelismic clan|Gamelismic or ~~Latrizo~~ clan]] (P8, P5/3)

; [[Gamelismic clan|Gamelismic or Latrizoti clan]] (P8, P5/3)

: This clan tempers out the gamelisma, {{nowrap|{{Monzo| -10 1 0 3 }} {{=}} 1029/1024}}. Three ~8/7 generators equals a 5th. 7/4 is equated to an 8ve minus a generator. Five generators is slightly flat of 2/1, making this a [[cluster temperament]]. See also ~~Sawa~~ and ~~Lasepzo~~.

: This clan tempers out the gamelisma, {{nowrap|{{Monzo| -10 1 0 3 }} {{=}} 1029/1024}}. Three ~8/7 generators equals a 5th. 7/4 is equated to an 8ve minus a generator. Five generators is slightly flat of 2/1, making this a [[cluster temperament]]. See also Sawati and Lasepzoti.

: A particularly noteworthy member of the gamelismic clan is miracle, but other members include valentine, unidec, mothra, rodan, and hemithirds. Miracle temperament divides the fifth into 6 equal steps, thus it's a weak extension. Its 21-note scale called "blackjack" and 31-note scale called "canasta" have some useful properties. It is the most efficient 11-limit temperament for many purposes, with a tuning close to 72EDO.

; ~~Trizo~~ clan (P8, P5/3)

; Trizoti clan (P8, P5/3)

: This clan tempers out the Trizo comma, {{nowrap|{{Monzo| -2 -4 0 3 }} {{=}} 343/324}}, a low-accuracy temperament. Three ~7/6 generators equals a 5th, and four equal ~7/4. An obvious interpretation of the ~234¢ generator is 8/7, leading to the much more accurate Gamelismic or ~~Latrizo~~ temperament.

: This clan tempers out the Trizo comma, {{nowrap|{{Monzo| -2 -4 0 3 }} {{=}} 343/324}}, a low-accuracy temperament. Three ~7/6 generators equals a 5th, and four equal ~7/4. An obvious interpretation of the ~234¢ generator is 8/7, leading to the much more accurate Gamelismic or Latrizoti temperament.

~~; Triru clan (P8/3, P5)~~

; Lee or Latriruti clan (P8, P11/3)

: This clan tempers out the Triru comma, {{nowrap|{{Monzo| -1 6 0 -3 }} {{=}} 729/686}}, a low-accuracy temperament. Three ~9/7 periods equals an 8ve. The generator is ~3/2, and two generators minus a period equals ~7/4. An obvious 5-limit interpretation of the ~400¢ period is 5/4, leading to the [[augmented]] temperament.

; Lee or ~~Latriru~~ clan (P8, P11/3)

: This clan tempers out the Latriru comma, {{nowrap|{{Monzo| -9 11 0 -3 }} {{=}} 177147/175616}}. The generator is {{nowrap|~112/81 {{=}} ~566¢}}, and three such generators equals ~8/3. 7/4 is equated to 11 generators minus 5 octaves. An obvious 2.3.5.7 interpretation of the generator is 7/5, leading to the [[liese]] temperament, which is a weak extension of Meantone.

; [[Stearnsmic clan|Stearnsmic or ~~Latribiru~~ clan]] (P8/2, P4/3)

; [[Stearnsmic clan|Stearnsmic or Latribiruti clan]] (P8/2, P4/3)

: This clan temper out the stearnsma, {{nowrap|{{Monzo| 1 10 0 -6 }} {{=}} 118098/117649}}. The period is {{nowrap|~486/343 {{=}} ~600¢}}. The generator is {{nowrap|~9/7 {{=}} ~434¢}}, or alternatively one period minus ~9/7, which equals {{nowrap|~54/49 {{=}} ~166¢}}. Three of these alternate generators equals ~4/3. 7/4 is equated to 5 ~9/7 generators minus an octave. Equating the ~54/49 generator to ~10/9 creates a weak extension of the [[porcupine]] temperament, as does equating the period to ~7/5.

; Buzzardismic or ~~Saquadru~~ clan (P8, P12/4)

; Skwares or Laquadruti clan (P8, P11/4)

: This clan tempers out the Laquadru comma, {{nowrap|{{Monzo| -3 9 0 -4 }} {{=}} 19683/19208}}. its generator is ~9/7. Four generators equals ~8/3. 7/4 is equated to 4 octaves minus 9 generators. This clan includes as a strong extension the [[squares]] temperament, which is a weak extension of meantone.

; Buzzardismic or Saquadruti clan (P8, P12/4)

: This clan tempers out the ''buzzardisma'', {{nowrap|{{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. This clan includes as a strong extension the [[Vulture family|vulture]] temperament, which is in the vulture family.

~~; Skwares or Laquadru clan (P8, P11/4)~~

; [[Cloudy clan|Cloudy or Laquinzoti clan]] (P8/5, P5)

: This clan tempers out the Laquadru comma, {{nowrap|{{Monzo| -3 9 0 -4 }} {{=}} 19683/19208}}. its generator is ~9/7. Four generators equals ~8/3. 7/4 is equated to 4 octaves minus 9 generators. This clan includes as a strong extension the [[squares]] temperament, which is a weak extension of meantone.

: This clan tempers out the [[cloudy comma]], {{nowrap|{{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.

; [[Cloudy clan|Cloudy or ~~Laquinzo~~ clan]] (P8/5, P5)

: This clan tempers out the [[cloudy comma]], {{nowrap|{{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 ~~Sawa~~ family, ~3/2 is not equated with three-fifths of an octave, resulting in very small intervals.

; Bleu or ~~Quinru~~ clan (P8, P5/5)

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

: This clan tempers out the Quinru comma, {{nowrap|{{Monzo| 3 7 0 -5 }} {{=}} 17496/16807}}. The ~54/49 generator is about 139¢. Two of them equal ~7/6, three equal ~9/7, five equal ~3/2, and seven equal ~7/4.

; ~~Saquinzo~~ clan (P8, P12/5)

; Saquinzoti clan (P8, P12/5)

: This clan tempers out the Saquinzo comma, {{nowrap|{{Monzo| 5 -12 0 5 }} {{=}} 537824/531441}}. Its generator is {{nowrap|~243/196 {{=}} ~380¢}}. 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.

; ~~Lasepzo~~ clan (P8, P11/7)

; Lasepzoti clan (P8, P11/7)

: This clan tempers out the Lasepzo comma {{nowrap|{{Monzo| -18 -1 0 7 }} {{=}} 823543/786432}}. Its generator is ~8/7. Six generators equals ~7/3, and seven generators equals ~8/3. Three generators is ~30¢ sharp of 3/2, and five generators is ~15¢ sharp of 2/1, making this a [[cluster temperament]]. See also ~~Sawa~~ and ~~Latrizo~~.

: This clan tempers out the Lasepzo comma {{nowrap|{{Monzo| -18 -1 0 7 }} {{=}} 823543/786432}}. Its generator is ~8/7. Six generators equals ~7/3, and seven generators equals ~8/3. Three generators is ~30¢ sharp of 3/2, and five generators is ~15¢ sharp of 2/1, making this a [[cluster temperament]]. See also Sawati and Latrizoti.

; Septiness or ~~Sasasepru~~ clan (P8, P11/7)

; Septiness or Sasasepruti clan (P8, P11/7)

: This clan tempers out the ''septiness'' comma {{nowrap|{{Monzo| 26 -4 0 -7 }} {{=}} 67108864/66706983}}. Its generator is ~147/128, four of them gives ~7/4, and seven of them gives ~8/3. Five generators is ~12.5¢ sharp of 2/1, making this a [[cluster temperament]].

; ~~Sepru~~ clan (P8, P12/7)

; Sepruti clan (P8, P12/7)

: This clan tempers out the sepru comma, {{nowrap|{{Monzo| 7 8 0 -7 }} {{=}} 839808/823543}}. Its generator is ~7/6. Seven generators equals ~3/1. 7/4 is equated to 8 generators minus 1 octave. This clan includes as a strong extension the [[orwell]] temperament, which is in the Semicomma family.

; [[~~Tritrizo~~ clan]] (P8/9, P5)

; [[Tritrizoti clan]] (P8/9, P5)

: This clan tempers out the ''[[Septimal ennealimma|septiennealimma]]'' (tritrizo comma), {{nowrap|{{Monzo| -11 -9 0 9 }} {{=}} 40353607/40310784}}. It has a period of 1/9 octave, which represents ~7/6. The generator is ~3/2. This clan includes a number of regular temperaments including [[enneaportent]], [[ennealimmal]], and [[Kleismic family #Novemkleismic|novemkleismic]].

Line 251:

See also [[subgroup temperaments]].

; ~~Lulubi~~ clan (P8/2, P5)

; Lulubiti clan (P8/2, P5)

: This low-accuracy 2.3.11 clan tempers out the Alpharabian limma, [[128/121]]. Both 11/8 and 16/11 are equated to half-octave period. This clan includes as a strong extension the pajaric temperament, which is in the diaschismic family.

; [[Rastmic clan|Rastmic or ~~Lulu~~ clan]] (P8, P5/2)

; [[Rastmic clan|Rastmic or Luluti clan]] (P8, P5/2)

: This 2.3.11 clan tempers out {{nowrap|[[243/242]] {{=}} {{monzo| -1 5 0 0 -2 }}}}. Its generator is ~11/9. Two generators equals ~3/2. 11/8 is equated to 5 generators minus an octave. This clan includes as a strong extension the [[dicot]] temperament, which is in the dicot family.

; [[Nexus clan|Nexus or ~~Tribilo Clan~~]] (P8/3, P4/2)

; [[Nexus clan|Nexus or Tribiloti clan]] (P8/3, P4/2)

: This 2.3.11 clan tempers out the [[nexus comma]] {{monzo| -16 -3 0 0 6 }}. Its third-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.

; Alphaxenic or ~~Laquadlo~~ clan (P8/2, M2/4)

; Alphaxenic or Laquadloti 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 ~~saquadyobi~~ temperament, which is in the comic family.

: 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 comic family.

=== Clans defined by a 2.3.13 (tha) comma ===

See also [[subgroup temperaments]].

; ~~Thuthu~~ clan (P8, P5/2)

; Thuthuti clan (P8, P5/2)

: This 2.3.13 clan tempers out {{nowrap|[[512/507]] {{=}} {{monzo| 9 -1 0 0 0 -2 }}}}. Its generator is ~16/13. Two generators equals ~3/2. 13/8 is equated to 1 octave minus 1 generator. This clan includes as a strong extension the [[Dicot]] temperament, which is in the Dicot family.

; Threedie or ~~Satritho~~ clan (P8, P11/3)

; Threedie or Satrithoti clan (P8, P11/3)

: This 2.3.13 clan tempers out the threedie, {{nowrap|[[2197/2187]] {{=}} {{monzo| 0 -7 0 0 0 3 }}}}. Its generator is ~18/13, and three generators equals ~8/3. 13/8 is equated to 7 generators minus three octaves. This clan is related to the ~~Latriru~~ clan.

: This 2.3.13 clan tempers out the threedie, {{nowrap|[[2197/2187]] {{=}} {{monzo| 0 -7 0 0 0 3 }}}}. Its generator is ~18/13, and three generators equals ~8/3. 13/8 is equated to 7 generators minus three octaves. This clan is related to the Latriruti clan.

=== Clans defined by a 2.5.7 (yaza nowa) comma ===

These are defined by a yaza nowa or 7-limit-no-threes comma. See also [[subgroup temperaments]]. The pergen's multigen (the 2nd term, omitting any fraction) is always a 5-limit-no-threes ratio such as 5/4, 8/5, 25/8, etc.

; [[Jubilismic clan|Jubilismic or ~~Biruyo~~ Nowa clan]] (P8/2, M3)

; [[Jubilismic clan|Jubilismic or Biruyoti Nowa clan]] (P8/2, M3)

: This clan tempers out the jubilisma, [[50/49]], which is the difference between 10/7 and 7/5. The generator is the nowa major 3rd (~5/4). The half-octave period is ~7/5 or ~10/7. 7/4 is equated to 1 period plus 1 generator.

; Bapbo or ~~Rurugu~~ Nowa clan (P8, M3/2)

; Bapbo or Ruruguti Nowa clan (P8, M3/2)

: This clan tempers out the bapbo comma, [[256/245]]. The genarator is {{nowrap|~8/7 {{=}} ~202¢}} and two of them equals ~5/4.

; [[Hemimean clan|Hemimean or ~~Zozoquingu~~ Nowa clan]] (P8, M3/2)

; [[Hemimean clan|Hemimean or Zozoquinguti Nowa clan]] (P8, M3/2)

: This clan tempers out the hemimean comma, {{nowrap|{{monzo| 6 0 -5 2 }} {{=}} 3136/3125}}. The generator is {{nowrap|~28/25 {{=}} ~194¢}}. Two generators equals the nowa major 3rd (~5/4), three of them equals ~7/5, and five of them equals ~7/4.

; [[Mabilismic clan|Mabilismic or Latrizo-~~aquiniyo~~ Nowa clan]] (P8, cM3/3)

; [[Mabilismic clan|Mabilismic or Latrizo-aquiniyoti Nowa clan]] (P8, cM3/3)

: This clan tempers out the mabilisma, {{nowrap|{{monzo| -20 0 5 3 }} {{=}} 1071875/1048576}}. The generator is {{nowrap|~175/128 {{=}} ~527¢}}. Three generators equals ~5/2 and five of them equals ~32/7.

; Vorwell or Sasatriru-~~aquadbigu~~ Nowa clan (P8, m6/3)

; Vorwell or Sasatriru-aquadbiguti Nowa clan (P8, m6/3)

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

; Rainy or Quinzo-~~atriyo~~ Nowa clan (P8, M3/5)

; Rainy or Quinzo-atriyoti Nowa clan (P8, M3/5)

: This clan tempers out the [[rainy comma]], {{nowrap|{{monzo| -21 0 3 5 }} {{=}} 2100875/2097152}}. The rurugu generator is {{nowrap|~256/245 {{=}} ~77¢}}. Three generators equals ~8/7 and five of them equals the classic major third (~5/4).

; [[Llywelynsmic clan|Llywelynsmic or Sasepru-~~agu~~ Nowa clan]] (P8, cM3/7)

; [[Llywelynsmic clan|Llywelynsmic or Sasepru-aguti Nowa clan]] (P8, cM3/7)

: This clan tempers out the [[llywelynsma]], {{nowrap|{{monzo| 22 0 -1 -7 }} {{=}} 4194304/4117715}}. The generator is {{nowrap|~8/7 {{=}} ~227¢}} and seven of them equals ~5/2.

; [[Quince clan|Quince or Lasepzo-~~agugu~~ Nowa clan]] (P8, m6/7)

; [[Quince clan|Quince or Lasepzo-aguguti Nowa clan]] (P8, m6/7)

: This clan tempers out the quince, {{nowrap|{{monzo| -15 0 -2 7 }} {{=}} 823543/819200}}. The trizo-agu generator is {{nowrap|~343/320 {{=}} ~116¢}}. Two generators equals ~8/7, five generators equals ~7/5, and seven generators equals the nowa minor 6th ~8/5. An obvious 5-limit interpretation of the generator is 16/15, leading to the [[miracle]] temperament, which is in the gamelismic clan.

; Slither or Satritriru-~~aquadyo~~ Nowa clan (P8, ccm6/9)

; Slither or Satritriru-aquadyoti Nowa clan (P8, ccm6/9)

: This clan tempers out the slither comma, {{nowrap|{{monzo| 16 0 4 -9 }} {{=}} 40960000/40353607}}. The generator is {{nowrap|~49/40 {{=}} ~357¢}}. Four generators equals ~16/7, five of them equals ~14/5, and nine of them equals a double-compound minor 6th of ~32/5.

Line 305:

These are defined by a yaza noca or 7-limit-no-twos comma. Any no-twos comma is a ratio of odd numbers. If no other commas are tempered out, It is a non-octave tuning, with a period of a perfect 12th or tritave, 3/1 (or some fraction of that). See also [[subgroup temperaments]]. The pergen's multigen (the 2nd term, omitting any fraction) is always a 5-limit-no-twos ratio such as 5/3, 9/5, 25/9, etc. In any noca subgroup, "compound" means increased by 3/1 not 2/1.

; [[Arcturus clan|Arcturus or ~~Rutribiyo~~ Noca clan]] (P12, M6)

; [[Arcturus clan|Arcturus or Rutribiyoti Noca clan]] (P12, M6)

: This 3.5.7 clan tempers out the Arcturus comma {{nowrap|{{Monzo| 0 -7 6 -1 }} {{=}} 15625/15309}}. The generator is the noca major 6th (~5/3), and six generators equals ~21/1.

; [[Sensamagic clan|Sensamagic or ~~Zozoyo~~ Noca clan]] (P12, M6/2)

; [[Sensamagic clan|Sensamagic or Zozoyoti Noca clan]] (P12, M6/2)

: This 3.5.7 clan tempers out the sensamagic comma {{nowrap|{{Monzo| 0 -5 1 2 }} {{=}} 245/243}}. The generator is ~9/7, and two generators equals the classic major 6th (~5/3).

; [[Gariboh clan|Gariboh or Triru-~~aquinyo~~ Noca clan]] (P12, M6/3)

; [[Gariboh clan|Gariboh or Triru-aquinyoti Noca clan]] (P12, M6/3)

: This 3.5.7 clan tempers out the gariboh comma {{nowrap|{{Monzo| 0 -2 5 -3 }} {{=}} 3125/3087}}. The generator is ~25/21, two generators equals ~7/5, and three generators equals the noca major 6th (~5/3).

; [[Mirkwai clan|Mirkwai or Quinru-~~aquadyo~~ Noca clan]] (P12, cm7/5)

; [[Mirkwai clan|Mirkwai or Quinru-aquadyoti Noca clan]] (P12, cm7/5)

: This 3.5.7 clan tempers out the mirkwai comma, {{nowrap|{{Monzo| 0 3 4 -5 }} {{=}} 16875/16807}}. The generator is ~7/5, four generators equals ~27/7, and five generators equals the noca compound minor 7th (~27/5).

; Procyon or Sasepzo-~~atrigu~~ Noca clan (P12, m7/7)

; Procyon or Sasepzo-atriguti Noca clan (P12, m7/7)

: This 3.5.7 clan tempers out the Procyon comma {{nowrap|{{Monzo| 0 -8 -3 7 }} {{=}} 823543/820125}}. The generator is ~49/45, three generators equals ~9/7, four equals ~7/5, and seven equals the classic minor seventh (~9/5).

; Betelgeuse or Satritrizo-~~agugu~~ Noca clan (P12, c3M6/9)

; Betelgeuse or Satritrizo-aguguti Noca clan (P12, c3M6/9)

: This 3.5.7 clan tempers out the Betelgeuse comma {{nowrap|{{Monzo| 0 -13 -2 9 }} {{=}} 40353607/39858075}}. The generator is ~3645/2401, two generators equals ~7/3, and nine generators equals the noca triple-compound major 6th (~45/1).

; Izar or Saquadtrizo-~~asepgu~~ Noca clan (P12, c5m7/12)

; Izar or Saquadtrizo-asepguti Noca clan (P12, c5m7/12)

: This 3.5.7 clan tempers out the Izar comma (also known as bapbo schismina), {{nowrap|{{Monzo| 0 -11 -7 12 }} {{=}} 13841287201/13839609375}}. The generator is ~16807/10125, five generators give ~63/5, seven give ~243/7, and twelve give ~2187/5.

Line 329:

These are defined by a full 7-limit (or yaza) comma.

; [[Septisemi temperaments|Septisemi or ~~Zogu~~ temperaments]]

; [[Septisemi temperaments|Septisemi or Zoguti temperaments]]

: These are very low complexity temperaments tempering out the minor septimal semitone, [[21/20]] and hence equating 5/3 with 7/4.

; [[Greenwoodmic temperaments|Greenwoodmic or ~~Ruruyo~~ temperaments]]

; [[Greenwoodmic temperaments|Greenwoodmic or Ruruyoti temperaments]]

: These temper out the greenwoodma, {{nowrap|{{Monzo| -3 4 1 -2 }} {{=}} 405/392}}.

; [[Keegic temperaments|Keegic or ~~Trizogu~~ temperaments]]

; [[Keegic temperaments|Keegic or Trizoguti temperaments]]

: Keegic rank-two temperaments temper out the keega, {{nowrap|{{Monzo| -3 1 -3 3 }} {{=}} 1029/1000}}.

; [[Mint temperaments|Mint or ~~Rugu~~ temperaments]]

; [[Mint temperaments|Mint or Ruguti temperaments]]

: Mint rank-two temperaments temper out the septimal quarter-tone 36/35, equating 7/6 with 6/5, and 5/4 with 9/7.

; [[Avicennmic temperaments|Avicennmic or ~~Zoyoyo~~ temperaments]]

; [[Avicennmic temperaments|Avicennmic or Zoyoyoti temperaments]]

: These temper out the avicennma, {{nowrap|{{Monzo| -9 1 2 1 }} {{=}} 525/512}}, also known as Avicenna's enharmonic diesis.

