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Tour of regular temperaments: Difference between revisions

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


===[[Marvel temperaments|Marvel or Ruyoyo temperaments]]===
===[[Septisemi temperaments|Septisemi or Zogu temperaments]]===
Marvel rank-two temperaments temper out {{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.
These are very low complexity temperaments tempering out the minor septimal semitone, [[21/20]] and hence equating 5/3 with 7/4.
 
===[[Starling temperaments|Starling or Zotrigu temperaments]]===
Starling rank-two temperaments temper out the septimal semicomma or starling comma {{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.


===[[Greenwoodmic temperaments|Greenwoodmic or Ruruyo temperaments]]===
===[[Greenwoodmic temperaments|Greenwoodmic or Ruruyo temperaments]]===
These temper out the greenwoodma, {{Monzo|-3 4 1 -2}} = 405/392.
These temper out the greenwoodma, {{Monzo|-3 4 1 -2}} = 405/392.
===[[Mint temperaments|Mint or Rugu 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 Zoyoyo temperaments]]===
These temper out the avicennma, {{Monzo|-9 1 2 1}} = 525/512, also known as Avicenna's enharmonic diesis.
These temper out the avicennma, {{Monzo|-9 1 2 1}} = 525/512, also known as Avicenna's enharmonic diesis.
===[[Sengic temperaments|Sengic or Trizo-agugu temperaments]]===
Sengic rank-two temperaments temper out the senga, {{Monzo|1 -3 -2 3}} = 686/675.


===[[Keemic temperaments|Keemic or Zotriyo temperaments]]===
===[[Keemic temperaments|Keemic or Zotriyo temperaments]]===
Keemic rank-two temperaments temper out the keema, {{Monzo|-5 -3 3 1}} = 875/864.
Keemic rank-two temperaments temper out the keema, {{Monzo|-5 -3 3 1}} = 875/864.


===[[Orwellismic temperaments|Orwellismic or Triru-agu temperaments]]===
===[[Secanticorn temperaments|Secanticorn or Laruquingu temperaments]]===
Orwellismic rank-two temperaments temper out orwellisma, {{Monzo|6 3 -1 -3}} = 1728/1715.
Secanticorn rank-two temperaments temper out the ''secanticornisma'' (named by [[User:Xenllium|Xenllium]]), {{monzo|-3 11 -5 -1}} = 177147/175000.


===[[Nuwell temperaments|Nuwell or Quadru-ayo temperaments]]===
===[[Nuwell temperaments|Nuwell or Quadru-ayo temperaments]]===
Nuwell rank-two temperaments temper out the nuwell comma, {{Monzo|1 5 1 -4}} = 2430/2401.
Nuwell rank-two temperaments temper out the nuwell comma, {{Monzo|1 5 1 -4}} = 2430/2401.
===[[Ragismic microtemperaments|Ragismic or Zoquadyo microtemperaments]]===
Ragismic rank-two microtemperaments temper out the ragisma, {{Monzo|-1 -7 4 1}} = 4375/4374.
===[[Hemifamity temperaments|Hemifamity or Saruyo temperaments]]===
Hemifamity rank-two temperaments temper out the hemifamity comma, {{Monzo|10 -6 1 -1}} = 5120/5103.
===[[Horwell temperaments|Horwell or Lazoquinyo temperaments]]===
Horwell rank-two temperaments temper out the horwell comma, {{Monzo|-16 1 5 1}} = 65625/65536.
===[[Hemimage temperaments|Hemimage or Satrizo-agu temperaments]]===
Hemimage rank-two temperaments temper out the hemimage comma, {{Monzo|5 -7 -1 3}} = 10976/10935.


===[[Tolermic temperaments|Tolermic or Sazoyoyo temperaments]]===
===[[Tolermic temperaments|Tolermic or Sazoyoyo temperaments]]===
These temper out the tolerma, {{Monzo|10 -11 2 1}} = 179200/177147.
These temper out the tolerma, {{Monzo|10 -11 2 1}} = 179200/177147.
===[[Mint temperaments|Mint or Rugu 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.
===[[Septisemi temperaments|Septisemi or Zogu temperaments]]===
These are very low complexity temperaments tempering out the minor septimal semitone, [[21/20]] and hence equating 5/3 with 7/4.
===[[Cataharry temperaments|Cataharry or Labirugu temperaments]]===
Cataharry rank-two temperaments temper out the cataharry comma, {{Monzo|-4 9 -2