; Sengic or Trizo-~~agugu~~ temperaments

; Sengic or Trizo-aguguti temperaments

: Sengic rank-two temperaments temper out the senga, {{nowrap|{{Monzo| 1 -3 -2 3 }} {{=}} 686/675}}.

; [[Keemic temperaments|Keemic or ~~Zotriyo~~ temperaments]]

; [[Keemic temperaments|Keemic or Zotriyoti temperaments]]

: Keemic rank-two temperaments temper out the keema, {{nowrap|{{Monzo| -5 -3 3 1 }} {{=}} 875/864}}.

; Secanticorn or ~~Laruquingu~~ temperaments

; Secanticorn or Laruquinguti temperaments

: Secanticorn rank-two temperaments temper out the ''secanticornisma'', {{nowrap|{{monzo| -3 11 -5 -1 }} {{=}} 177147/175000}}.

; Nuwell or Quadru-~~ayo~~ temperaments

; Nuwell or Quadru-ayoti temperaments

: Nuwell rank-two temperaments temper out the nuwell comma, {{nowrap|{{Monzo| 1 5 1 -4 }} {{=}} 2430/2401}}.

; Mermismic or ~~Sepruyo~~ temperaments

; Mermismic or Sepruyoti temperaments

: Mermismic rank-two temperaments temper out the ''mermisma'', {{nowrap|{{Monzo| 5 -1 7 -7 }} {{=}} 2500000/2470629}}.

; Negricorn or ~~Saquadzogu~~ temperaments

; Negricorn or Saquadzoguti temperaments

: Negricorn rank-two temperaments temper out the ''negricorn'' comma, {{nowrap|{{Monzo| 6 -5 -4 4 }} {{=}} 153664/151875}}.

; Tolermic or ~~Sazoyoyo~~ temperaments

; Tolermic or Sazoyoyoti temperaments

: These temper out the tolerma, {{nowrap|{{Monzo| 10 -11 2 1 }} {{=}} 179200/177147}}.

; Valenwuer or ~~Sarutribigu~~ temperaments

; Valenwuer or Sarutribiguti temperaments

: Valenwuer rank-two temperaments temper out the ''valenwuer'' comma, {{nowrap|{{Monzo| 12 3 -6 -1 }} {{=}} 110592/109375}}.

; [[Mirwomo temperaments|Mirwomo or ~~Labizoyo~~ temperaments]]

; [[Mirwomo temperaments|Mirwomo or Labizoyoti temperaments]]

: Mirwomo rank-two temperaments temper out the mirwomo comma, {{nowrap|{{Monzo| -15 3 2 2 }} {{=}} 33075/32768}}.

; Catasyc or ~~Laruquadbiyo~~ temperaments

; Catasyc or Laruquadbiyoti temperaments

: Catasyc rank-two temperaments temper out the ''catasyc'' comma, {{nowrap|{{Monzo| -11 -3 8 -1 }} {{=}} 390625/387072}}.

; Compass or ~~Quinruyoyo~~ temperaments

; Compass or Quinruyoyoti temperaments

: Compass rank-two temperaments temper out the compass comma, {{nowrap|{{Monzo| -6 -2 10 -5 }} {{=}} 9765625/9680832}}.

; Trimyna or ~~Quinzogu~~ temperaments

; Trimyna or Quinzoguti temperaments

: The trimyna rank-two temperaments temper out the trimyna comma, {{nowrap|{{Monzo| -4 1 -5 5 }} {{=}} 50421/50000}}.

; [[Starling temperaments|Starling or ~~Zotrigu~~ temperaments]]

; [[Starling temperaments|Starling or Zotriguti temperaments]]

: Starling rank-two temperaments temper out the septimal semicomma or starling comma {{nowrap|{{Monzo| 1 2 -3 1 }} {{=}} [[126/125]]}}, the difference between three 6/5s plus one 7/6, and an octave. It includes myna, sensi, valentine, casablanca and nusecond temperaments, not to mention meantone, keemun, muggles and opossum.

; [[Octagar temperaments|Octagar or ~~Rurutriyo~~ temperaments]]

; [[Octagar temperaments|Octagar or Rurutriyoti temperaments]]

: Octagar rank-two temperaments temper out the octagar comma, {{nowrap|{{Monzo| 5 -4 3 -2 }} {{=}} 4000/3969}}.

; [[Orwellismic temperaments|Orwellismic or Triru-~~agu~~ temperaments]]

; [[Orwellismic temperaments|Orwellismic or Triru-aguti temperaments]]

: Orwellismic rank-two temperaments temper out orwellisma, {{nowrap|{{Monzo| 6 3 -1 -3 }} {{=}} 1728/1715}}.

; Mynaslendric or Sepru-~~ayo~~ temperaments

; Mynaslendric or Sepru-ayoti temperaments

: Mynaslendric rank-two temperaments temper out the ''mynaslender'' comma, {{nowrap|{{Monzo| 11 4 1 -7 }} {{=}} 829440/823543}}.

; [[Mistismic temperaments|Mistismic or ~~Sazoquadgu~~ temperaments]]

; [[Mistismic temperaments|Mistismic or Sazoquadguti temperaments]]

: Mistismic rank-two temperaments temper out the ''mistisma'', {{nowrap|{{Monzo| 16 -6 -4 1 }} {{=}} 458752/455625}}.

; [[Varunismic temperaments|Varunismic or ~~Labizogugu~~ temperaments]]

; [[Varunismic temperaments|Varunismic or Labizoguguti temperaments]]

: Varunismic rank-two temperaments temper out the varunisma, {{nowrap|{{monzo| -9 8 -4 2 }} {{=}} 321489/320000}}.

; [[Marvel temperaments|Marvel or ~~Ruyoyo~~ temperaments]]

; [[Marvel temperaments|Marvel or Ruyoyoti temperaments]]

: Marvel rank-two temperaments temper out {{nowrap|{{Monzo| -5 2 2 -1 }} {{=}} [[225/224]]}}. It includes negri, sharp, mavila, wizard, tritonic, septimin, slender, triton, escapade and marvo. Considered elsewhere are meantone, miracle, magic, pajara, orwell, catakleismic, garibaldi, august and compton.

; Dimcomp or ~~Quadruyoyo~~ temperaments

; Dimcomp or Quadruyoyoti temperaments

: Dimcomp rank-two temperaments temper out the dimcomp comma, {{nowrap|{{Monzo| -1 -4 8 -4 }} {{=}} 390625/388962}}.

; [[Cataharry temperaments|Cataharry or ~~Labirugu~~ temperaments]]

; [[Cataharry temperaments|Cataharry or Labiruguti temperaments]]

: Cataharry rank-two temperaments temper out the cataharry comma, {{nowrap|{{Monzo| -4 9 -2 -2 }} {{=}} 19683/19600}}.

; [[Canousmic temperaments|Canousmic or Saquadzo-~~atriyo~~ temperaments]]

; [[Canousmic temperaments|Canousmic or Saquadzo-atriyoti temperaments]]

: Canousmic rank-two temperaments temper out the canousma, {{nowrap|{{Monzo| 4 -14 3 4 }} {{=}} 4802000/4782969}}.

; [[Triwellismic temperaments|Triwellismic or Tribizo-~~asepgu~~ temperaments]]

; [[Triwellismic temperaments|Triwellismic or Tribizo-asepguti temperaments]]

: Triwellismic rank-two temperaments temper out the ''triwellisma'', {{nowrap|{{Monzo| 1 -1 -7 6 }} {{=}} 235298/234375}}.

; [[Hemimage temperaments|Hemimage or Satrizo-~~agu~~ temperaments]]

; [[Hemimage temperaments|Hemimage or Satrizo-aguti temperaments]]

: Hemimage rank-two temperaments temper out the hemimage comma, {{nowrap|{{Monzo| 5 -7 -1 3 }} {{=}} 10976/10935}}.

; [[Hemifamity temperaments|Hemifamity or ~~Saruyo~~ temperaments]]

; [[Hemifamity temperaments|Hemifamity or Saruyoti temperaments]]

: Hemifamity rank-two temperaments temper out the hemifamity comma, {{nowrap|{{Monzo| 10 -6 1 -1 }} {{=}} 5120/5103}}.

; [[Parkleiness temperaments|Parkleiness or ~~Zotritrigu~~ temperaments]]

; [[Parkleiness temperaments|Parkleiness or Zotritriguti temperaments]]

: Parkleiness rank-two temperaments temper out the ''parkleiness'' comma, {{nowrap|{{Monzo| 7 7 -9 1 }} {{=}} 1959552/1953125}}.

; [[Porwell temperaments|Porwell or ~~Sarurutrigu~~ temperaments]]

; [[Porwell temperaments|Porwell or Sarurutriguti temperaments]]

: Porwell rank-two temperaments temper out the porwell comma, {{nowrap|{{Monzo| 11 1 -3 -2 }} {{=}} 6144/6125}}.

; [[Cartoonismic temperaments|Cartoonismic or Satritrizo-~~asepbigu~~ temperaments]]

; [[Cartoonismic temperaments|Cartoonismic or Satritrizo-asepbiguti temperaments]]

: Cartoonismic temperaments temper out the cartoonisma, {{nowrap|{{monzo| 12 -3 -14 9 }} {{=}} 165288374272/164794921875}}.

; [[Hemfiness temperaments|Hemfiness or Saquinru-~~atriyo~~ temperaments]]

; [[Hemfiness temperaments|Hemfiness or Saquinru-atriyoti temperaments]]

: Hemfiness rank-two temperaments temper out the ''hemfiness'' comma, {{nowrap|{{Monzo| 15 -5 3 -5 }} {{=}} 4096000/4084101}}.

; [[Hewuermera temperaments|Hewuermera or Satribiru-~~agu~~ temperaments]]

; [[Hewuermera temperaments|Hewuermera or Satribiru-aguti temperaments]]

: Hewuermera rank-two temperaments temper out the ''hewuermera'' comma, {{nowrap|{{Monzo| 16 2 -1 -6 }} {{=}} 589824/588245}}.

; [[Lokismic temperaments|Lokismic or Sasa-~~bizotrigu~~ temperaments]]

; [[Lokismic temperaments|Lokismic or Sasa-bizotriguti temperaments]]

: Lokismic rank-two temperaments temper out the ''lokisma'', {{nowrap|{{Monzo| 21 -8 -6 2 }} {{=}} 102760448/102515625}}.

; Decovulture or ~~Sasabirugugu~~ temperaments

; Decovulture or Sasabiruguguti temperaments

: Decovulture rank-two temperaments temper out the ''decovulture'' comma, {{nowrap|{{Monzo| 26 -7 -4 -2 }} {{=}} 67108864/66976875}}.

; Pontiqak or ~~Lazozotritriyo~~ temperaments

; Pontiqak or Lazozotritriyoti temperaments

: Pontiqak rank-two temperaments temper out the ''pontiqak'' comma, {{nowrap|{{Monzo| -17 -6 9 2 }} {{=}} 95703125/95551488}}.

; [[Mitonismic temperaments|Mitonismic or Laquadzo-~~agu~~ temperaments]]

; [[Mitonismic temperaments|Mitonismic or Laquadzo-aguti temperaments]]

: Mitonismic rank-two temperaments temper out the ''mitonisma'', {{nowrap|{{Monzo| -20 7 -1 4 }} {{=}} 5250987/5242880}}.

; [[Horwell temperaments|Horwell or ~~Lazoquinyo~~ temperaments]]

; [[Horwell temperaments|Horwell or Lazoquinyoti temperaments]]

: Horwell rank-two temperaments temper out the horwell comma, {{nowrap|{{Monzo| -16 1 5 1 }} {{=}} 65625/65536}}.

; Neptunismic or ~~Laruruleyo~~ temperaments

; Neptunismic or Laruruleyoti temperaments

: Neptunismic rank-two temperaments temper out the ''neptunisma'', {{nowrap|{{Monzo| -12 -5 11 -2 }} {{=}} 48828125/48771072}}.

; [[Metric microtemperaments|Metric or Latriru-~~asepyo~~ temperaments]]

; [[Metric microtemperaments|Metric or Latriru-asepyoti temperaments]]

: Metric rank-two temperaments temper out the meter comma, {{nowrap|{{Monzo| -11 2 7 -3 }} {{=}} 703125/702464}}.

; [[Wizmic microtemperaments|Wizmic or Quinzo-~~ayoyo~~ temperaments]]

; [[Wizmic microtemperaments|Wizmic or Quinzo-ayoyoti temperaments]]

: Wizmic rank-two temperaments temper out the wizma, {{nowrap|{{Monzo| -6 -8 2 5 }} {{=}} 420175/419904}}.

; [[Supermatertismic temperaments|Supermatertismic or Lasepru-~~atritriyo~~ temperaments]]

; [[Supermatertismic temperaments|Supermatertismic or Lasepru-atritriyoti temperaments]]

: Supermatertismic rank-two temperaments temper out the ''supermatertisma'', {{nowrap|{{Monzo| -6 3 9 -7 }} {{=}} 52734375/52706752}}.

; [[Breedsmic temperaments|Breedsmic or ~~Bizozogu~~ temperaments]]

; [[Breedsmic temperaments|Breedsmic or Bizozoguti temperaments]]

: Breedsmic rank-two temperaments temper out the breedsma, {{nowrap|{{Monzo| -5 -1 -2 4 }} {{=}} 2401/2400}}.

; Supermasesquartismic or Laquadbiru-~~aquinyo~~ temperaments

; Supermasesquartismic or Laquadbiru-aquinyoti temperaments

: Supermasesquartismic rank-two temperaments temper out the ''supermasesquartisma'', {{nowrap|{{Monzo| -5 10 5 -8 }} {{=}} 184528125/184473632}}.

; [[Ragismic microtemperaments|Ragismic or ~~Zoquadyo~~ temperaments]]

; [[Ragismic microtemperaments|Ragismic or Zoquadyoti temperaments]]

: Ragismic rank-two temperaments temper out the ragisma, {{nowrap|{{Monzo| -1 -7 4 1 }} {{=}} 4375/4374}}.

; Akjaysmic or Trisa-~~seprugu~~ temperaments

; Akjaysmic or Trisa-sepruguti temperaments

: Akjaysmic rank-two temperaments temper out the akjaysma, {{Monzo| 47 -7 -7 -7 }}. These have a period of 1/7 octave, and five periods equals ~105/64. Unlike the Whitewood or ~~Lawa~~ family, ~3/2 is not equated with four-sevenths of an octave, resulting in small intervals.

: Akjaysmic rank-two temperaments temper out the akjaysma, {{Monzo| 47 -7 -7 -7 }}. These have a period of 1/7 octave, and five periods equals ~105/64. Unlike the Whitewood or Lawati family, ~3/2 is not equated with four-sevenths of an octave, resulting in small intervals.

; [[Landscape microtemperaments|Landscape or ~~Trizogugu~~ temperaments]]

; [[Landscape microtemperaments|Landscape or Trizoguguti temperaments]]

: Landscape rank-two temperaments temper out the landscape comma, {{nowrap|{{Monzo| -4 6 -6 3 }} {{=}} 250047/250000}}. These have a period of 1/3 octave, but ~5/4 is not equated with a period, resulting in small intervals.

Line 482:

Every ya or 5-limit comma defines a rank-3 family, thus every comma in the list of rank-two 2.3.5 families could be included here. If nothing else is tempered out, the prime subgroup is assumed to be 2.3.5.7, and we have a yaza or 7-limit temperament in which one of the generators is ~7/1. This generator can be reduced to ~7/4, which can be reduced further to ~64/63. Hence in all the pergens below, the ^1 or /1 generator is ~64/63. An additional 7-limit or 11-limit comma creates a yazala or 11-limit temperament, and so forth. All these examples are yaza:

; [[Didymus rank three family|Didymus or Gu rank three family]] (P8, P5, ^1)

; [[Didymus rank three family|Didymus or Guti rank three family]] (P8, P5, ^1)

: These are the rank three temperaments tempering out the didymus or meantone comma, 81/80.

; [[Diaschismic rank three family|Diaschismic or ~~Sagugu~~ rank three family]] (P8/2, P5, /1)

; [[Diaschismic rank three family|Diaschismic or Saguguti rank three family]] (P8/2, P5, /1)

: These are the rank three temperaments tempering out the dischisma, {{nowrap|{{Monzo| 11 -4 -2 }} {{=}} 2048/2025}}. The half-octave period is ~45/32.

; [[Porcupine rank three family|Porcupine or ~~Triyo~~ rank three family]] (P8, P4/3, /1)

; [[Porcupine rank three family|Porcupine or Triyoti rank three family]] (P8, P4/3, /1)

: These are the rank three temperaments tempering out the porcupine comma or maximal diesis, {{nowrap|{{Monzo| 1 -5 3 }} {{=}} 250/243}}. In the pergen, P4/3 is ~10/9.

; [[Kleismic rank three family|Kleismic or ~~Tribiyo~~ rank three family]] (P8, P12/6, /1)

; [[Kleismic rank three family|Kleismic or Tribiyoti rank three family]] (P8, P12/6, /1)

: These are the rank three temperaments tempering out the kleisma, {{nowrap|{{Monzo| -6 -5 6 }} {{=}} 15625/15552}}. In the pergen, P12/6 is ~6/5.

Line 497:

Every za or 7-limit-no-fives comma defines a rank-3 family, thus every comma in the list of rank-two 2.3.7 families could be included here. If nothing else is tempered out, the prime subgroup is assumed to be 2.3.5.7, and we have a yaza or 7-limit temperament in which one of the generators is ~5/1. This generator can be reduced to ~5/4, which may be reduced further to ~81/80. Hence in all the pergens below, {{nowrap|^1 {{=}} ~81/80}}. An additional 5-limit or 11-limit comma creates a yazala or 11-limit temperament, and so forth. All these examples are yaza:

; [[Archytas family|Archytas or Ru family]] (P8, P5, ^1)

; [[Archytas family|Archytas or Ruti family]] (P8, P5, ^1)

: Archytas temperament tempers out 64/63. This comma equates every 7-limit interval to some 3-limit interval. If 81/80 were tempered out too, the otonal tetrad 4:5:6:7 would be identified with the dominant seventh chord.

; [[Garischismic family|Garischismic or ~~Sasaru~~ family]] (P8, P5, ^1)

; [[Garischismic family|Garischismic or Sasaruti family]] (P8, P5, ^1)

: A garischismic temperament is one which tempers out the garischisma, {{nowrap|{{Monzo| 25 -14 0 -1 }} {{=}} 33554432/33480783}}.

; [[Semiphore family|Semiphore or ~~Zozo~~ family]] (P8, P4/2, ^1)

; Laruruti clan (P8/2, P5)

: Semiphore temperament tempers out 49/48 and thereby identifies the septimal minor third 7/6 with the septimal whole tone 8/7. It also splits the fourth into two of these intervals; hence the name, which sounds like "semi-fourth". See also ~~{{monzo|~~[Semaphore~~|Sem'''<u}}a'''phore~~]] and [[Slendro clan|Slendro]].

: This clan tempers out the Laruru comma, {{nowrap|{{Monzo| -7 8 0 -2 }} {{=}} 6561/6272}}. Two ~81/56 periods equal an 8ve. The generator is ~3/2, and four generators minus three periods equals ~7/4. The major 2nd ~9/8 is divided in half, with each half equated to ~28/27. See also the Diaschismic or Saguguti temperament and the Jubilismic or Biruyoti temperament.

; [[Semiphore family|Semiphore or Zozoti family]] (P8, P4/2, ^1)

: Semiphore temperament tempers out 49/48 and thereby identifies the septimal minor third 7/6 with the septimal whole tone 8/7. It also splits the fourth into two of these intervals; hence the name, which sounds like "semi-fourth". See also [[Semaphore]] and [[Slendro clan|Slendro]].

; [[Gamelismic family|Gamelismic or ~~Latrizo~~ family]] (P8, P5/3, ^1)

; [[Gamelismic family|Gamelismic or Latrizoti family]] (P8, P5/3, ^1)

: Not to be confused with the gamelismic clan of rank two temperaments, the gamelismic family are those rank three temperaments which temper out the gamelisma, {{nowrap|{{Monzo| -10 1 0 3 }} {{=}} 1029/1024}}. In the pergen, P5/3 is ~8/7.

; Stearnsmic or ~~Latribiru~~ family (P8/2, P4/3, ^1)

; Stearnsmic or Latribiruti family (P8/2, P4/3, ^1)

: Stearnsmic temperaments temper out the stearnsma, {{nowrap|{{Monzo| 1 10 0 -6 }} {{=}} 118098/117649}}. In the pergen, P8/2 is ~343/243 and P4/3 is ~54/49.

=== Families defined by a 2.3.5.7 (yaza) comma ===

; [[Marvel family|Marvel or ~~Ruyoyo~~ family]] (P8, P5, ^1)

; [[Marvel family|Marvel or Ruyoyoti family]] (P8, P5, ^1)

: The head of the marvel family is marvel, which tempers out {{nowrap|{{Monzo| -5 2 2 -1 }} {{=}} [[225/224]]}}. It divides 8/7 into two 16/15s, or equivalently, two 15/14s. It has a number of 11-limit children, including unidecimal marvel, prodigy, minerva and spectacle.

The marvel comma equates every 7-limit interval to some 5-limit interval, therefore the generators are the same as for 5-limit JI: 2/1, 3/1 and 5/1. These may be reduced to 2/1, 3/2 and 5/4, and 5/4 may be reduced further to 81/80. Hence in the pergen, {{nowrap|^1 {{=}} ~81/80}}.

; [[Starling family|Starling or ~~Zotrigu~~ family]] (P8, P5, ^1)

; [[Starling family|Starling or Zotriguti family]] (P8, P5, ^1)

: Starling tempers out the septimal semicomma or starling comma {{nowrap|{{Monzo| 1 2 -3 1 }} {{=}} [[126/125]]}}, the difference between three 6/5s plus one 7/6, and an octave. It divides 10/7 into two 6/5s. Like marvel, it has the same generators as 5-limit JI. An excellent tuning for starling is [[77edo|77EDO]], but 31, 46 or 58 also work nicely. In the pergen, {{nowrap|^1 {{=}} ~81/80}}.

; [[Sensamagic family|Sensamagic or ~~Zozoyo~~ family]] (P8, P5, ^1)

; [[Sensamagic family|Sensamagic or Zozoyoti family]] (P8, P5, ^1)

: These temper out {{nowrap|{{Monzo| 0 -5 1 2 }} {{=}} 245/243}}, which divides 16/15 into two 28/27s. In the pergen, {{nowrap|^1 {{=}} ~64/63}}.

; Greenwoodmic or ~~Ruruyo~~ family (P8, P5, ^1)

; Greenwoodmic or Ruruyoti family (P8, P5, ^1)

: These temper out the greenwoodma, {{nowrap|{{Monzo| -3 4 1 -2 }} {{=}} 405/392}}, which divides 10/9 into two 15/14s. In the pergen, {{nowrap|^1 {{=}} ~64/63}}.

; Avicennmic or ~~Lazoyoyo~~ family (P8, P5, ^1)

; Avicennmic or Lazoyoyoti family (P8, P5, ^1)

: These temper out the avicennma, {{nowrap|{{Monzo| -9 1 2 1 }} {{=}} 525/512}}, which divides 7/6 into two 16/15s. In the pergen, {{nowrap|^1 {{=}} ~81/80}}.

; [[Keemic family|Keemic or ~~Zotriyo~~ family]] (P8, P5, ^1)

; [[Keemic family|Keemic or Zotriyoti family]] (P8, P5, ^1)

: These temper out the keema {{nowrap|{{Monzo| -5 -3 3 1 }} {{=}} 875/864}}, which divides 15/14 into two 25/24s. In the pergen, {{nowrap|^1 {{=}} ~81/80}}.

; [[Orwellismic family|Orwellismic or Triru-~~agu~~ family]] (P8, P5, ^1)

; [[Orwellismic family|Orwellismic or Triru-aguti family]] (P8, P5, ^1)

: These temper out {{nowrap|{{Monzo| 6 3 -1 -3 }} {{=}} 1728/1715}}. In the pergen, {{nowrap|^1 {{=}} ~64/63}}.

; [[Nuwell family|Nuwell or Quadru-~~ayo~~ family]] (P8, P5, ^1)

; [[Nuwell family|Nuwell or Quadru-ayoti family]] (P8, P5, ^1)

: These temper out the nuwell comma, {{nowrap|{{Monzo| 1 5 1 -4 }} {{=}} 2430/2401}}. In the pergen, {{nowrap|^1 {{=}} ~64/63}}.

; [[Ragisma family|Ragisma or ~~Zoquadyo~~ family]] (P8, P5, ^1)

; [[Ragisma family|Ragisma or Zoquadyoti family]] (P8, P5, ^1)

: The 7-limit rank three microtemperament which tempers out the ragisma, {{nowrap|{{Monzo| -1 -7 4 1 }} {{=}} 4375/4374}}, extends to various higher limit rank three 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}}.

; [[Hemifamity family|Hemifamity or ~~Saruyo~~ family]] (P8, P5, ^1)

; [[Hemifamity family|Hemifamity or Saruyoti family]] (P8, P5, ^1)

: The hemifamity family of rank three temperaments tempers out the hemifamity comma, {{nowrap|{{Monzo| 10 -6 1 -1 }} {{=}} 5120/5103}}, which divides 10/7 into three 9/8s. In the pergen, {{nowrap|^1 {{=}} ~81/80}}.

; [[Horwell family|Horwell or ~~Lazoquinyo~~ family]] (P8, P5, ^1)

; [[Horwell family|Horwell or Lazoquinyoti family]] (P8, P5, ^1)

: The horwell family of rank three temperaments tempers out the horwell comma, {{nowrap|{{Monzo| -16 1 5 1 }} {{=}} 65625/65536}}. In the pergen, {{nowrap|^1 {{=}} ~81/80}}.

; [[Hemimage family|Hemimage or Satrizo-~~agu~~ family]] (P8, P5, ^1)

; [[Hemimage family|Hemimage or Satrizo-aguti family]] (P8, P5, ^1)

: The hemimage family of rank three temperaments tempers out the hemimage comma, {{nowrap|{{Monzo| 5 -7 -1 3 }} {{=}} 10976/10935}}, which divides 10/9 into three 28/27s. In the pergen, {{nowrap|^1 {{=}} ~64/63}}.

; [[Mint family|Mint or ~~Rugu~~ family]] (P8, P5, ^1)

; [[Mint family|Mint or Ruguti family]] (P8, P5, ^1)

: The mint temperament is a low complexity, high error temperament, tempering out the septimal quarter-tone 36/35, equating 7/6 with 6/5, and 5/4 with 9/7. In the pergen, {{nowrap|^1 {{=}} ~81/80}} or ~64/63.

; Septisemi or ~~Zogu~~ family (P8, P5, ^1)

; Septisemi or Zoguti family (P8, P5, ^1)

: These are very low accuracy temperaments tempering out the minor septimal semitone, [[21/20]] and hence equating 5/3 with 7/4. In the pergen, {{nowrap|^1 {{=}} ~81/80}}.

; [[Jubilismic family|Jubilismic or ~~Biruyo~~ family]] (P8/2, P5, ^1)

; [[Jubilismic family|Jubilismic or Biruyoti family]] (P8/2, P5, ^1)

: Jubilismic temperament tempers out 50/49 and thereby equates the two septimal tritones, 7/5 and 10/7. This is the half-octave period. In the pergen, {{nowrap|^1 {{=}} ~81/80}}.

; [[Cataharry family|Cataharry or ~~Labirugu~~ family]] (P8, P4/2, ^1)

; [[Cataharry family|Cataharry or Labiruguti family]] (P8, P4/2, ^1)

: Cataharry temperaments temper out the cataharry comma, {{nowrap|{{Monzo| -4 9 -2 -2 }} {{=}} 19683/19600}}. In the pergen, half a 4th is ~81/70, and {{nowrap|^1 {{=}} ~81/80}}.

; [[Breed family|Breed or ~~Bizozogu~~ family]] (P8, P5/2, ^1)

; [[Breed family|Breed or Bizozoguti family]] (P8, P5/2, ^1)

: Breed is a 7-limit microtemperament which tempers out {{nowrap|{{Monzo| -5 -1 -2 4 }} {{=}} 2401/2400}}. While it is so accurate it hardly matters what is used to temper it, or whether it is even tempered at all, 2749EDO will certainly do the trick. Breed has generators of 2/1, a 49/40-cum-60/49 neutral third, and ~64/63.

; [[Sengic family|Sengic or Trizo-~~agugu~~ family]] (P8, P5, vm3/2)

; [[Sengic family|Sengic or Trizo-aguguti family]] (P8, P5, vm3/2)

: These temper out the senga, {{nowrap|{{Monzo| 1 -3 -2 3 }} {{=}} 686/675}}. One generator is ~15/14, two give ~7/6 (the downminor 3rd in the pergen), and three give ~6/5.

; [[Porwell family|Porwell or ~~Sarurutrigu~~ family]] (P8, P5, ^m3/2)

; [[Porwell family|Porwell or Sarurutriguti family]] (P8, P5, ^m3/2)

: The porwell family of rank three temperaments tempers out the porwell comma, {{nowrap|{{Monzo| 11 1 -3 -2 }} {{=}} 6144/6125}}. Two ~35/32 generators equal the pergen's upminor 3rd of ~6/5.

; [[Octagar family|Octagar or ~~Rurutriyo~~ family]] (P8, P5, ^m6/2)

; [[Octagar family|Octagar or Rurutriyoti family]] (P8, P5, ^m6/2)

: The octagar family of rank three temperaments tempers out the octagar comma, {{nowrap|{{Monzo| 5 -4 3 -2 }} {{=}} 4000/3969}}. Two ~80/63 generators equal the pergen's upminor 6th of ~8/5.

; [[Hemimean family|Hemimean or ~~Zozoquingu~~ family]] (P8, P5, vM3/2)

; [[Hemimean family|Hemimean or Zozoquinguti family]] (P8, P5, vM3/2)

: The hemimean family of rank three temperaments tempers out the hemimean comma, {{nowrap|{{Monzo| 6 0 -5 2 }} {{=}} 3136/3125}}. Two ~28/25 generators equal the pergen's downmajor 3rd of ~5/4.

; Wizmic or Quinzo-~~ayoyo~~ family (P8, P5, vm7/2)

; Wizmic or Quinzo-ayoyoti family (P8, P5, vm7/2)

: A wizmic temperament is one which tempers out the wizma, {{nowrap|{{Monzo| -6 -8 2 5 }} {{=}} 420175/419904}}. Two ~324/245 generators equal the pergen's downminor 7th of ~7/4.

; [[Landscape family|Landscape or ~~Trizogugu~~ family]] (P8/3, P5, ^1)

; [[Landscape family|Landscape or Trizoguguti family]] (P8/3, P5, ^1)

: The 7-limit rank three microtemperament which tempers out the lanscape comma, {{nowrap|{{Monzo| -4 6 -6 3 }} {{=}} 250047/250000}}, extends to various higher limit rank three temperaments such as tyr and odin. In the pergen, the third-octave period is ~63/50, and {{nowrap|^1 {{=}} ~81/80}}.

; [[Gariboh family|Gariboh or Triru-~~aquinyo~~ family]] (P8, P5, vM6/3)

; [[Gariboh family|Gariboh or Triru-aquinyoti family]] (P8, P5, vM6/3)

: The gariboh family of rank three temperaments tempers out the gariboh comma, {{nowrap|{{monzo| 0 -2 5 -3 }} {{=}} 3125/3087}}. Three ~25/21 generators equal the pergen's downmajor 6th of ~5/3.

; [[Canou family|Canou or Saquadzo-~~atriyo~~ family]] (P8, P5, vm6/3)

; [[Canou family|Canou or Saquadzo-atriyoti family]] (P8, P5, vm6/3)

: The canou family of rank three temperaments tempers out the canousma, {{nowrap|{{Monzo| 4 -14 3 4 }} {{=}} 4802000/4782969}}. Three ~81/70 generators equal the pergen's downminor 6th of ~14/9.

; [[Dimcomp family|Dimcomp or ~~Quadruyoyo~~ family]] (P8/4, P5, ^1)

; [[Dimcomp family|Dimcomp or Quadruyoyoti family]] (P8/4, P5, ^1)

: The dimcomp family of rank three temperaments tempers out the dimcomp comma, {{nowrap|{{Monzo| -1 -4 8 -4 }} {{=}} 390625/388962}}. In the pergen, the quarter-octave period is ~25/21, and {{nowrap|^1 {{=}} ~81/80}}.

; [[Mirkwai family|Mirkwai or Quinru-~~aquadyo~~ family]] (P8, P5, c^M7/4)

; [[Mirkwai family|Mirkwai or Quinru-aquadyoti family]] (P8, P5, c^M7/4)

: The mirkwai family of rank three temperaments tempers out the mirkwai comma, {{nowrap|{{Monzo| 0 3 4 -5 }} {{=}} 16875/16807}}. Four ~7/5 generators equal the pergen's compound upmajor 7th of ~27/7.

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

; [[Ptolemismic clan|Ptolemismic or ~~Luyoyo~~ clan]] (P8, P5, ^1)

; [[Ptolemismic clan|Ptolemismic or Luyoyoti clan]] (P8, P5, ^1)

: These temper out the ptolemisma, {{nowrap|{{monzo| 2 -2 2 0 -1 }} {{=}} 100/99}}. 11/8 is equated to 25/18, which is an octave minus two 6/5's. Since 25/18 is a 5-limit interval, every 2.3.5.11 interval is equated to a 5-limit interval, and both the pergen and the lattice are identical to that of 5-limit JI. In the pergen, {{nowrap|^1 {{=}} ~81/80}}.

; [[Biyatismic clan|Biyatismic or ~~Lologu~~ clan]] (P8, P5, ^1)

; [[Biyatismic clan|Biyatismic or Lologuti clan]] (P8, P5, ^1)

: These temper out the biyatisma, {{nowrap|{{monzo| -3 -1 -1 0 2 }} {{=}} 121/120}}. 5/4 is equated to 121/96, which is two 11/8's minus a 3/2 fifth. Since 121/96 is an ila (11-limit no-fives no-sevens) interval, every 2.3.5.11 interval is equated to an ila interval, and both the pergen and the lattice are identical to that of ila JI. In the pergen, ^1 is either ~33/32 or ~729/704.

; [[Valinorsmic clan|Valinorsmic or ~~Lorugugu~~ clan]]

; [[Valinorsmic clan|Valinorsmic or Loruguguti clan]]

: These temper out the valinorsma, {{nowrap|{{monzo| 4 0 -2 -1 1 }} {{=}} 176/175}}. 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.

; [[Rastmic rank three clan|Rastmic or ~~Lulu~~ rank-3 clan]]

; [[Rastmic rank three clan|Rastmic or Luluti rank-3 clan]]

: These temper out the rastma, {{nowrap|{{monzo| 1 5 0 0 -2 }} {{=}} 243/242}}. In the corresponding [[Tour of regular temperaments#Clans defined by a 2.3.11 .28ila.29 comma|2.3.11 rank-2 temperament]], the pergen is (P8, P5/2).

; [[Pentacircle clan|Pentacircle or ~~Saluzo~~ clan]] (P8, P5, ^1)

; [[Pentacircle clan|Pentacircle or Saluzoti clan]] (P8, P5, ^1)

: These temper out the pentacircle comma, {{nowrap|{{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.

; [[Semicanousmic clan|Semicanousmic or Quadlo-~~agu~~ clan]] (P8, P5, ^1)

; [[Semicanousmic clan|Semicanousmic or Quadlo-aguti clan]] (P8, P5, ^1)

: These temper out the semicanousma, {{nowrap|{{monzo| -2 -6 -1 0 4 }} {{=}} 14641/14580}}. 5/4 is equated to an ila (2.3.11) interval, thus every 2.3.5.11 interval is equated to an ila interval, and both the pergen and the lattice are identical to that of ila JI. In the pergen, ^1 is either ~33/32 or ~729/704.

; [[Semiporwellismic clan|Semiporwellismic or ~~Salulugu~~ clan]] (P8, P5, ^1)

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

: These temper out the semiporwellisma, {{nowrap|{{monzo| 14 -3 -1 0 -2 }} {{=}} 16384/16335}}. 5/4 is equated to an ila (2.3.11) interval, thus every 2.3.5.11 interval is equated to an ila interval, and both the pergen and the lattice are identical to that of ila JI. In the pergen, ^1 is either ~33/32 or ~729/704.

; [[Olympic clan|Olympic or ~~Salururu~~ clan]] (P8, P5, ^1)

; [[Olympic clan|Olympic or Salururuti clan]] (P8, P5, ^1)

: These temper out the olympia, {{nowrap|{{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}}.

; [[Alphaxenic rank three clan|Alphaxenic or ~~Laquadlo~~ rank-3 clan]]

; [[Alphaxenic rank three clan|Alphaxenic or Laquadloti rank-3 clan]]

: These temper out the Alpharabian comma, {{nowrap|{{monzo| -17 2 0 0 4 }} {{=}} 131769/131072}}. In the corresponding [[Tour of regular temperaments#Clans defined by a 2.3.11 .28ila.29 comma|2.3.11 rank-2 temperament]], the pergen is (P8/2, M2/4).

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Even less explored than rank three temperaments are rank four temperaments. In fact, unless one counts 7-limit JI they don't seem to have been explored at all. However, they could be used; for example [[Hobbits|hobbit scales]] can be constructed for them.

; [[Keenanismic temperaments|Keenanismic or ~~Lozoyo~~ temperaments]] (P8, P5, ^1, /1)

; [[Keenanismic temperaments|Keenanismic or Lozoyoti temperaments]] (P8, P5, ^1, /1)

: These temper out the keenanisma, {{nowrap|{{monzo| -7 -1 1 1 1 }} {{=}} 385/384}}. In the pergen, ^1 could be either ~81/80 or ~64/63, and /1 could be either ~64/63 (if ^1 isn't), ~33/32 or ~729/704.

;[[Werckismic temperaments|Werckismic or ~~Luzozogu~~ temperaments]] (P8, P5, ^1, /1)

;[[Werckismic temperaments|Werckismic or Luzozoguti temperaments]] (P8, P5, ^1, /1)

: These temper out the werckisma, {{nowrap|{{monzo| -3 2 -1 2 -1 }} {{=}} 441/440}}. 11/8 is equated to {{monzo| -6 2 -1 2 }} and 5/4 is equated to {{monzo| -5 2 0 2 -1 }}, thus the lattice can be thought of as either 7-limit JI or 11-limit no-fives JI. In the pergen, ^1 is ~64/63, and /1 is either ~81/80, ~33/32 or ~729/704.

;[[Swetismic temperaments|Swetismic or ~~Lururuyo~~ temperaments]] (P8, P5, ^1, /1)

;[[Swetismic temperaments|Swetismic or Lururuyoti temperaments]] (P8, P5, ^1, /1)

: These temper out the swetisma, {{nowrap|{{monzo| 2 3 1 -2 -1 }} {{=}} 540/539}}. 11/8 is equated to {{nowrap| -1 3 1 -2 {{=}} 135/98}} and 5/4 is equated to {{monzo| -4 -3 0 2 1 }}, thus the lattice can be thought of as either 7-limit JI or 11-limit no-fives JI. In the pergen, ^1 is ~64/63, and /1 can be either ~81/80, ~33/32 or ~729/704.

; [[Lehmerismic temperaments|Lehmerismic or ~~Loloruyoyo~~ temperaments]] (P8, P5, ^1, /1)

; [[Lehmerismic temperaments|Lehmerismic or Loloruyoyoti temperaments]] (P8, P5, ^1, /1)

: These temper out the lehmerisma, {{nowrap|{{monzo| -4 -3 2 -1 2 }} {{=}} 3025/3024}}. Since 7/4 is equated to a yala (11-limit no-sevens) interval, both the pergen and the lattice are identical to that of yala JI. In the pergen, {{nowrap|^1 {{=}} ~81/80}} and/1 = either ~33/32 or ~729/704.

;[[Kalismic temperaments|Kalismic or ~~Bilorugu~~ temperaments]] (P8/2, P5, ^1, /1)

;[[Kalismic temperaments|Kalismic or Biloruguti temperaments]] (P8/2, P5, ^1, /1)

: These temper out the kalisma, {{nowrap|{{monzo| -3 4 -2 -2 2 }} {{=}} 9801/9800}}. The octave is split into two ~99/70 periods. In the pergen, ^1 could be either ~81/80 or ~64/63, and /1 could be either ~64/63 (if ^1 isn't), ~33/32 or ~729/704.

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By a ''commatic realm'' is meant the whole collection of regular temperaments of various ranks and for [[subgroup]]s (including full [[prime limit]]s) tempering out a given comma. For some commas, looking at the full commatic realm seems the best approach to discussing associated temperaments.

; [[The Biosphere|The Biosphere or ~~Thozogu~~]]

; [[The Biosphere|The Biosphere or Thozoguti]]

: The Biosphere is the name given to the commatic realm of the [[13-limit]] comma 91/90.

; [[Marveltwin|Marveltwin or ~~Thoyoyo~~]]

; [[Marveltwin|Marveltwin or Thoyoyoti]]

: This is the commatic realm of the 13-limit comma 325/324, the [[marveltwin comma]].

; [[The Archipelago|The Archipelago or ~~Bithogu~~]]

; [[The Archipelago|The Archipelago or Bithoguti]]

: The Archipelago is a name which has been given to the commatic realm of the 13-limit comma {{nowrap|676/675 {{=}} {{monzo| 2 -3 -2 0 0 2 }}}}, the [[island comma]].

; [[The Jacobins|The Jacobins or Thotrilu-~~agu~~]]

; [[The Jacobins|The Jacobins or Thotrilu-aguti]]

: This is the commatic realm of the 13-limit comma 6656/6655, the [[jacobin comma]].

Line 667:

Line 670:

: This is the commatic realm of [[7777/7776]], the pulsar comma.

; [[Orgonia|Orgonia or Satrilu-~~aruru~~]]

; [[Orgonia|Orgonia or Satrilu-aruruti]]

: This is the commatic realm of the 11-limit comma {{nowrap|65536/65219 {{=}} {{monzo| 16 0 0 -2 -3 }}}}, the [[orgonisma]].

; [[The Nexus|The Nexus or ~~Tribilo~~]]

; [[The Nexus|The Nexus or Tribiloti]]

: This is the commatic realm of the 11-limit comma {{nowrap|1771561/1769472 {{=}} {{monzo| -16 -3 0 0 6 }}}}, the [[nexus comma]].

; [[The Quartercache|The Quartercache or Saquinlu-~~azo~~]]

; [[The Quartercache|The Quartercache or Saquinlu-azoti]]

: This is the commatic realm of the 11-limit comma {{nowrap|117440512/117406179 {{=}} {{monzo| 24 -6 0 1 -5 }}}}, the [[quartisma]].

@@ Line 29: / Line 29: @@
 These are families defined by a ya or 5-limit comma. As we go up in rank two, the various 5-limit temperaments often break up as families of related temperaments, depending on how higher primes are mapped (or equivalently, on which higher limit commas are introduced.) The same comment applies to 7-limit temperaments and rank three, etc. Members of families and their relationships can be classified by the [[Normal lists|normal comma list]] of the various temperaments. Families include weak extensions as well as strong, in other words, the [[pergen]] shown here may change.
-; [[Meantone family|Meantone or Gu family]] (P8, P5)
+; [[Meantone family|Meantone or Guti family]] (P8, P5)
 : The meantone family tempers out [[81/80]], also called the syntonic comma. This comma manifests as the difference between a stack of four 3/2's (81/16, or (3/2)^4) and 5/1 harmonic (5/1, or 80/16). It is so named because it splits the major third into two equal sized tones, signifying that 9/8 and 10/9 are equated, with each tone being sized as a mean of the two tones. It has a flattened fifth or sharpened fourth as generator. Some meantone tunings are [[12edo|12]], [[19edo|19]], [[31edo|31]], [[43edo|43]], [[50edo|50]], [[55edo|55]] and [[81edo|81]] EDOs. Aside from tuning meantone as a subset of some equal division of the octave, some common rank-2 tunings include having a generator of 3/2 flattened by 1/3, 2/7, 1/4, 1/5 or 1/6 of the syntonic comma.
-; [[Schismatic family|Schismatic or Layo family]] (P8, P5)
+; [[Schismatic family|Schismatic or Layoti family]] (P8, P5)
 : The schismatic family tempers out the schisma of {{nowrap|{{Monzo| -15 8 1 }} {{=}} [[32805/32768]]}}, which is the amount by which the Pythagorean comma exceeds the syntonic comma. The 5-limit version of the temperament is a [[microtemperament]] which flattens the fifth by a fraction of a schisma, but other members of the family are less accurate. As a 5-limit system, it is far more accurate than meantone but still with manageable complexity; whereas meantone equates four 3/2's with 5/1, schismatic equates eight 4/3's with 10/1, so that the Pythagorean diminished fourth of 8192/6561 is equated with 5/4. Tunings include [[12edo|12]], [[29edo|29]], [[41edo|41]], [[53edo|53]], and [[118edo|118]] EDOs.
-; [[Pelogic family|Pelogic or Layobi family]] (P8, P5)
+; [[Pelogic family|Pelogic or Layobiti family]] (P8, P5)
 : This tempers out the pelogic comma, {{nowrap|{{Monzo| -7 3 1 }} {{=}} [[135/128]]}}, also known as the major chroma or major limma. These temperaments are notable for having 3/2's tuned so flat that four of them, when stacked together, leads you to 6/5 + 2 octaves instead of 5/4 + 2 octaves, and one consequence of this is that it generates [[2L 5s]] "anti-diatonic" scales. 5/4 is equated to 3 fourths minus 1 octave. Mavila and Armodue are some of the most notable temperaments associated with the pelogic comma. Tunings include [[9edo|9]], [[16edo|16]], [[23edo|23]], and [[25edo|25]] EDOs.
-; [[Father family|Father or Gubi family]] (P8, P5)
+; [[Father family|Father or Gubiti family]] (P8, P5)
 : This tempers out [[16/15]], the just diatonic semitone, and equates 5/4 with 4/3.
-; [[Diaschismic family|Diaschismic or Sagugu family]] (P8/2, P5)
+; [[Diaschismic family|Diaschismic or Saguguti family]] (P8/2, P5)
 : The diaschismic family tempers out the [[diaschisma]], {{nowrap|{{Monzo| 11 -4 -2 }} {{=}} 2048/2025}}, such that two classic major thirds and a [[81/64|Pythagorean major third]] stack to an octave (i.e. {{nowrap|5/4 &times; 5/4 &times; 81/64 &rarr; 2/1}}). It has a half-octave period of an approximate 45/32 or 64/45, and its generator is an approximate 3/2. 5/4 is equated to 3 periods minus 2 fifths. The major 2nd ~9/8 is divided in half, with each half equated to ~16/15. Diaschismic tunings include [[12edo|12]], [[22edo|22]], [[34edo|34]], [[46edo|46]], [[56edo|56]], [[58edo|58]] and [[80edo|80]] EDOs. An obvious 7-limit interpretation of the period is 7/5, which makes [[pajara]] temperament, where the intervals 50/49 and 64/63 are tempered out. [[22edo|22EDO]] is an excellent pajara tuning.
-; [[Bug family|Bug or Gugu family]] (P8, P4/2)
+; [[Bug family|Bug or Guguti family]] (P8, P4/2)
-: This low-accuracy family of temperaments tempers out [[27/25]], the large limma or bug comma. The generator is an approximate 6/5 or {{nowrap|10/9 {{=}} ~250¢}}, two of which make ~4/3. 5/4 is equated to 1 octave minus 3 generators. An obvious 7-limit interpretation of the generator is 7/6, which makes Slendro aka Semaphore or Zozo.
+: This low-accuracy family of temperaments tempers out [[27/25]], the large limma or bug comma. The generator is an approximate 6/5 or {{nowrap|10/9 {{=}} ~250¢}}, two of which make ~4/3. 5/4 is equated to 1 octave minus 3 generators. An obvious 7-limit interpretation of the generator is 7/6, which makes Slendro aka Semaphore or Zozoti.
-; [[Immunity family|Immunity or Sasa-yoyo family]] (P8, P4/2)
+; [[Immunity family|Immunity or Sasa-yoyoti family]] (P8, P4/2)
-: This tempers out the immunity comma, {{Monzo| 16 -13 2 }} (1638400/1594323). Its generator is {{nowrap|~729/640 {{=}} ~247¢}}, two of which make ~4/3. 5/4 is equated to 3 octaves minus 13 generators. An obvious 7-limit interpretation of the generator is 7/6, which leads to Slendro aka Semaphore or Zozo.
+: This tempers out the immunity comma, {{Monzo| 16 -13 2 }} (1638400/1594323). Its generator is {{nowrap|~729/640 {{=}} ~247¢}}, two of which make ~4/3. 5/4 is equated to 3 octaves minus 13 generators. An obvious 7-limit interpretation of the generator is 7/6, which leads to Slendro aka Semaphore or Zozoti.
-; [[Dicot family|Dicot or Yoyo family]] (P8, P5/2)
+; [[Dicot family|Dicot or Yoyoti family]] (P8, P5/2)
-: The dicot family is a low-accuracy family of temperaments which temper out the chromatic semitone, [[25/24]] (the difference between 5/4 and 6/5, or alternatively the difference between two 5/4's and 3/2 OR two 6/5's and 3/2). This temperament hence equates major and minor thirds, evening them out into a neutral-sized 3rd of ~350¢ that is taken to approximate both. [[7edo|7EDO]] makes for a "good" dicot tuning, although it is questionable whether this temperament bears any actual resemblance to 5-limit harmony. Two of the "neutral" dicot 3rds span a 3/2. Tunings include 7EDO, [[10edo|10EDO]], and [[17edo|17EDO]]. An obvious 2.3.11 interpretation of the generator is ~11/9, which leads to Rastmic aka Neutral or Lulu.
+: The dicot family is a low-accuracy family of temperaments which temper out the chromatic semitone, [[25/24]] (the difference between 5/4 and 6/5, or alternatively the difference between two 5/4's and 3/2 OR two 6/5's and 3/2). This temperament hence equates major and minor thirds, evening them out into a neutral-sized 3rd of ~350¢ that is taken to approximate both. [[7edo|7EDO]] makes for a "good" dicot tuning, although it is questionable whether this temperament bears any actual resemblance to 5-limit harmony. Two of the "neutral" dicot 3rds span a 3/2. Tunings include 7EDO, [[10edo|10EDO]], and [[17edo|17EDO]]. An obvious 2.3.11 interpretation of the generator is ~11/9, which leads to Rastmic aka Neutral or Luluti.
-; [[Augmented family|Augmented or Trigu  family]] (P8/3, P5)
+; [[Augmented family|Augmented or Triguti family]] (P8/3, P5)
 : The augmented family tempers out the diesis of {{nowrap|{{Monzo| 7 0 -3 }} {{=}} [[128/125]]}}, the difference between three 5/4 major thirds and a 2/1 octave, and so identifies the major third with the third-octave. Hence it has the same 400-cent 5/4-approximations as [[12edo|12EDO]], which is an excellent tuning for augmented. It is the temperament that results in what is commonly called the "augmented scale" ([[3L 3s]]) in common 12-based music theory, as well as what is commonly called "[http://www.tcherepnin.com/alex/basic_elem1.htm#9step Tcherepnin's scale]" ([[3L 6s]]).
-; [[Misty family|Misty or Sasa-trigu family]] (P8/3, P5)
+; [[Misty family|Misty or Sasa-triguti family]] (P8/3, P5)
 : The misty family tempers out the [[misty comma]] of {{monzo| 26 -12 -3 }}, the difference between the [[Pythagorean comma]] and a stack of three [[Schisma|schismas]]. The period is ~512/405 and the generator is ~3/2 (or alternatively ~135/128). 5/4 is equated to 8 periods minus 4 fifths, thus 5/4 is split into 4 equal parts, each 2 periods minus a fifth.
-; [[Porcupine family|Porcupine or Triyo family]] (P8, P4/3)
+; [[Porcupine family|Porcupine or Triyoti family]] (P8, P4/3)
 : The porcupine family tempers out {{nowrap|{{Monzo| 1 -5 3 }} {{=}} [[250/243]]}}, the difference between three 10/9's (1000/729) and 4/3, known as the maximal diesis or porcupine comma. It subdivides the fourth into three equal parts, each taken as an approximated 10/9, of which two approximate 6/5. It also manifests itself as the difference between three 6/5's and 16/9, as the difference between 10/9 and 27/25, and as the difference between 81/80 and 25/24. 5/4 is equated to 1 octave minus 5 generators. Some porcupine temperaments include [[15edo|15]], [[22edo|22]], [[37edo|37]], and [[59edo|59]] EDOs. An important 7-limit extension also tempers out 64/63.
-; [[Tricot family|Tricot or Quadsa-triyo family]] (P8, P11/3)
+; [[Tricot family|Tricot or Quadsa-triyoti family]] (P8, P11/3)
-: The tricot family tempers out the [[Tricot|tricot comma]], {{Monzo| 39 -29 3 }}. The generator is {{nowrap|~59049/40960 {{=}} {{monzo| -13 10 -1 }} {{=}} 633¢}}, or its octave inverse {{nowrap|~81920/59049 {{=}} 567¢}}. Three of the latter generators equals a compound 4th of ~8/3. 5/4 is equated to 14 octaves minus 29 of these generators. An obvious 7-limit interpretation of the generator is {{nowrap|81/56 {{=}} 639¢}}, a much simpler ratio which leads to the [[Tour of Regular Temperaments#Latriru clan (P8, P11/3)|Latriru clan]]. An obvious 13-limit interpretation is {{nowrap|13/9 {{=}} 637¢}}, an even simpler ratio implying the [[Tour of Regular Temperaments #Satritho clan (P8, P11/3)|Satritho clan]].
+: The tricot family tempers out the [[Tricot|tricot comma]], {{Monzo| 39 -29 3 }}. The generator is {{nowrap|~59049/40960 {{=}} {{monzo| -13 10 -1 }} {{=}} 633¢}}, or its octave inverse {{nowrap|~81920/59049 {{=}} 567¢}}. Three of the latter generators equals a compound 4th of ~8/3. 5/4 is equated to 14 octaves minus 29 of these generators. An obvious 7-limit interpretation of the generator is {{nowrap|81/56 {{=}} 639¢}}, a much simpler ratio which leads to the [[Tour of Regular Temperaments#Latriruti clan (P8, P11/3)|Latriruti clan]]. An obvious 13-limit interpretation is {{nowrap|13/9 {{=}} 637¢}}, an even simpler ratio implying the [[Tour of Regular Temperaments #Satrithoti clan (P8, P11/3)|Satrithoti clan]].
-; [[Dimipent family|Dimipent or Quadgu family]] (P8/4, P5)
+; [[Dimipent family|Dimipent or Quadguti family]] (P8/4, P5)
 : The dimipent (or diminished) family tempers out the major diesis or diminished comma, {{Monzo| 3 4 -4 }} or [[648/625]], the amount by which four 6/5 minor thirds exceed an octave, and so identifies the minor third with the quarter-octave. Hence it has the same 300-cent 6/5-approximations as [[12edo|12EDO]]. 5/4 is equated to 1 fifth minus 1 period.
-; [[Undim family|Undim or Trisa-quadgu family]] (P8/4, P5)
+; [[Undim family|Undim or Trisa-quadguti family]] (P8/4, P5)
 : The undim family tempers out the [[undim comma]] of {{monzo| 41 -20 -4 }}, the difference between the Pythagorean comma and a stack of four schismas.
-; [[Negri|Negri or Laquadyo family]] (P8, P4/4)
+; [[Negri|Negri or Laquadyoti family]] (P8, P4/4)
 : This tempers out the [[negri comma]], {{Monzo| -14 3 4 }}. Its generator is ~16/15, four of which make ~4/3. 5/4 is equated to 3 generators.
-; [[Tetracot family|Tetracot or Saquadyo family]] (P8, P5/4)
+; [[Tetracot family|Tetracot or Saquadyoti family]] (P8, P5/4)
 : The tetracot family is a much higher accuracy affair than the dicot family. Instead of taking two neutral thirds to reach 3/2, it takes four minor (10/9) whole tones. Four of these exceed 3/2 by {{Monzo| 5 -9 4 }} (20000/19683), the minimal diesis or [[tetracot comma]]. 5/4 is equated to 9 generators minus an octave. [[7edo|7EDO]] can also be considered a tetracot tuning, as can [[20edo|20EDO]], [[27edo|27EDO]], [[34edo|34EDO]], and [[41edo|41EDO]].
-; [[Smate family|Smate or Saquadgu family]] (P8, P11/4)
+; [[Smate family|Smate or Saquadguti family]] (P8, P11/4)
 : This tempers out the symbolic comma, {{nowrap|{{Monzo| 11 -1 -4 }} {{=}} 2048/1875}}. Its generator is {{nowrap|~5/4 {{=}} ~421¢}}, four of which make ~8/3.
-; [[Vulture family|Vulture or Sasa-quadyo family]] (P8, P12/4)
+; [[Vulture family|Vulture or Sasa-quadyoti family]] (P8, P12/4)
-: This tempers out the [[vulture comma]], {{Monzo| 24 -21 4 }}. Its generator is {{nowrap|~320/243 {{=}} ~475¢}}, four of which make ~3/1. 5/4 is equated to 21 generators minus 8 octaves. An obvious 7-limit interpretation of the generator is 21/16, which makes Saquadru.
+: This tempers out the [[vulture comma]], {{Monzo| 24 -21 4 }}. Its generator is {{nowrap|~320/243 {{=}} ~475¢}}, four of which make ~3/1. 5/4 is equated to 21 generators minus 8 octaves. An obvious 7-limit interpretation of the generator is 21/16, which makes Saquadruti.
-; [[Pental family|Pental or Trila-quingu family]] (P8/5, P5)
+; [[Pental family|Pental or Trila-quinguti family]] (P8/5, P5)
-: This tempers out the pental comma, {{nowrap|847288609443/838860800000 {{=}} {{Monzo| -28 25 -5 }}}}. The period is ~59049/51200, and 5 periods make an octave. The generator is a 5th, or equivalently, 3/5 of an 8ve minus a 5th. This alternate generator is only about 18¢, thus the scales have a very lopsided L/s ratio.  5/4 is equated to 2/5 of an octave minus 5 of these 18¢ generators. An obvious 7-limit interpretation of the generator is 8/7, which leads to Laquinzo.
+: This tempers out the pental comma, {{nowrap|847288609443/838860800000 {{=}} {{Monzo| -28 25 -5 }}}}. The period is ~59049/51200, and 5 periods make an octave. The generator is a 5th, or equivalently, 3/5 of an 8ve minus a 5th. This alternate generator is only about 18¢, thus the scales have a very lopsided L/s ratio.  5/4 is equated to 2/5 of an octave minus 5 of these 18¢ generators. An obvious 7-limit interpretation of the generator is 8/7, which leads to Laquinzoti.
-; [[Ripple family|Ripple or Quingu family]] (P8, P4/5)
+; [[Ripple family|Ripple or Quinguti family]] (P8, P4/5)
 : This tempers out the ripple comma, {{nowrap|6561/6250 {{=}} {{monzo| -1 8 -5 }}}}, which equates a stack of four [[10/9]]'s with [[8/5]], and five of them with [[16/9]]. The generator is [[27/25]], two of which equals 10/9, three of which equals [[6/5]], and five of which equals [[4/3]]. 5/4 is equated to an octave minus 8 generators. As one might expect, [[12edo|12EDO]] is about as accurate as it can be.
-; [[Passion family|Passion or Saquingu family]] (P8, P4/5)
+; [[Passion family|Passion or Saquinguti family]] (P8, P4/5)
 : This tempers out the passion comma, {{nowrap|262144/253125 {{=}} {{monzo| 18 -4 -5 }}}}, which equates a stack of four [[16/15]]'s with [[5/4]], and five of them with [[4/3]].
-; [[Quintaleap family|Quintaleap or Trisa-quingu family]] (P8, P4/5)
+; [[Quintaleap family|Quintaleap or Trisa-quinguti family]] (P8, P4/5)
-: This tempers out the ''quintaleap'' comma, {{monzo| 37 -16 -5 }}. The generator is ~135/128, five of them gives ~4/3, and sixteen of them gives [[5/2]]. An obvious 17-limit interpretation of the generator is ~18/17, which makes saquinso.
+: This tempers out the ''quintaleap'' comma, {{monzo| 37 -16 -5 }}. The generator is ~135/128, five of them gives ~4/3, and sixteen of them gives [[5/2]]. An obvious 17-limit interpretation of the generator is ~18/17, which makes Saquinsoti.
-; [[Quindromeda family|Quindromeda or Quinsa-quingu family]] (P8, P4/5)
+; [[Quindromeda family|Quindromeda or Quinsa-quinguti family]] (P8, P4/5)
-: This tempers out the ''quindromeda'' comma, {{monzo| 56 -28 -5 }}. The generator is ~4428675/4194304, five of them gives ~4/3, and 28 of them gives the fifth harmonic, [[5/1]]. An obvious 17-limit interpretation of the generator is ~18/17, which makes saquinso.
+: This tempers out the ''quindromeda'' comma, {{monzo| 56 -28 -5 }}. The generator is ~4428675/4194304, five of them gives ~4/3, and 28 of them gives the fifth harmonic, [[5/1]]. An obvious 17-limit interpretation of the generator is ~18/17, which makes Saquinsoti.
-; [[Amity family|Amity or Saquinyo family]] (P8, P11/5)
+; [[Amity family|Amity or Saquinyoti family]] (P8, P11/5)
-: This tempers out the [[amity comma]], {{nowrap|1600000/1594323 {{=}} {{monzo| 9 -13 5 }}}}. The generator is {{nowrap|243/200 {{=}} ~339.5¢}}, five of which make ~8/3. 5/4 is equated to 4 octaves minus 13 generators, or 2 fifths minus 3 generators. An obvious 11-limit interpretation of the generator is 11/9, which makes Saquinlo. An obvious 13-limit interpretation of the generator is 39/32, which makes Lala-quintho.
+: This tempers out the [[amity comma]], {{nowrap|1600000/1594323 {{=}} {{monzo| 9 -13 5 }}}}. The generator is {{nowrap|243/200 {{=}} ~339.5¢}}, five of which make ~8/3. 5/4 is equated to 4 octaves minus 13 generators, or 2 fifths minus 3 generators. An obvious 11-limit interpretation of the generator is 11/9, which makes Saquinloti. An obvious 13-limit interpretation of the generator is 39/32, which makes Lala-quinthoti.
-; [[Magic family|Magic or Laquinyo family]] (P8, P12/5)
+; [[Magic family|Magic or Laquinyoti family]] (P8, P12/5)
 : The magic family tempers out {{Monzo| -10 -1 5 }} (3125/3072), known as the [[magic comma]] or small diesis, which is the difference between five 5/4's (3125/2048) and a 3/1. The generator is itself an approximate 5/4. The magic family includes [[16edo|16]], [[19edo|19]], [[22edo|22]], [[25edo|25]], and [[41edo|41]] EDOs among its possible tunings, with the latter being near-optimal.
-; [[Fifive family|Fifive or Saquinbiyo family]] (P8/2, P5/5)
+; [[Fifive family|Fifive or Saquinbiyoti family]] (P8/2, P5/5)
 : This tempers out the fifive comma, {{nowrap|{{Monzo| -1 -14 10 }} {{=}} 9765625/9565938}}. The period is ~{{nowrap|4374/3125 {{=}} {{monzo| 1 7 -5 }}}}, two of which make an octave. The generator is ~27/25, five of which make ~3/2.  5/4 is equated to 7 generators minus 1 period.
-; [[Quintosec family|Quintosec or Quadsa-quinbigu family]] (P8/5, P5/2)
+; [[Quintosec family|Quintosec or Quadsa-quinbiguti family]] (P8/5, P5/2)
 : This tempers out the quintosec comma, {{nowrap|140737488355328/140126044921875 {{=}} {{monzo| 47 -15 -10 }}}}. The period is ~{{nowrap|524288/455625 {{=}} {{monzo| 19 -6 -4 }}}}, five of which equals an octave. The generator is ~16/15. A period plus a generator makes half a fifth. 5/4 is equated to 3 periods minus 3 generators. An obvious 7-limit interpretation of the period is 8/7.
-; [[Trisedodge family|Trisedodge or Saquintrigu family]] (P8/5, P4/3)
+; [[Trisedodge family|Trisedodge or Saquintriguti family]] (P8/5, P4/3)
 : This tempers out the trisedodge comma, {{nowrap|30958682112/30517578125 {{=}} {{monzo| 19 10 -15 }}}}. The period is {{nowrap|~144/125 {{=}} 240¢}}. The generator is ~6/5. Six periods minus three generators equals ~4/3. 5/4 is equated to 2 generators minus 1 period. An obvious 7-limit interpretation of the period is 8/7.
-; [[Ampersand|Ampersand or Lala-tribiyo family]] (P8, P5/6)
+; [[Ampersand|Ampersand or Lala-tribiyoti family]] (P8, P5/6)
 : This tempers out Ampersand's comma, {{nowrap|34171875/33554432 {{=}} {{monzo| -25 7 6 }}}}. The generator is ~16/15, of which six make ~3/2. 5/4 is equated to 1 octave minus 7 generators. If the generator is also equated to ~15/14, and three generators to ~11/9, one gets the [[Miracle]] temperament.
-; [[Kleismic family|Kleismic or Tribiyo family]] (P8, P12/6)
+; [[Kleismic family|Kleismic or Tribiyoti family]] (P8, P12/6)
 : The kleismic family of temperaments tempers out the [[kleisma]] {{nowrap|{{Monzo| -6 -5 6 }} {{=}} 15625/15552}}, which is the difference between six 6/5's and 3/1. It takes a slightly sharpened minor third as a generator, optimally tuned about 1.4 cents sharp.  5/4 is equated to 5 generators minus 1 octave. The kleismic family includes [[15edo|15]], [[19edo|19]], [[34edo|34]], [[49edo|49]], [[53edo|53]], [[72edo|72]], [[87edo|87]] and [[140edo|140]] EDOs among its possible tunings.
-; [[Semicomma family|Orson, semicomma or Lasepyo family]] (P8, P12/7)
+; [[Semicomma family|Orson, semicomma or Lasepyoti family]] (P8, P12/7)
 : The [[semicomma]] (also known as Fokker's comma), {{nowrap|2109375/2097152 {{=}} {{monzo| -21 3 7 }}}}, is tempered out by the members of the semicomma family. Its generator is ~75/64, seven of which equals ~3/1. 5/4 is equated to 1 octave minus 3 generators. This temperament doesn't have much independent existence as a 5-limit temperament, since its generator has a natural interpretation as ~7/6, leading to [[orwell|Orwell or Sepru]] temperament.
-; [[Wesley family|Wesley or Lasepyobi family]] (P8, ccP4/7)
+; [[Wesley family|Wesley or Lasepyobiti family]] (P8, ccP4/7)
-: This tempers out the wesley comma, {{nowrap|{{Monzo| -13 -2 7 }} {{=}} 78125/73728}}. The generator is {{nowrap|~125/96 {{=}} ~412¢}}. Seven generators equals a double-compound 4th of ~16/3. 5/4 is equated to 1 octave minus 2 generators. An obvious 7-limit interpretation of the generator is 9/7, leading to the Lasepru temperament. An obvious 3-limit interpretation of the generator is 81/64, implying [[29edo|29EDO]].
+: This tempers out the wesley comma, {{nowrap|{{Monzo| -13 -2 7 }} {{=}} 78125/73728}}. The generator is {{nowrap|~125/96 {{=}} ~412¢}}. Seven generators equals a double-compound 4th of ~16/3. 5/4 is equated to 1 octave minus 2 generators. An obvious 7-limit interpretation of the generator is 9/7, leading to the Lasepruti temperament. An obvious 3-limit interpretation of the generator is 81/64, implying [[29edo|29EDO]].
-; [[Sensipent family|Sensipent or Sepgu family]] (P8, ccP5/7)
+; [[Sensipent family|Sensipent or Sepguti family]] (P8, ccP5/7)
-: The sensipent (sensi) family tempers out the [[sensipent comma]], {{Monzo| 2 9 -7 }} (78732/78125), also known as the medium semicomma. Its generator is {{nowrap|~162/125 {{=}} ~443¢}}. Seven generators equals a double-compound 5th of ~6/1. 5/4 is equated to 9 generators minus 3 octaves. Tunings include [[8edo|8EDO]], [[19edo|19EDO]], [[46edo|46EDO]], and [[65edo|65EDO]]. An obvious 7-limit interpretation of the generator is 9/7, leading to the Sasepzo temperament.
+: The sensipent (sensi) family tempers out the [[sensipent comma]], {{Monzo| 2 9 -7 }} (78732/78125), also known as the medium semicomma. Its generator is {{nowrap|~162/125 {{=}} ~443¢}}. Seven generators equals a double-compound 5th of ~6/1. 5/4 is equated to 9 generators minus 3 octaves. Tunings include [[8edo|8EDO]], [[19edo|19EDO]], [[46edo|46EDO]], and [[65edo|65EDO]]. An obvious 7-limit interpretation of the generator is 9/7, leading to the Sasepzoti temperament.
-; [[Vishnuzmic family|Vishnuzmic or Sasepbigu family]] (P8/2, P4/7)
+; [[Vishnuzmic family|Vishnuzmic or Sasepbiguti 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)^7. The period is ~{{Monzo| -11 -3 7 }} and the generator is ~25/24. 5/4 is equated to 1 period minus 3 generators.
-; [[Unicorn family|Unicorn or Laquadbigu family]] (P8, P4/8)
+; [[Unicorn family|Unicorn or Laquadbiguti family]] (P8, P4/8)
 : This tempers out the unicorn comma, {{nowrap|1594323/1562500 {{=}} {{monzo| -2 13 -8 }}}}. The generator is {{nowrap|~250/243 {{=}} ~62¢}} and eight of them equal ~4/3.
-; [[Würschmidt family|Würschmidt or Saquadbigu family]] (P8, ccP5/8)
+; [[Würschmidt family|Würschmidt or Saquadbiguti family]] (P8, ccP5/8)
 : The würschmidt (or wuerschmidt) family tempers out the {{monzo|[Würschmidt comma]], {{nowrap|393216/390625 {{=}} {{monzo| 17 1 -8 }}}}. Würschmidt itself has a generator of a major third, eight of which give a 6/1 (the 6th harmonic, or a double-compound perfect 5th); that is, {{nowrap|(5/4)<sup}}8</sup> * (393216/390625) {{=}} 6}}. It tends to generate the same MOSs as [[Magic_family|magic temperament]], but is tuned slightly more accurately. Both [[31edo|31EDO]] and [[34edo|34EDO]] can be used as würschmidt tunings, as can [[65edo|65EDO]], which is quite accurate.
-; [[Escapade family|Escapade or Sasa-tritrigu family]] (P8, P4/9)
+; [[Escapade family|Escapade or Sasa-tritriguti family]] (P8, P4/9)
-: This tempers out the [[escapade comma]], {{Monzo| 32 -7 -9 }}, which is the difference between nine just major thirds and seven just fourths. The generator is {{nowrap|{{Monzo| -14 3 4 }} {{=}} ~55¢}} and nine of them equal ~4/3. Seven of them equal ~5/4, thus two of them equal ~16/15. An obvious 11-limit interpretation of the generator is 33/32, leading to the Trisa-tritrilu temperament.
+: This tempers out the [[escapade comma]], {{Monzo| 32 -7 -9 }}, which is the difference between nine just major thirds and seven just fourths. The generator is {{nowrap|{{Monzo| -14 3 4 }} {{=}} ~55¢}} and nine of them equal ~4/3. Seven of them equal ~5/4, thus two of them equal ~16/15. An obvious 11-limit interpretation of the generator is 33/32, leading to the Trisa-tritriluti temperament.
-; [[Shibboleth family|Shibboleth or Tritriyo family]] (P8, ccP4/9)
+; [[Shibboleth family|Shibboleth or Tritriyoti family]] (P8, ccP4/9)
 : This tempers out the shibboleth comma, {{nowrap|{{Monzo| -5 -10 9 }} {{=}} 1953125/1889568}}. Nine generators of ~6/5 equal a double compound 4th of ~16/3.  5/4 is equated to 3 octaves minus 10 generators.
-; [[Mabila family|Mabila or Sasa-quinbigu family]] (P8, c4P4/10)
+; [[Mabila family|Mabila or Sasa-quinbiguti family]] (P8, c4P4/10)
 : The mabila family tempers out the mabila comma, {{nowrap|{{Monzo| 28 -3 -10 }} {{=}} 268435456/263671875}}. The generator is {{nowrap|~512/375 {{=}} ~530¢}}, three generators equals ~5/2 and ten of them equals a quadruple-compound 4th of ~64/3. An obvious 11-limit interpretation of the generator is ~15/11.
-; [[Sycamore family|Sycamore or Laleyo family]] (P8, P5/11)
+; [[Sycamore family|Sycamore or Laleyoti family]] (P8, P5/11)
 : The sycamore family tempers out the sycamore comma, {{nowrap|{{Monzo| -16 -6 11 }} {{=}} 48828125/47775744}}, which is the amount by which five stacked chromatic semitones, 25/24, exceed 6/5, and hence also the amount six exceeds 5/4. Eleven of these generators equals ~3/2.
-; [[Quartonic family|Quartonic or Saleyo family]] (P8, P4/11)
+; [[Quartonic family|Quartonic or Saleyoti family]] (P8, P4/11)
 : The quartonic family tempers out the quartonic comma, {{nowrap|{{Monzo| 3 -18 11 }} {{=}} 390625000/387420489}}. The generator is {{nowrap|~250/243 {{=}} ~45¢}}, seven generators equals ~6/5, and eleven generators equals ~4/3. An obvious 7-limit interpretation of the generator is ~36/35.
-; [[Lafa family|Lafa or Tribisa-quadtrigu family]] (P8, P12/12)
+; [[Lafa family|Lafa or Tribisa-quadtriguti family]] (P8, P12/12)
 : This tempers out the lafa comma, {{Monzo| 77 -31 -12 }}. The generator is {{nowrap|~4982259375/4294967296 {{=}} ~258.6¢}}. Twelve generators equals a twelfth (~3/1). 5/4 is equated to 7 octaves minus 31 generators.
-; [[Ditonmic family|Ditonmic or Lala-theyo family]] (P8, c4P4/13)
+; [[Ditonmic family|Ditonmic or Lala-theyoti family]] (P8, c4P4/13)
 : This tempers out the ditonma, {{nowrap|{{Monzo| -27 -2 13 }} {{=}} 1220703125/1207959552}}. Thirteen ~{{Monzo| -12 -1 6 }} generators of about 407¢ equals a quadruple-compound 4th.  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.
-; [[Luna family|Luna or Sasa-quintrigu family]] (P8, ccP4/15)
+; [[Luna family|Luna or Sasa-quintriguti family]] (P8, ccP4/15)
 : This tempers out the luna comma, {{nowrap|{{Monzo| 38 -2 -15 }} {{=}} 274877906944/274658203125}}. The generator is {{nowrap|~{{Monzo| 18 -1 -7 }} {{=}} ~193¢}}. Two generators equals ~5/4, and fifteen generators equals a double-compound 4th of ~16/3.
-; [[Vavoom family|Vavoom or Quinla-seyo family]] (P8, P12/17)
+; [[Vavoom family|Vavoom or Quinla-seyoti family]] (P8, P12/17)
 : This tempers out the vavoom comma, {{Monzo| -68 18 17 }}. The generator is {{nowrap|~16/15 {{=}} ~111.9¢}}. Seventeen generators equals a twelfth (~3/1). 5/4 is equated to two octaves minus 18 generators.
-; [[Minortonic family|Minortonic or Trila-segu family]] (P8, ccP5/17)
+; [[Minortonic family|Minortonic or Trila-seguti 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 5th (~6/1). 5/4 is equated to 35 generators minus 5 octaves.
-; [[Maja family|Maja or Saseyo family]] (P8, c6P4/17)
+; [[Maja family|Maja or Saseyoti family]] (P8, c<sup>6</sup>P4/17)
 : This tempers out the maja comma, {{nowrap|{{Monzo| -3 -23 17 }} {{=}} 762939453125/753145430616}}. The generator is {{nowrap|~162/125 {{=}} ~453¢}}. Seventeen generators equals a sextuple-compound 4th. 5/4 is equated to 9 octaves minus 23 generators.
-; [[Maquila family|Maquila or Trisa-segu family]] (P8, c7P5/17)
+; [[Maquila family|Maquila or Trisa-seguti family]] (P8, c<sup>7</sup>P5/17)
-: This tempers out the maquila comma, {{nowrap|562949953421312/556182861328125 {{=}} {{monzo| 49 -6 -17 }}}}. The generator is {{nowrap|~512/375 {{=}} ~535¢}}. Seventeen generators equals a septuple-compound 5th.  5/4 is equated to 3 octaves minus 6 generators. An obvious 11-limit interpretation of the generator is 11/8, leading to the Lala-selo temperament. However, Lala-selo isn't nearly as accurate as Trisa-segu.
+: This tempers out the maquila comma, {{nowrap|562949953421312/556182861328125 {{=}} {{monzo| 49 -6 -17 }}}}. The generator is {{nowrap|~512/375 {{=}} ~535¢}}. Seventeen generators equals a septuple-compound 5th.  5/4 is equated to 3 octaves minus 6 generators. An obvious 11-limit interpretation of the generator is 11/8, leading to the Lala-seloti temperament. However, Lala-seloti isn't nearly as accurate as Trisa-seguti.
-; [[Gammic family|Gammic or Laquinquadyo family]] (P8, P5/20)
+; [[Gammic family|Gammic or Laquinquadyoti family]] (P8, P5/20)
 : The gammic family tempers out the gammic comma, {{Monzo| -29 -11 20 }}. Nine generators of about 35¢ 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 Neptune temperament.
@@ Line 181: / Line 181: @@
 If a 5-limit comma defines a family of rank two temperaments, then we might say a comma belonging to another [[Just_intonation_subgroups|subgroup]] of the 7-limit can define a clan. In particular we might say a triprime comma (one with exactly three primes in the factorization) can define a clan. We can modify the definition of [[Normal_lists|normal comma list]] for clans by changing the ordering of prime numbers, and using this to sort out clan relationships.
-; [[Archytas clan|Archytas or Ru clan]] (P8, P5)
+; [[Archytas clan|Archytas or Ruti clan]] (P8, P5)
 : This clan tempers out the Archytas comma, [[64/63]]. It equates 7/4 with 16/9. The clan consists of rank two temperaments, and should not be confused with the [[archytas family]] of rank three temperaments. Its best downward extension is [[superpyth]].
-; [[Trienstonic clan|Trienstonic or Zo clan]] (P8, P5)
+; [[Trienstonic clan|Trienstonic or Zoti clan]] (P8, P5)
 : This clan tempers out the septimal third-tone [[28/27]], a low-accuracy temperament that equates 7/6 with 9/8, and 7/4 with 27/16.
-; [[Harrison's comma|Harrison or Laru clan]] (P8, P5)
+; [[Harrison's comma|Harrison or Laruti clan]] (P8, P5)
 : This clan tempers out the Laru comma, {{nowrap|{{Monzo| -13 10 0 -1 }} {{=}} 59049/57344}}. It equates 7/4 to an augmented 6th. Its best downward extension is [[Meantone family|septimal meantone]].
-; [[Garischismic clan|Garischismic or Sasaru clan]] (P8, P5)
+; [[Garischismic clan|Garischismic or Sasaruti clan]] (P8, P5)
 : This clan tempers out the [[garischisma]], {{nowrap|{{Monzo| 25 -14 0 -1 }} {{=}} 33554432/33480783}}. It equates 8/7 to two apotomes ({{nowrap|{{Monzo| -11 7 }} {{=}} 2187/2048}}) and 7/4 to a double-diminished 8ve {{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]].
-; Leapfrog or Sasazo clan (P8, P5)
+; Leapfrog or Sasazoti clan (P8, P5)
 : This clan tempers out the Sasazo comma, {{nowrap|{{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]].
-; [[Slendro clan|Slendro (Semaphore) or Zozo clan]] (P8, P4/2)
+; Laruruti clan (P8/2, P5)
+: This clan tempers out the Laruru comma, {{nowrap|{{Monzo| -7 8 0 -2 }} {{=}} 6561/6272}}. Two ~81/56 periods equal an 8ve. The generator is ~3/2, and four generators minus three periods equals ~7/4. The major 2nd ~9/8 is divided in half, with each half equated to ~28/27. See also the Diaschismic or Saguguti temperament and the Jubilismic or Biruyoti temperament.
+; [[Slendro clan|Slendro (Semaphore) or Zozoti clan]] (P8, P4/2)
 : This clan tempers out the slendro diesis, [[49/48]]. Its generator is ~8/7 or ~7/6. Its best downward extension is [[godzilla]]. See also [[Semaphore]].
-; Laruru clan (P8/2, P5)
+; Parahemif or Sasa-zozoti clan (P8, P5/2)
-: This clan tempers out the Laruru comma, {{nowrap|{{Monzo| -7 8 0 -2 }} {{=}} 6561/6272}}. Two ~81/56 periods equal an 8ve. The generator is ~3/2, and four generators minus three periods equals ~7/4. The major 2nd ~9/8 is divided in half, with each half equated to ~28/27. See also the Diaschismic or Sagugu temperament and the Jubilismic or Biruyo temperament.
+: This clan tempers out the parahemif comma, {{nowrap|{{Monzo| 15 -13 0 2 }} {{=}} 1605632/1594323}}, and includes the [[hemif]] temperament and its strong extension [[hemififths]]. 7/4 is equated to 13 generators minus 3 octaves. An obvious 11-limit interpretation of the ~351¢ generator is 11/9, leading to the Luluti temperament.
-; Parahemif or Sasa-zozo clan (P8, P5/2)
+; Triruti clan (P8/3, P5)
-: This clan tempers out the parahemif comma, {{nowrap|{{Monzo| 15 -13 0 2 }} {{=}} 1605632/1594323}}, and includes the [[hemif]] temperament and its strong extension [[hemififths]]. 7/4 is equated to 13 generators minus 3 octaves. An obvious 11-limit interpretation of the ~351¢ generator is 11/9, leading to the Lulu temperament.
+: This clan tempers out the Triru comma, {{nowrap|{{Monzo| -1 6 0 -3 }} {{=}} 729/686}}, a low-accuracy temperament. Three ~9/7 periods equals an 8ve. The generator is ~3/2, and two generators minus a period equals ~7/4. An obvious 5-limit interpretation of the ~400¢ period is 5/4, leading to the [[augmented]] temperament.
-; [[Gamelismic clan|Gamelismic or Latrizo clan]] (P8, P5/3)
+; [[Gamelismic clan|Gamelismic or Latrizoti clan]] (P8, P5/3)
-: This clan tempers out the gamelisma, {{nowrap|{{Monzo| -10 1 0 3 }} {{=}} 1029/1024}}. Three ~8/7 generators equals a 5th. 7/4 is equated to an 8ve minus a generator. Five generators is slightly flat of 2/1, making this a [[cluster temperament]]. See also Sawa and Lasepzo.
+: This clan tempers out the gamelisma, {{nowrap|{{Monzo| -10 1 0 3 }} {{=}} 1029/1024}}. Three ~8/7 generators equals a 5th. 7/4 is equated to an 8ve minus a generator. Five generators is slightly flat of 2/1, making this a [[cluster temperament]]. See also Sawati and Lasepzoti.
 : A particularly noteworthy member of the gamelismic clan is miracle, but other members include valentine, unidec, mothra, rodan, and hemithirds. Miracle temperament divides the fifth into 6 equal steps, thus it's a weak extension. Its 21-note scale called "blackjack" and 31-note scale called "canasta" have some useful properties. It is the most efficient 11-limit temperament for many purposes, with a tuning close to 72EDO.
-; Trizo clan (P8, P5/3)
+; Trizoti clan (P8, P5/3)
-: This clan tempers out the Trizo comma, {{nowrap|{{Monzo| -2 -4 0 3 }} {{=}} 343/324}}, a low-accuracy temperament. Three ~7/6 generators equals a 5th, and four equal ~7/4. An obvious interpretation of the ~234¢ generator is 8/7, leading to the much more accurate Gamelismic or Latrizo temperament.
+: This clan tempers out the Trizo comma, {{nowrap|{{Monzo| -2 -4 0 3 }} {{=}} 343/324}}, a low-accuracy temperament. Three ~7/6 generators equals a 5th, and four equal ~7/4. An obvious interpretation of the ~234¢ generator is 8/7, leading to the much more accurate Gamelismic or Latrizoti temperament.
-; Triru clan (P8/3, P5)
+; Lee or Latriruti clan (P8, P11/3)
-: This clan tempers out the Triru comma, {{nowrap|{{Monzo| -1 6 0 -3 }} {{=}} 729/686}}, a low-accuracy temperament. Three ~9/7 periods equals an 8ve. The generator is ~3/2, and two generators minus a period equals ~7/4. An obvious 5-limit interpretation of the ~400¢ period is 5/4, leading to the [[augmented]] temperament.
-; Lee or Latriru clan (P8, P11/3)
 : This clan tempers out the Latriru comma, {{nowrap|{{Monzo| -9 11 0 -3 }} {{=}} 177147/175616}}. The generator is {{nowrap|~112/81 {{=}} ~566¢}}, and three such generators equals ~8/3. 7/4 is equated to 11 generators minus 5 octaves. An obvious 2.3.5.7 interpretation of the generator is 7/5, leading to the [[liese]] temperament, which is a weak extension of Meantone.
-; [[Stearnsmic clan|Stearnsmic or Latribiru clan]] (P8/2, P4/3)
+; [[Stearnsmic clan|Stearnsmic or Latribiruti clan]] (P8/2, P4/3)
 : This clan temper out the stearnsma, {{nowrap|{{Monzo| 1 10 0 -6 }} {{=}} 118098/117649}}. The period is {{nowrap|~486/343 {{=}} ~600¢}}. The generator is {{nowrap|~9/7 {{=}} ~434¢}}, or alternatively one period minus ~9/7, which equals {{nowrap|~54/49 {{=}} ~166¢}}. Three of these alternate generators equals ~4/3. 7/4 is equated to 5 ~9/7 generators minus an octave. Equating the ~54/49 generator to ~10/9 creates a weak extension of the [[porcupine]] temperament, as does equating the period to ~7/5.
-; Buzzardismic or Saquadru clan (P8, P12/4)
+; Skwares or Laquadruti clan (P8, P11/4)
+: This clan tempers out the Laquadru comma, {{nowrap|{{Monzo| -3 9 0 -4 }} {{=}} 19683/19208}}. its generator is ~9/7. Four generators equals ~8/3. 7/4 is equated to 4 octaves minus 9 generators. This clan includes as a strong extension the [[squares]] temperament, which is a weak extension of meantone.
+; Buzzardismic or Saquadruti clan (P8, P12/4)
 : This clan tempers out the ''buzzardisma'', {{nowrap|{{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. This clan includes as a strong extension the [[Vulture family|vulture]] temperament, which is in the vulture family.
-; Skwares or Laquadru clan (P8, P11/4)
+; [[Cloudy clan|Cloudy or Laquinzoti clan]] (P8/5, P5)
-: This clan tempers out the Laquadru comma, {{nowrap|{{Monzo| -3 9 0 -4 }} {{=}} 19683/19208}}. its generator is ~9/7. Four generators equals ~8/3. 7/4 is equated to 4 octaves minus 9 generators. This clan includes as a strong extension the [[squares]] temperament, which is a weak extension of meantone.
+: This clan tempers out the [[cloudy comma]], {{nowrap|{{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.
-; [[Cloudy clan|Cloudy or Laquinzo clan]] (P8/5, P5)
-: This clan tempers out the [[cloudy comma]], {{nowrap|{{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 Sawa family, ~3/2 is not equated with three-fifths of an octave, resulting in very small intervals.
-; Bleu or Quinru clan (P8, P5/5)
+; Bleu or Quinruti clan (P8, P5/5)
 : This clan tempers out the Quinru comma, {{nowrap|{{Monzo| 3 7 0 -5 }} {{=}} 17496/16807}}. The ~54/49 generator is about 139¢. Two of them equal ~7/6, three equal ~9/7, five equal ~3/2, and seven equal ~7/4.
-; Saquinzo clan (P8, P12/5)
+; Saquinzoti clan (P8, P12/5)
 : This clan tempers out the Saquinzo comma, {{nowrap|{{Monzo| 5 -12 0 5 }} {{=}} 537824/531441}}. Its generator is {{nowrap|~243/196 {{=}} ~380¢}}. 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.
-; Lasepzo clan (P8, P11/7)
+; Lasepzoti clan (P8, P11/7)
-: This clan tempers out the Lasepzo comma {{nowrap|{{Monzo| -18 -1 0 7 }} {{=}} 823543/786432}}. Its generator is ~8/7. Six generators equals ~7/3, and seven generators equals ~8/3. Three generators is ~30¢ sharp of 3/2, and five generators is ~15¢ sharp of 2/1, making this a [[cluster temperament]]. See also Sawa and Latrizo.
+: This clan tempers out the Lasepzo comma {{nowrap|{{Monzo| -18 -1 0 7 }} {{=}} 823543/786432}}. Its generator is ~8/7. Six generators equals ~7/3, and seven generators equals ~8/3. Three generators is ~30¢ sharp of 3/2, and five generators is ~15¢ sharp of 2/1, making this a [[cluster temperament]]. See also Sawati and Latrizoti.
-; Septiness or Sasasepru clan (P8, P11/7)
+; Septiness or Sasasepruti clan (P8, P11/7)
 : This clan tempers out the ''septiness'' comma {{nowrap|{{Monzo| 26 -4 0 -7 }} {{=}} 67108864/66706983}}. Its generator is ~147/128, four of them gives ~7/4, and seven of them gives ~8/3. Five generators is ~12.5¢ sharp of 2/1, making this a [[cluster temperament]].
-; Sepru clan (P8, P12/7)
+; Sepruti clan (P8, P12/7)
 : This clan tempers out the sepru comma, {{nowrap|{{Monzo| 7 8 0 -7 }} {{=}} 839808/823543}}. Its generator is ~7/6. Seven generators equals ~3/1. 7/4 is equated to 8 generators minus 1 octave. This clan includes as a strong extension the [[orwell]] temperament, which is in the Semicomma family.
-; [[Tritrizo clan]] (P8/9, P5)
+; [[Tritrizoti clan]] (P8/9, P5)
 : This clan tempers out the ''[[Septimal ennealimma|septiennealimma]]'' (tritrizo comma), {{nowrap|{{Monzo| -11 -9 0 9 }} {{=}} 40353607/40310784}}. It has a period of 1/9 octave, which represents ~7/6. The generator is ~3/2. This clan includes a number of regular temperaments including [[enneaportent]], [[ennealimmal]], and [[Kleismic family #Novemkleismic|novemkleismic]].
@@ Line 251: / Line 251: @@
 See also [[subgroup temperaments]].
-; Lulubi clan (P8/2, P5)
+; Lulubiti clan (P8/2, P5)
 : This low-accuracy 2.3.11 clan tempers out the Alpharabian limma, [[128/121]]. Both 11/8 and 16/11 are equated to half-octave period. This clan includes as a strong extension the pajaric temperament, which is in the diaschismic family.
-; [[Rastmic clan|Rastmic or Lulu clan]] (P8, P5/2)
+; [[Rastmic clan|Rastmic or Luluti clan]] (P8, P5/2)
 : This 2.3.11 clan tempers out {{nowrap|[[243/242]] {{=}} {{monzo| -1 5 0 0 -2 }}}}. Its generator is ~11/9. Two generators equals ~3/2. 11/8 is equated to 5 generators minus an octave. This clan includes as a strong extension the [[dicot]] temperament, which is in the dicot family.
-; [[Nexus clan|Nexus or Tribilo Clan]] (P8/3, P4/2)
+; [[Nexus clan|Nexus or Tribiloti clan]] (P8/3, P4/2)
 : This 2.3.11 clan tempers out the [[nexus comma]] {{monzo| -16 -3 0 0 6 }}. Its third-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.
-; Alphaxenic or Laquadlo clan (P8/2, M2/4)
+; Alphaxenic or Laquadloti 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 saquadyobi temperament, which is in the comic family.
+: 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 comic family.
 === Clans defined by a 2.3.13 (tha) comma ===
 See also [[subgroup temperaments]].
-; Thuthu clan (P8, P5/2)
+; Thuthuti clan (P8, P5/2)
 : This 2.3.13 clan tempers out {{nowrap|[[512/507]] {{=}} {{monzo| 9 -1 0 0 0 -2 }}}}. Its generator is ~16/13. Two generators equals ~3/2. 13/8 is equated to 1 octave minus 1 generator. This clan includes as a strong extension the [[Dicot]] temperament, which is in the Dicot family.
-; Threedie or Satritho clan (P8, P11/3)
+; Threedie or Satrithoti clan (P8, P11/3)
-: This 2.3.13 clan tempers out the threedie, {{nowrap|[[2197/2187]] {{=}} {{monzo| 0 -7 0 0 0 3 }}}}. Its generator is ~18/13, and three generators equals ~8/3. 13/8 is equated to 7 generators minus three octaves. This clan is related to the Latriru clan.
+: This 2.3.13 clan tempers out the threedie, {{nowrap|[[2197/2187]] {{=}} {{monzo| 0 -7 0 0 0 3 }}}}. Its generator is ~18/13, and three generators equals ~8/3. 13/8 is equated to 7 generators minus three octaves. This clan is related to the Latriruti clan.
 === Clans defined by a 2.5.7 (yaza nowa) comma ===
 These are defined by a yaza nowa or 7-limit-no-threes comma. See also [[subgroup temperaments]]. The pergen's multigen (the 2nd term, omitting any fraction) is always a 5-limit-no-threes ratio such as 5/4, 8/5, 25/8, etc.
-; [[Jubilismic clan|Jubilismic or Biruyo Nowa clan]] (P8/2, M3)
+; [[Jubilismic clan|Jubilismic or Biruyoti Nowa clan]] (P8/2, M3)
 : This clan tempers out the jubilisma, [[50/49]], which is the difference between 10/7 and 7/5. The generator is the nowa major 3rd (~5/4). The half-octave period is ~7/5 or ~10/7. 7/4 is equated to 1 period plus 1 generator.
-; Bapbo or Rurugu Nowa clan (P8, M3/2)
+; Bapbo or Ruruguti Nowa clan (P8, M3/2)
 : This clan tempers out the bapbo comma, [[256/245]]. The genarator is {{nowrap|~8/7 {{=}} ~202¢}} and two of them equals ~5/4.
-; [[Hemimean clan|Hemimean or Zozoquingu Nowa clan]] (P8, M3/2)
+; [[Hemimean clan|Hemimean or Zozoquinguti Nowa clan]] (P8, M3/2)
 : This clan tempers out the hemimean comma, {{nowrap|{{monzo| 6 0 -5 2 }} {{=}} 3136/3125}}. The generator is {{nowrap|~28/25 {{=}} ~194¢}}. Two generators equals the nowa major 3rd  (~5/4), three of them equals ~7/5, and five of them equals ~7/4.
-; [[Mabilismic clan|Mabilismic or Latrizo-aquiniyo Nowa clan]] (P8, cM3/3)
+; [[Mabilismic clan|Mabilismic or Latrizo-aquiniyoti Nowa clan]] (P8, cM3/3)
 : This clan tempers out the mabilisma, {{nowrap|{{monzo| -20 0 5 3 }} {{=}} 1071875/1048576}}. The generator is {{nowrap|~175/128 {{=}} ~527¢}}. Three generators equals ~5/2 and five of them equals ~32/7.
-; Vorwell or Sasatriru-aquadbigu Nowa clan (P8, m6/3)
+; Vorwell or Sasatriru-aquadbiguti Nowa clan (P8, m6/3)
 : This clan tempers out the vorwell comma (named for being tempered in [[septimal vulture]] and [[orwell]]), {{nowrap|{{monzo| 27 0 -8 -3 }} {{=}} 134217728/133984375}}. The rutrigu generator is {{nowrap|~1024/875 {{=}} ~272¢}}. Three generators equals ~8/5 and eight of them equals ~7/2.
-; Rainy or Quinzo-atriyo Nowa clan (P8, M3/5)
+; Rainy or Quinzo-atriyoti Nowa clan (P8, M3/5)
 : This clan tempers out the [[rainy comma]], {{nowrap|{{monzo| -21 0 3 5 }} {{=}} 2100875/2097152}}. The rurugu generator is {{nowrap|~256/245 {{=}} ~77¢}}. Three generators equals ~8/7 and five of them equals the classic major third (~5/4).
-; [[Llywelynsmic clan|Llywelynsmic or Sasepru-agu Nowa clan]] (P8, cM3/7)
+; [[Llywelynsmic clan|Llywelynsmic or Sasepru-aguti Nowa clan]] (P8, cM3/7)
 : This clan tempers out the [[llywelynsma]], {{nowrap|{{monzo| 22 0 -1 -7 }} {{=}} 4194304/4117715}}. The generator is {{nowrap|~8/7 {{=}} ~227¢}} and seven of them equals ~5/2.
-; [[Quince clan|Quince or Lasepzo-agugu Nowa clan]] (P8, m6/7)
+; [[Quince clan|Quince or Lasepzo-aguguti Nowa clan]] (P8, m6/7)
 : This clan tempers out the quince, {{nowrap|{{monzo| -15 0 -2 7 }} {{=}} 823543/819200}}. The trizo-agu generator is {{nowrap|~343/320 {{=}} ~116¢}}. Two generators equals ~8/7, five generators equals ~7/5, and seven generators equals the nowa minor 6th ~8/5. An obvious 5-limit interpretation of the generator is 16/15, leading to the [[miracle]] temperament, which is in the gamelismic clan.
-; Slither or Satritriru-aquadyo Nowa clan (P8, ccm6/9)
+; Slither or Satritriru-aquadyoti Nowa clan (P8, ccm6/9)
 : This clan tempers out the slither comma, {{nowrap|{{monzo| 16 0 4 -9 }} {{=}} 40960000/40353607}}. The generator is {{nowrap|~49/40 {{=}} ~357¢}}. Four generators equals ~16/7, five of them equals ~14/5, and nine of them equals a double-compound minor 6th of ~32/5.
@@ Line 305: / Line 305: @@
 These are defined by a yaza noca or 7-limit-no-twos comma. Any no-twos comma is a ratio of odd numbers. If no other commas are tempered out, It is a non-octave tuning, with a period of a perfect 12th or tritave, 3/1 (or some fraction of that). See also [[subgroup temperaments]]. The pergen's multigen (the 2nd term, omitting any fraction) is always a 5-limit-no-twos ratio such as 5/3, 9/5, 25/9, etc. In any noca subgroup, "compound" means increased by 3/1 not 2/1.
-; [[Arcturus clan|Arcturus or Rutribiyo Noca clan]] (P12, M6)
+; [[Arcturus clan|Arcturus or Rutribiyoti Noca clan]] (P12, M6)
 : This 3.5.7 clan tempers out the Arcturus comma {{nowrap|{{Monzo| 0 -7 6 -1 }} {{=}} 15625/15309}}. The generator is the noca major 6th (~5/3), and six generators equals ~21/1.
-; [[Sensamagic clan|Sensamagic or Zozoyo Noca clan]] (P12, M6/2)
+; [[Sensamagic clan|Sensamagic or Zozoyoti Noca clan]] (P12, M6/2)
 : This 3.5.7 clan tempers out the sensamagic comma {{nowrap|{{Monzo| 0 -5 1 2 }} {{=}} 245/243}}. The generator is ~9/7, and two generators equals the classic major 6th (~5/3).
-; [[Gariboh clan|Gariboh or Triru-aquinyo Noca clan]] (P12, M6/3)
+; [[Gariboh clan|Gariboh or Triru-aquinyoti Noca clan]] (P12, M6/3)
 : This 3.5.7 clan tempers out the gariboh comma {{nowrap|{{Monzo| 0 -2 5 -3 }} {{=}} 3125/3087}}. The generator is ~25/21, two generators equals ~7/5, and three generators equals the noca major 6th (~5/3).
-; [[Mirkwai clan|Mirkwai or Quinru-aquadyo Noca clan]] (P12, cm7/5)
+; [[Mirkwai clan|Mirkwai or Quinru-aquadyoti Noca clan]] (P12, cm7/5)
 : This 3.5.7 clan tempers out the mirkwai comma, {{nowrap|{{Monzo| 0 3 4 -5 }} {{=}} 16875/16807}}. The generator is ~7/5, four generators equals ~27/7, and five generators equals the noca compound minor 7th (~27/5).
-; Procyon or Sasepzo-atrigu Noca clan (P12, m7/7)
+; Procyon or Sasepzo-atriguti Noca clan (P12, m7/7)
 : This 3.5.7 clan tempers out the Procyon comma {{nowrap|{{Monzo| 0 -8 -3 7 }} {{=}} 823543/820125}}. The generator is ~49/45, three generators equals ~9/7, four equals ~7/5, and seven equals the classic minor seventh (~9/5).
-; Betelgeuse or Satritrizo-agugu Noca clan (P12, c<sup>3</sup>M6/9)
+; Betelgeuse or Satritrizo-aguguti Noca clan (P12, c<sup>3</sup>M6/9)
 : This 3.5.7 clan tempers out the Betelgeuse comma {{nowrap|{{Monzo| 0 -13 -2 9 }} {{=}} 40353607/39858075}}. The generator is ~3645/2401, two generators equals ~7/3, and nine generators equals the noca triple-compound major 6th (~45/1).
-; Izar or Saquadtrizo-asepgu Noca clan (P12, c<sup>5</sup>m7/12)
+; Izar or Saquadtrizo-asepguti Noca clan (P12, c<sup>5</sup>m7/12)
 : This 3.5.7 clan tempers out the Izar comma (also known as bapbo schismina), {{nowrap|{{Monzo| 0 -11 -7 12 }} {{=}} 13841287201/13839609375}}. The generator is ~16807/10125, five generators give ~63/5, seven give ~243/7, and twelve give ~2187/5.
@@ Line 329: / Line 329: @@
 These are defined by a full 7-limit (or yaza) comma.
-; [[Septisemi temperaments|Septisemi or Zogu temperaments]]
+; [[Septisemi temperaments|Septisemi or Zoguti temperaments]]
 : These are very low complexity temperaments tempering out the minor septimal semitone, [[21/20]] and hence equating 5/3 with 7/4.
-; [[Greenwoodmic temperaments|Greenwoodmic or Ruruyo temperaments]]
+; [[Greenwoodmic temperaments|Greenwoodmic or Ruruyoti temperaments]]
 : These temper out the greenwoodma, {{nowrap|{{Monzo| -3 4 1 -2 }} {{=}} 405/392}}.
-; [[Keegic temperaments|Keegic or Trizogu temperaments]]
+; [[Keegic temperaments|Keegic or Trizoguti temperaments]]
 : Keegic rank-two temperaments temper out the keega, {{nowrap|{{Monzo| -3 1 -3 3 }} {{=}} 1029/1000}}.
-; [[Mint temperaments|Mint or Rugu temperaments]]
+; [[Mint temperaments|Mint or Ruguti temperaments]]
 : Mint rank-two temperaments temper out the septimal quarter-tone 36/35, equating 7/6 with 6/5, and 5/4 with 9/7.
-; [[Avicennmic temperaments|Avicennmic or Zoyoyo temperaments]]
+; [[Avicennmic temperaments|Avicennmic or Zoyoyoti temperaments]]
 : These temper out the avicennma, {{nowrap|{{Monzo| -9 1 2 1 }} {{=}} 525/512}}, also known as Avicenna's enharmonic diesis.
-; Sengic or Trizo-agugu temperaments
+; Sengic or Trizo-aguguti temperaments
 : Sengic rank-two temperaments temper out the senga, {{nowrap|{{Monzo| 1 -3 -2 3 }} {{=}} 686/675}}.
-; [[Keemic temperaments|Keemic or Zotriyo temperaments]]
+; [[Keemic temperaments|Keemic or Zotriyoti temperaments]]
 : Keemic rank-two temperaments temper out the keema, {{nowrap|{{Monzo| -5 -3 3 1 }} {{=}} 875/864}}.
-; Secanticorn or Laruquingu temperaments
+; Secanticorn or Laruquinguti temperaments
 : Secanticorn rank-two temperaments temper out the ''secanticornisma'', {{nowrap|{{monzo| -3 11 -5 -1 }} {{=}} 177147/175000}}.
-; Nuwell or Quadru-ayo temperaments
+; Nuwell or Quadru-ayoti temperaments
 : Nuwell rank-two temperaments temper out the nuwell comma, {{nowrap|{{Monzo| 1 5 1 -4 }} {{=}} 2430/2401}}.
-; Mermismic or Sepruyo temperaments
+; Mermismic or Sepruyoti temperaments
 : Mermismic rank-two temperaments temper out the ''mermisma'', {{nowrap|{{Monzo| 5 -1 7 -7 }} {{=}} 2500000/2470629}}.
-; Negricorn or Saquadzogu temperaments
+; Negricorn or Saquadzoguti temperaments
 : Negricorn rank-two temperaments temper out the ''negricorn'' comma, {{nowrap|{{Monzo| 6 -5 -4 4 }} {{=}} 153664/151875}}.
-; Tolermic or Sazoyoyo temperaments
+; Tolermic or Sazoyoyoti temperaments
 : These temper out the tolerma, {{nowrap|{{Monzo| 10 -11 2 1 }} {{=}} 179200/177147}}.
-; Valenwuer or Sarutribigu temperaments
+; Valenwuer or Sarutribiguti temperaments
 : Valenwuer rank-two temperaments temper out the ''valenwuer'' comma, {{nowrap|{{Monzo| 12 3 -6 -1 }} {{=}} 110592/109375}}.
-; [[Mirwomo temperaments|Mirwomo or Labizoyo temperaments]]
+; [[Mirwomo temperaments|Mirwomo or Labizoyoti temperaments]]
 : Mirwomo rank-two temperaments temper out the mirwomo comma, {{nowrap|{{Monzo| -15 3 2 2 }} {{=}} 33075/32768}}.
-; Catasyc or Laruquadbiyo temperaments
+; Catasyc or Laruquadbiyoti temperaments
 : Catasyc rank-two temperaments temper out the ''catasyc'' comma, {{nowrap|{{Monzo| -11 -3 8 -1 }} {{=}} 390625/387072}}.
-; Compass or Quinruyoyo temperaments
+; Compass or Quinruyoyoti temperaments
 : Compass rank-two temperaments temper out the compass comma, {{nowrap|{{Monzo| -6 -2 10 -5 }} {{=}} 9765625/9680832}}.
-; Trimyna or Quinzogu temperaments
+; Trimyna or Quinzoguti temperaments
 : The trimyna rank-two temperaments temper out the trimyna comma, {{nowrap|{{Monzo| -4 1 -5 5 }} {{=}} 50421/50000}}.
-; [[Starling temperaments|Starling or Zotrigu temperaments]]
+; [[Starling temperaments|Starling or Zotriguti temperaments]]
 : Starling rank-two temperaments temper out the septimal semicomma or starling comma {{nowrap|{{Monzo| 1 2 -3 1 }} {{=}} [[126/125]]}}, the difference between three 6/5s plus one 7/6, and an octave. It includes myna, sensi, valentine, casablanca and nusecond temperaments, not to mention meantone, keemun, muggles and opossum.
-; [[Octagar temperaments|Octagar or Rurutriyo temperaments]]
+; [[Octagar temperaments|Octagar or Rurutriyoti temperaments]]
 : Octagar rank-two temperaments temper out the octagar comma, {{nowrap|{{Monzo| 5 -4 3 -2 }} {{=}} 4000/3969}}.
-; [[Orwellismic temperaments|Orwellismic or Triru-agu temperaments]]
+; [[Orwellismic temperaments|Orwellismic or Triru-aguti temperaments]]
 : Orwellismic rank-two temperaments temper out orwellisma, {{nowrap|{{Monzo| 6 3 -1 -3 }} {{=}} 1728/1715}}.
-; Mynaslendric or Sepru-ayo temperaments
+; Mynaslendric or Sepru-ayoti temperaments
 : Mynaslendric rank-two temperaments temper out the ''mynaslender'' comma, {{nowrap|{{Monzo| 11 4 1 -7 }} {{=}} 829440/823543}}.
-; [[Mistismic temperaments|Mistismic or Sazoquadgu temperaments]]
+; [[Mistismic temperaments|Mistismic or Sazoquadguti temperaments]]
 : Mistismic rank-two temperaments temper out the ''mistisma'', {{nowrap|{{Monzo| 16 -6 -4 1 }} {{=}} 458752/455625}}.
-; [[Varunismic temperaments|Varunismic or Labizogugu temperaments]]
+; [[Varunismic temperaments|Varunismic or Labizoguguti temperaments]]
 : Varunismic rank-two temperaments temper out the varunisma, {{nowrap|{{monzo| -9 8 -4 2 }} {{=}} 321489/320000}}.
-; [[Marvel temperaments|Marvel or Ruyoyo temperaments]]
+; [[Marvel temperaments|Marvel or Ruyoyoti temperaments]]
 : Marvel rank-two temperaments temper out {{nowrap|{{Monzo| -5 2 2 -1 }} {{=}} [[225/224]]}}. It includes negri, sharp, mavila, wizard, tritonic, septimin, slender, triton, escapade and marvo. Considered elsewhere are meantone, miracle, magic, pajara, orwell, catakleismic, garibaldi, august and compton.
-; Dimcomp or Quadruyoyo temperaments
+; Dimcomp or Quadruyoyoti temperaments
 : Dimcomp rank-two temperaments temper out the dimcomp comma, {{nowrap|{{Monzo| -1 -4 8 -4 }} {{=}} 390625/388962}}.
-; [[Cataharry temperaments|Cataharry or Labirugu temperaments]]
+; [[Cataharry temperaments|Cataharry or Labiruguti temperaments]]
 : Cataharry rank-two temperaments temper out the cataharry comma, {{nowrap|{{Monzo| -4 9 -2 -2 }} {{=}} 19683/19600}}.
-; [[Canousmic temperaments|Canousmic or Saquadzo-atriyo temperaments]]
+; [[Canousmic temperaments|Canousmic or Saquadzo-atriyoti temperaments]]
 : Canousmic rank-two temperaments temper out the canousma, {{nowrap|{{Monzo| 4 -14 3 4 }} {{=}} 4802000/4782969}}.
-; [[Triwellismic temperaments|Triwellismic or Tribizo-asepgu temperaments]]
+; [[Triwellismic temperaments|Triwellismic or Tribizo-asepguti temperaments]]
 : Triwellismic rank-two temperaments temper out the ''triwellisma'', {{nowrap|{{Monzo| 1 -1 -7 6 }} {{=}} 235298/234375}}.
-; [[Hemimage temperaments|Hemimage or Satrizo-agu temperaments]]
+; [[Hemimage temperaments|Hemimage or Satrizo-aguti temperaments]]
 : Hemimage rank-two temperaments temper out the hemimage comma, {{nowrap|{{Monzo| 5 -7 -1 3 }} {{=}} 10976/10935}}.
-; [[Hemifamity temperaments|Hemifamity or Saruyo temperaments]]
+; [[Hemifamity temperaments|Hemifamity or Saruyoti temperaments]]
 : Hemifamity rank-two temperaments temper out the hemifamity comma, {{nowrap|{{Monzo| 10 -6 1 -1 }} {{=}} 5120/5103}}.
-; [[Parkleiness temperaments|Parkleiness or Zotritrigu temperaments]]
+; [[Parkleiness temperaments|Parkleiness or Zotritriguti temperaments]]
 : Parkleiness rank-two temperaments temper out the ''parkleiness'' comma, {{nowrap|{{Monzo| 7 7 -9 1 }} {{=}} 1959552/1953125}}.
-; [[Porwell temperaments|Porwell or Sarurutrigu temperaments]]
+; [[Porwell temperaments|Porwell or Sarurutriguti temperaments]]
 : Porwell rank-two temperaments temper out the porwell comma, {{nowrap|{{Monzo| 11 1 -3 -2 }} {{=}} 6144/6125}}.
-; [[Cartoonismic temperaments|Cartoonismic or Satritrizo-asepbigu temperaments]]
+; [[Cartoonismic temperaments|Cartoonismic or Satritrizo-asepbiguti temperaments]]
 : Cartoonismic temperaments temper out the cartoonisma, {{nowrap|{{monzo| 12 -3 -14 9 }} {{=}} 165288374272/164794921875}}.
-; [[Hemfiness temperaments|Hemfiness or Saquinru-atriyo temperaments]]
+; [[Hemfiness temperaments|Hemfiness or Saquinru-atriyoti temperaments]]
 : Hemfiness rank-two temperaments temper out the ''hemfiness'' comma, {{nowrap|{{Monzo| 15 -5 3 -5 }} {{=}} 4096000/4084101}}.
-; [[Hewuermera temperaments|Hewuermera or Satribiru-agu temperaments]]
+; [[Hewuermera temperaments|Hewuermera or Satribiru-aguti temperaments]]
 : Hewuermera rank-two temperaments temper out the ''hewuermera'' comma, {{nowrap|{{Monzo| 16 2 -1 -6 }} {{=}} 589824/588245}}.
-; [[Lokismic temperaments|Lokismic or Sasa-bizotrigu temperaments]]
+; [[Lokismic temperaments|Lokismic or Sasa-bizotriguti temperaments]]
 : Lokismic rank-two temperaments temper out the ''lokisma'', {{nowrap|{{Monzo| 21 -8 -6 2 }} {{=}} 102760448/102515625}}.
-; Decovulture or Sasabirugugu temperaments
+; Decovulture or Sasabiruguguti temperaments
 : Decovulture rank-two temperaments temper out the ''decovulture'' comma, {{nowrap|{{Monzo| 26 -7 -4 -2 }} {{=}} 67108864/66976875}}.
-; Pontiqak or Lazozotritriyo temperaments
+; Pontiqak or Lazozotritriyoti temperaments
 : Pontiqak rank-two temperaments temper out the ''pontiqak'' comma, {{nowrap|{{Monzo| -17 -6 9 2 }} {{=}} 95703125/95551488}}.
-; [[Mitonismic temperaments|Mitonismic or Laquadzo-agu temperaments]]
+; [[Mitonismic temperaments|Mitonismic or Laquadzo-aguti temperaments]]
 : Mitonismic rank-two temperaments temper out the ''mitonisma'', {{nowrap|{{Monzo| -20 7 -1 4 }} {{=}} 5250987/5242880}}.
-; [[Horwell temperaments|Horwell or Lazoquinyo temperaments]]
+; [[Horwell temperaments|Horwell or Lazoquinyoti temperaments]]
 : Horwell rank-two temperaments temper out the horwell comma, {{nowrap|{{Monzo| -16 1 5 1 }} {{=}} 65625/65536}}.
-; Neptunismic or Laruruleyo temperaments
+; Neptunismic or Laruruleyoti temperaments
 : Neptunismic rank-two temperaments temper out the ''neptunisma'', {{nowrap|{{Monzo| -12 -5 11 -2 }} {{=}} 48828125/48771072}}.
-; [[Metric microtemperaments|Metric or Latriru-asepyo temperaments]]
+; [[Metric microtemperaments|Metric or Latriru-asepyoti temperaments]]
 : Metric rank-two temperaments temper out the meter comma, {{nowrap|{{Monzo| -11 2 7 -3 }} {{=}} 703125/702464}}.
-; [[Wizmic microtemperaments|Wizmic or Quinzo-ayoyo temperaments]]
+; [[Wizmic microtemperaments|Wizmic or Quinzo-ayoyoti temperaments]]
 : Wizmic rank-two temperaments temper out the wizma, {{nowrap|{{Monzo| -6 -8 2 5 }} {{=}} 420175/419904}}.
-; [[Supermatertismic temperaments|Supermatertismic or Lasepru-atritriyo temperaments]]
+; [[Supermatertismic temperaments|Supermatertismic or Lasepru-atritriyoti temperaments]]
 : Supermatertismic rank-two temperaments temper out the ''supermatertisma'', {{nowrap|{{Monzo| -6 3 9 -7 }} {{=}} 52734375/52706752}}.
-; [[Breedsmic temperaments|Breedsmic or Bizozogu temperaments]]
+; [[Breedsmic temperaments|Breedsmic or Bizozoguti temperaments]]
 : Breedsmic rank-two temperaments temper out the breedsma, {{nowrap|{{Monzo| -5 -1 -2 4 }} {{=}} 2401/2400}}.
-; Supermasesquartismic or Laquadbiru-aquinyo temperaments
+; Supermasesquartismic or Laquadbiru-aquinyoti temperaments
 : Supermasesquartismic rank-two temperaments temper out the ''supermasesquartisma'', {{nowrap|{{Monzo| -5 10 5 -8 }} {{=}} 184528125/184473632}}.
-; [[Ragismic microtemperaments|Ragismic or Zoquadyo temperaments]]
+; [[Ragismic microtemperaments|Ragismic or Zoquadyoti temperaments]]
 : Ragismic rank-two temperaments temper out the ragisma, {{nowrap|{{Monzo| -1 -7 4 1 }} {{=}} 4375/4374}}.
-; Akjaysmic or Trisa-seprugu temperaments
+; Akjaysmic or Trisa-sepruguti temperaments
-: Akjaysmic rank-two temperaments temper out the akjaysma, {{Monzo| 47 -7 -7 -7 }}. These have a period of 1/7 octave, and five periods equals ~105/64. Unlike the Whitewood or Lawa family, ~3/2 is not equated with four-sevenths of an octave, resulting in small intervals.
+: Akjaysmic rank-two temperaments temper out the akjaysma, {{Monzo| 47 -7 -7 -7 }}. These have a period of 1/7 octave, and five periods equals ~105/64. Unlike the Whitewood or Lawati family, ~3/2 is not equated with four-sevenths of an octave, resulting in small intervals.
-; [[Landscape microtemperaments|Landscape or Trizogugu temperaments]]
+; [[Landscape microtemperaments|Landscape or Trizoguguti temperaments]]
 : Landscape rank-two temperaments temper out the landscape comma, {{nowrap|{{Monzo| -4 6 -6 3 }} {{=}} 250047/250000}}. These have a period of 1/3 octave, but ~5/4 is not equated with a period, resulting in small intervals.
@@ Line 482: / Line 482: @@
 Every ya or 5-limit comma defines a rank-3 family, thus every comma in the list of rank-two 2.3.5 families could be included here. If nothing else is tempered out, the prime subgroup is assumed to be 2.3.5.7, and we have a yaza or 7-limit temperament in which one of the generators is ~7/1. This generator can be reduced to ~7/4, which can be reduced further to ~64/63. Hence in all the pergens below, the ^1 or /1 generator is ~64/63. An additional 7-limit or 11-limit comma creates a yazala or 11-limit temperament, and so forth. All these examples are yaza:
-; [[Didymus rank three family|Didymus or Gu rank three family]] (P8, P5, ^1)
+; [[Didymus rank three family|Didymus or Guti rank three family]] (P8, P5, ^1)
 : These are the rank three temperaments tempering out the didymus or meantone comma, 81/80.
-; [[Diaschismic rank three family|Diaschismic or Sagugu rank three family]] (P8/2, P5, /1)
+; [[Diaschismic rank three family|Diaschismic or Saguguti rank three family]] (P8/2, P5, /1)
 : These are the rank three temperaments tempering out the dischisma, {{nowrap|{{Monzo| 11 -4 -2 }} {{=}} 2048/2025}}.  The half-octave period is ~45/32.
-; [[Porcupine rank three family|Porcupine or Triyo rank three family]] (P8, P4/3, /1)
+; [[Porcupine rank three family|Porcupine or Triyoti rank three family]] (P8, P4/3, /1)
 : These are the rank three temperaments tempering out the porcupine comma or maximal diesis, {{nowrap|{{Monzo| 1 -5 3 }} {{=}} 250/243}}. In the pergen, P4/3 is ~10/9.
-; [[Kleismic rank three family|Kleismic or Tribiyo rank three family]] (P8, P12/6, /1)
+; [[Kleismic rank three family|Kleismic or Tribiyoti rank three family]] (P8, P12/6, /1)
 : These are the rank three temperaments tempering out the kleisma, {{nowrap|{{Monzo| -6 -5 6 }} {{=}} 15625/15552}}.  In the pergen, P12/6 is ~6/5.
@@ Line 497: / Line 497: @@
 Every za or 7-limit-no-fives comma defines a rank-3 family, thus every comma in the list of rank-two 2.3.7 families could be included here. If nothing else is tempered out, the prime subgroup is assumed to be 2.3.5.7, and we have a yaza or 7-limit temperament in which one of the generators is ~5/1. This generator can be reduced to ~5/4, which may be reduced further to ~81/80. Hence in all the pergens below, {{nowrap|^1 {{=}} ~81/80}}. An additional 5-limit or 11-limit comma creates a yazala or 11-limit temperament, and so forth. All these examples are yaza:
-; [[Archytas family|Archytas or Ru family]] (P8, P5, ^1)
+; [[Archytas family|Archytas or Ruti family]] (P8, P5, ^1)
 : Archytas temperament tempers out 64/63. This comma equates every 7-limit interval to some 3-limit interval. If 81/80 were tempered out too, the otonal tetrad 4:5:6:7 would be identified with the dominant seventh chord.
-; [[Garischismic family|Garischismic or Sasaru family]] (P8, P5, ^1)
+; [[Garischismic family|Garischismic or Sasaruti family]] (P8, P5, ^1)
 : A garischismic temperament is one which tempers out the garischisma, {{nowrap|{{Monzo| 25 -14 0 -1 }} {{=}} 33554432/33480783}}.
-; [[Semiphore family|Semiphore or Zozo family]] (P8, P4/2, ^1)
+; Laruruti clan (P8/2, P5)
-: Semiphore temperament tempers out 49/48 and thereby identifies the septimal minor third 7/6 with the septimal whole tone 8/7. It also splits the fourth into two of these intervals; hence the name, which sounds like "semi-fourth". See also {{monzo|[Semaphore|Sem'''<u}}a</u>'''phore]] and [[Slendro clan|Slendro]].
+: This clan tempers out the Laruru comma, {{nowrap|{{Monzo| -7 8 0 -2 }} {{=}} 6561/6272}}. Two ~81/56 periods equal an 8ve. The generator is ~3/2, and four generators minus three periods equals ~7/4. The major 2nd ~9/8 is divided in half, with each half equated to ~28/27. See also the Diaschismic or Saguguti temperament and the Jubilismic or Biruyoti temperament.
+; [[Semiphore family|Semiphore or Zozoti family]] (P8, P4/2, ^1)
+: Semiphore temperament tempers out 49/48 and thereby identifies the septimal minor third 7/6 with the septimal whole tone 8/7. It also splits the fourth into two of these intervals; hence the name, which sounds like "semi-fourth". See also [[Semaphore]] and [[Slendro clan|Slendro]].
-; [[Gamelismic family|Gamelismic or Latrizo family]] (P8, P5/3, ^1)
+; [[Gamelismic family|Gamelismic or Latrizoti family]] (P8, P5/3, ^1)
 : Not to be confused with the gamelismic clan of rank two temperaments, the gamelismic family are those rank three temperaments which temper out the gamelisma,  {{nowrap|{{Monzo| -10 1 0 3 }} {{=}} 1029/1024}}. In the pergen, P5/3 is ~8/7.
-; Stearnsmic or Latribiru family (P8/2, P4/3, ^1)
+; Stearnsmic or Latribiruti family (P8/2, P4/3, ^1)
 : Stearnsmic temperaments temper out the stearnsma, {{nowrap|{{Monzo| 1 10 0 -6 }} {{=}} 118098/117649}}. In the pergen, P8/2 is ~343/243 and P4/3 is ~54/49.
 === Families defined by a 2.3.5.7 (yaza) comma ===
-; [[Marvel family|Marvel or Ruyoyo family]] (P8, P5, ^1)
+; [[Marvel family|Marvel or Ruyoyoti family]] (P8, P5, ^1)
 : The head of the marvel family is marvel, which tempers out {{nowrap|{{Monzo| -5 2 2 -1 }} {{=}} [[225/224]]}}. It divides 8/7 into two 16/15s, or equivalently, two 15/14s. It has a number of 11-limit children, including unidecimal marvel, prodigy, minerva and spectacle.
 The marvel comma equates every 7-limit interval to some 5-limit interval, therefore the generators are the same as for 5-limit JI: 2/1, 3/1 and 5/1. These may be reduced to 2/1, 3/2 and 5/4, and 5/4 may be reduced further to 81/80. Hence in the pergen, {{nowrap|^1 {{=}} ~81/80}}.
-; [[Starling family|Starling or Zotrigu family]] (P8, P5, ^1)
+; [[Starling family|Starling or Zotriguti family]] (P8, P5, ^1)
 : Starling tempers out the septimal semicomma or starling comma {{nowrap|{{Monzo| 1 2 -3 1 }} {{=}} [[126/125]]}}, the difference between three 6/5s plus one 7/6, and an octave. It divides 10/7 into two 6/5s. Like marvel, it has the same generators as 5-limit JI. An excellent tuning for starling is [[77edo|77EDO]], but 31, 46 or 58 also work nicely. In the pergen, {{nowrap|^1 {{=}} ~81/80}}.
-; [[Sensamagic family|Sensamagic or Zozoyo family]] (P8, P5, ^1)
+; [[Sensamagic family|Sensamagic or Zozoyoti family]] (P8, P5, ^1)
 : These temper out {{nowrap|{{Monzo| 0 -5 1 2 }} {{=}} 245/243}}, which divides 16/15 into two 28/27s. In the pergen, {{nowrap|^1 {{=}} ~64/63}}.
-; Greenwoodmic or Ruruyo family (P8, P5, ^1)
+; Greenwoodmic or Ruruyoti family (P8, P5, ^1)
 : These temper out the greenwoodma, {{nowrap|{{Monzo| -3 4 1 -2 }} {{=}} 405/392}}, which divides 10/9 into two 15/14s. In the pergen, {{nowrap|^1 {{=}} ~64/63}}.
-; Avicennmic or Lazoyoyo family (P8, P5, ^1)
+; Avicennmic or Lazoyoyoti family (P8, P5, ^1)
 : These temper out the avicennma, {{nowrap|{{Monzo| -9 1 2 1 }} {{=}} 525/512}}, which divides 7/6 into two 16/15s. In the pergen, {{nowrap|^1 {{=}} ~81/80}}.
-; [[Keemic family|Keemic or Zotriyo family]] (P8, P5, ^1)
+; [[Keemic family|Keemic or Zotriyoti family]] (P8, P5, ^1)
 : These temper out the keema {{nowrap|{{Monzo| -5 -3 3 1 }} {{=}} 875/864}}, which divides 15/14 into two 25/24s. In the pergen, {{nowrap|^1 {{=}} ~81/80}}.
-; [[Orwellismic family|Orwellismic or Triru-agu family]] (P8, P5, ^1)
+; [[Orwellismic family|Orwellismic or Triru-aguti family]] (P8, P5, ^1)
 : These temper out {{nowrap|{{Monzo| 6 3 -1 -3 }} {{=}} 1728/1715}}. In the pergen, {{nowrap|^1 {{=}} ~64/63}}.
-; [[Nuwell family|Nuwell or Quadru-ayo family]] (P8, P5, ^1)
+; [[Nuwell family|Nuwell or Quadru-ayoti family]] (P8, P5, ^1)
 : These temper out the nuwell comma, {{nowrap|{{Monzo| 1 5 1 -4 }} {{=}} 2430/2401}}. In the pergen, {{nowrap|^1 {{=}} ~64/63}}.
-; [[Ragisma family|Ragisma or Zoquadyo family]] (P8, P5, ^1)
+; [[Ragisma family|Ragisma or Zoquadyoti family]] (P8, P5, ^1)
 : The 7-limit rank three microtemperament which tempers out the ragisma, {{nowrap|{{Monzo| -1 -7 4 1 }} {{=}} 4375/4374}}, extends to various higher limit rank three 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}}.
-; [[Hemifamity family|Hemifamity or Saruyo family]] (P8, P5, ^1)
+; [[Hemifamity family|Hemifamity or Saruyoti family]] (P8, P5, ^1)
 : The hemifamity family of rank three temperaments tempers out the hemifamity comma, {{nowrap|{{Monzo| 10 -6 1 -1 }} {{=}} 5120/5103}}, which divides 10/7 into three 9/8s. In the pergen, {{nowrap|^1 {{=}} ~81/80}}.
-; [[Horwell family|Horwell or Lazoquinyo family]] (P8, P5, ^1)
+; [[Horwell family|Horwell or Lazoquinyoti family]] (P8, P5, ^1)
 : The horwell family of rank three temperaments tempers out the horwell comma, {{nowrap|{{Monzo| -16 1 5 1 }} {{=}} 65625/65536}}. In the pergen, {{nowrap|^1 {{=}} ~81/80}}.
-; [[Hemimage family|Hemimage or Satrizo-agu family]] (P8, P5, ^1)
+; [[Hemimage family|Hemimage or Satrizo-aguti family]] (P8, P5, ^1)
 : The hemimage family of rank three temperaments tempers out the hemimage comma, {{nowrap|{{Monzo| 5 -7 -1 3 }} {{=}} 10976/10935}}, which divides 10/9 into three 28/27s. In the pergen, {{nowrap|^1 {{=}} ~64/63}}.
-; [[Mint family|Mint or Rugu family]] (P8, P5, ^1)
+; [[Mint family|Mint or Ruguti family]] (P8, P5, ^1)
 : The mint temperament is a low complexity, high error temperament, tempering out the septimal quarter-tone 36/35, equating 7/6 with 6/5, and 5/4 with 9/7. In the pergen, {{nowrap|^1 {{=}} ~81/80}} or ~64/63.
-; Septisemi or Zogu family (P8, P5, ^1)
+; Septisemi or Zoguti family (P8, P5, ^1)
 : These are very low accuracy temperaments tempering out the minor septimal semitone, [[21/20]] and hence equating 5/3 with 7/4. In the pergen, {{nowrap|^1 {{=}} ~81/80}}.
-; [[Jubilismic family|Jubilismic or Biruyo family]] (P8/2, P5, ^1)
+; [[Jubilismic family|Jubilismic or Biruyoti family]] (P8/2, P5, ^1)
 : Jubilismic temperament tempers out 50/49 and thereby equates the two septimal tritones, 7/5 and 10/7. This is the half-octave period. In the pergen, {{nowrap|^1 {{=}} ~81/80}}.
-; [[Cataharry family|Cataharry or Labirugu family]] (P8, P4/2, ^1)
+; [[Cataharry family|Cataharry or Labiruguti family]] (P8, P4/2, ^1)
 : Cataharry temperaments temper out the cataharry comma, {{nowrap|{{Monzo| -4 9 -2 -2 }} {{=}} 19683/19600}}. In the pergen, half a 4th is ~81/70, and {{nowrap|^1 {{=}} ~81/80}}.
-; [[Breed family|Breed or Bizozogu family]] (P8, P5/2, ^1)
+; [[Breed family|Breed or Bizozoguti family]] (P8, P5/2, ^1)
 : Breed is a 7-limit microtemperament which tempers out {{nowrap|{{Monzo| -5 -1 -2 4 }} {{=}} 2401/2400}}. While it is so accurate it hardly matters what is used to temper it, or whether it is even tempered at all, 2749EDO will certainly do the trick. Breed has generators of 2/1, a 49/40-cum-60/49 neutral third, and ~64/63.
-; [[Sengic family|Sengic or Trizo-agugu family]] (P8, P5, vm3/2)
+; [[Sengic family|Sengic or Trizo-aguguti family]] (P8, P5, vm3/2)
 : These temper out the senga, {{nowrap|{{Monzo| 1 -3 -2 3 }} {{=}} 686/675}}. One generator is ~15/14, two give ~7/6 (the downminor 3rd in the pergen), and three give ~6/5.
-; [[Porwell family|Porwell or Sarurutrigu family]] (P8, P5, ^m3/2)
+; [[Porwell family|Porwell or Sarurutriguti family]] (P8, P5, ^m3/2)
 : The porwell family of rank three temperaments tempers out the porwell comma, {{nowrap|{{Monzo| 11 1 -3 -2 }} {{=}} 6144/6125}}. Two ~35/32 generators equal the pergen's upminor 3rd of ~6/5.
-; [[Octagar family|Octagar or Rurutriyo family]] (P8, P5, ^m6/2)
+; [[Octagar family|Octagar or Rurutriyoti family]] (P8, P5, ^m6/2)
 : The octagar family of rank three temperaments tempers out the octagar comma, {{nowrap|{{Monzo| 5 -4 3 -2 }} {{=}} 4000/3969}}. Two ~80/63 generators equal the pergen's upminor 6th of ~8/5.
-; [[Hemimean family|Hemimean or Zozoquingu family]] (P8, P5, vM3/2)
+; [[Hemimean family|Hemimean or Zozoquinguti family]] (P8, P5, vM3/2)
 : The hemimean family of rank three temperaments tempers out the hemimean comma, {{nowrap|{{Monzo| 6 0 -5 2 }} {{=}} 3136/3125}}.  Two ~28/25 generators equal the pergen's downmajor 3rd of ~5/4.
-; Wizmic or Quinzo-ayoyo family (P8, P5, vm7/2)
+; Wizmic or Quinzo-ayoyoti family (P8, P5, vm7/2)
 : A wizmic temperament is one which tempers out the wizma, {{nowrap|{{Monzo| -6 -8 2 5 }} {{=}} 420175/419904}}. Two ~324/245 generators equal the pergen's downminor 7th of ~7/4.
-; [[Landscape family|Landscape or Trizogugu family]] (P8/3, P5, ^1)
+; [[Landscape family|Landscape or Trizoguguti family]] (P8/3, P5, ^1)
 : The 7-limit rank three microtemperament which tempers out the lanscape comma, {{nowrap|{{Monzo| -4 6 -6 3 }} {{=}} 250047/250000}}, extends to various higher limit rank three temperaments such as tyr and odin. In the pergen, the third-octave period is ~63/50, and {{nowrap|^1 {{=}} ~81/80}}.
-; [[Gariboh family|Gariboh or Triru-aquinyo family]] (P8, P5, vM6/3)
+; [[Gariboh family|Gariboh or Triru-aquinyoti family]] (P8, P5, vM6/3)
 : The gariboh family of rank three temperaments tempers out the gariboh comma, {{nowrap|{{monzo| 0 -2 5 -3 }} {{=}} 3125/3087}}. Three ~25/21 generators equal the pergen's downmajor 6th of ~5/3.
-; [[Canou family|Canou or Saquadzo-atriyo family]] (P8, P5, vm6/3)
+; [[Canou family|Canou or Saquadzo-atriyoti family]] (P8, P5, vm6/3)
 : The canou family of rank three temperaments tempers out the canousma, {{nowrap|{{Monzo| 4 -14 3 4 }} {{=}} 4802000/4782969}}. Three ~81/70 generators equal the pergen's downminor 6th of ~14/9.
-; [[Dimcomp family|Dimcomp or Quadruyoyo family]] (P8/4, P5, ^1)
+; [[Dimcomp family|Dimcomp or Quadruyoyoti family]] (P8/4, P5, ^1)
 : The dimcomp family of rank three temperaments tempers out the dimcomp comma, {{nowrap|{{Monzo| -1 -4 8 -4 }} {{=}} 390625/388962}}. In the pergen, the quarter-octave period is ~25/21, and {{nowrap|^1 {{=}} ~81/80}}.
-; [[Mirkwai family|Mirkwai or Quinru-aquadyo family]] (P8, P5, c^M7/4)
+; [[Mirkwai family|Mirkwai or Quinru-aquadyoti family]] (P8, P5, c^M7/4)
 : The mirkwai family of rank three temperaments tempers out the mirkwai comma, {{nowrap|{{Monzo| 0 3 4 -5 }} {{=}} 16875/16807}}. Four ~7/5 generators equal the pergen's compound upmajor 7th of  ~27/7.
 === Temperaments defined by an 11-limit comma ===
-; [[Ptolemismic clan|Ptolemismic or Luyoyo clan]] (P8, P5, ^1)
+; [[Ptolemismic clan|Ptolemismic or Luyoyoti clan]] (P8, P5, ^1)
 : These temper out the ptolemisma, {{nowrap|{{monzo| 2 -2 2 0 -1 }} {{=}} 100/99}}. 11/8 is equated to 25/18, which is an octave minus two 6/5's. Since 25/18 is a 5-limit interval, every 2.3.5.11 interval is equated to a 5-limit interval, and both the pergen and the lattice are identical to that of 5-limit JI. In the pergen, {{nowrap|^1 {{=}} ~81/80}}.
-; [[Biyatismic clan|Biyatismic or Lologu clan]] (P8, P5, ^1)
+; [[Biyatismic clan|Biyatismic or Lologuti clan]] (P8, P5, ^1)
 : These temper out the biyatisma, {{nowrap|{{monzo| -3 -1 -1 0 2 }} {{=}} 121/120}}. 5/4 is equated to 121/96, which is two 11/8's minus a 3/2 fifth. Since 121/96 is an ila (11-limit no-fives no-sevens) interval, every 2.3.5.11 interval is equated to an ila interval, and both the pergen and the lattice are identical to that of ila JI.  In the pergen, ^1 is either ~33/32 or ~729/704.
-; [[Valinorsmic clan|Valinorsmic or Lorugugu clan]]
+; [[Valinorsmic clan|Valinorsmic or Loruguguti clan]]
 : These temper out the valinorsma, {{nowrap|{{monzo| 4 0 -2 -1 1 }} {{=}} 176/175}}. 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.
-; [[Rastmic rank three clan|Rastmic or Lulu rank-3 clan]]
+; [[Rastmic rank three clan|Rastmic or Luluti rank-3 clan]]
 : These temper out the rastma, {{nowrap|{{monzo| 1 5 0 0 -2 }} {{=}} 243/242}}. In the corresponding [[Tour of regular temperaments#Clans defined by a 2.3.11 .28ila.29 comma|2.3.11 rank-2 temperament]], the pergen is (P8, P5/2).
-; [[Pentacircle clan|Pentacircle or Saluzo clan]] (P8, P5, ^1)
+; [[Pentacircle clan|Pentacircle or Saluzoti clan]] (P8, P5, ^1)
 : These temper out the pentacircle comma, {{nowrap|{{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.
-; [[Semicanousmic clan|Semicanousmic or Quadlo-agu clan]] (P8, P5, ^1)
+; [[Semicanousmic clan|Semicanousmic or Quadlo-aguti clan]] (P8, P5, ^1)
 : These temper out the semicanousma, {{nowrap|{{monzo| -2 -6 -1 0 4 }} {{=}} 14641/14580}}. 5/4 is equated to an ila (2.3.11) interval, thus every 2.3.5.11 interval is equated to an ila interval, and both the pergen and the lattice are identical to that of ila JI.  In the pergen, ^1 is either ~33/32 or ~729/704.
-; [[Semiporwellismic clan|Semiporwellismic or Salulugu clan]] (P8, P5, ^1)
+; [[Semiporwellismic clan|Semiporwellismic or Saluluguti clan]] (P8, P5, ^1)
 : These temper out the semiporwellisma, {{nowrap|{{monzo| 14 -3 -1 0 -2 }} {{=}} 16384/16335}}. 5/4 is equated to an ila (2.3.11) interval, thus every 2.3.5.11 interval is equated to an ila interval, and both the pergen and the lattice are identical to that of ila JI. In the pergen, ^1 is either ~33/32 or ~729/704.
-; [[Olympic clan|Olympic or Salururu clan]] (P8, P5, ^1)
+; [[Olympic clan|Olympic or Salururuti clan]] (P8, P5, ^1)
 : These temper out the olympia, {{nowrap|{{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}}.
-; [[Alphaxenic rank three clan|Alphaxenic or Laquadlo rank-3 clan]]
+; [[Alphaxenic rank three clan|Alphaxenic or Laquadloti rank-3 clan]]
 : These temper out the Alpharabian comma, {{nowrap|{{monzo| -17 2 0 0 4 }} {{=}} 131769/131072}}. In the corresponding [[Tour of regular temperaments#Clans defined by a 2.3.11 .28ila.29 comma|2.3.11 rank-2 temperament]], the pergen is (P8/2, M2/4).
@@ Line 629: / Line 632: @@
 Even less explored than rank three temperaments are rank four temperaments. In fact, unless one counts 7-limit JI they don't seem to have been explored at all. However, they could be used; for example [[Hobbits|hobbit scales]] can be constructed for them.
-; [[Keenanismic temperaments|Keenanismic or Lozoyo temperaments]] (P8, P5, ^1, /1)
+; [[Keenanismic temperaments|Keenanismic or Lozoyoti temperaments]] (P8, P5, ^1, /1)
 : These temper out the keenanisma, {{nowrap|{{monzo| -7 -1 1 1 1 }} {{=}} 385/384}}. In the pergen, ^1 could be either ~81/80 or ~64/63, and /1 could be either ~64/63 (if ^1 isn't), ~33/32 or ~729/704.
-;[[Werckismic temperaments|Werckismic or Luzozogu temperaments]] (P8, P5, ^1, /1)
+;[[Werckismic temperaments|Werckismic or Luzozoguti temperaments]] (P8, P5, ^1, /1)
 : These temper out the werckisma, {{nowrap|{{monzo| -3 2 -1 2 -1 }} {{=}} 441/440}}. 11/8 is equated to {{monzo| -6 2 -1 2 }} and 5/4 is equated to {{monzo| -5 2 0 2 -1 }}, thus the lattice can be thought of as either 7-limit JI or 11-limit no-fives JI. In the pergen, ^1 is ~64/63, and /1 is either ~81/80, ~33/32 or ~729/704.
-;[[Swetismic temperaments|Swetismic or Lururuyo temperaments]] (P8, P5, ^1, /1)
+;[[Swetismic temperaments|Swetismic or Lururuyoti temperaments]] (P8, P5, ^1, /1)
 : These temper out the swetisma, {{nowrap|{{monzo| 2 3 1 -2 -1 }} {{=}} 540/539}}. 11/8 is equated to {{nowrap| -1 3 1 -2 {{=}} 135/98}} and 5/4 is equated to {{monzo| -4 -3 0 2 1 }}, thus the lattice can be thought of as either 7-limit JI or 11-limit no-fives JI. In the pergen, ^1 is ~64/63, and /1 can be either ~81/80, ~33/32 or ~729/704.
-; [[Lehmerismic temperaments|Lehmerismic or Loloruyoyo temperaments]] (P8, P5, ^1, /1)
+; [[Lehmerismic temperaments|Lehmerismic or Loloruyoyoti temperaments]] (P8, P5, ^1, /1)
 : These temper out the lehmerisma, {{nowrap|{{monzo| -4 -3 2 -1 2 }} {{=}} 3025/3024}}. Since 7/4 is equated to a yala (11-limit no-sevens) interval, both the pergen and the lattice are identical to that of yala JI. In the pergen, {{nowrap|^1 {{=}} ~81/80}} and/1&nbsp;= either ~33/32 or ~729/704.
-;[[Kalismic temperaments|Kalismic or Bilorugu temperaments]] (P8/2, P5, ^1, /1)
+;[[Kalismic temperaments|Kalismic or Biloruguti temperaments]] (P8/2, P5, ^1, /1)
 : These temper out the kalisma, {{nowrap|{{monzo| -3 4 -2 -2 2 }} {{=}} 9801/9800}}. The octave is split into two ~99/70 periods. In the pergen, ^1 could be either ~81/80 or ~64/63, and /1 could be either ~64/63 (if ^1 isn't), ~33/32 or ~729/704.
@@ Line 652: / Line 655: @@
 By a ''commatic realm'' is meant the whole collection of regular temperaments of various ranks and for [[subgroup]]s (including full [[prime limit]]s) tempering out a given comma. For some commas, looking at the full commatic realm seems the best approach to discussing associated temperaments.
-; [[The Biosphere|The Biosphere or Thozogu]]
+; [[The Biosphere|The Biosphere or Thozoguti]]
 : The Biosphere is the name given to the commatic realm of the [[13-limit]] comma 91/90.
-; [[Marveltwin|Marveltwin or Thoyoyo]]
+; [[Marveltwin|Marveltwin or Thoyoyoti]]
 : This is the commatic realm of the 13-limit comma 325/324, the [[marveltwin comma]].
-; [[The Archipelago|The Archipelago or Bithogu]]
+; [[The Archipelago|The Archipelago or Bithoguti]]
 : The Archipelago is a name which has been given to the commatic realm of the 13-limit comma {{nowrap|676/675 {{=}} {{monzo| 2 -3 -2 0 0 2 }}}}, the [[island comma]].
-; [[The Jacobins|The Jacobins or Thotrilu-agu]]
+; [[The Jacobins|The Jacobins or Thotrilu-aguti]]
 : This is the commatic realm of the 13-limit comma 6656/6655, the [[jacobin comma]].
@@ Line 667: / Line 670: @@
 : This is the commatic realm of [[7777/7776]], the pulsar comma.
-; [[Orgonia|Orgonia or Satrilu-aruru]]
+; [[Orgonia|Orgonia or Satrilu-aruruti]]
 : This is the commatic realm of the 11-limit comma {{nowrap|65536/65219 {{=}} {{monzo| 16 0 0 -2 -3 }}}}, the [[orgonisma]].
-; [[The Nexus|The Nexus or Tribilo]]
+; [[The Nexus|The Nexus or Tribiloti]]
 : This is the commatic realm of the 11-limit comma {{nowrap|1771561/1769472 {{=}} {{monzo| -16 -3 0 0 6 }}}}, the [[nexus comma]].
-; [[The Quartercache|The Quartercache or Saquinlu-azo]]
+; [[The Quartercache|The Quartercache or Saquinlu-azoti]]
 : This is the commatic realm of the 11-limit comma {{nowrap|117440512/117406179 {{=}} {{monzo| 24 -6 0 1 -5 }}}}, the [[quartisma]].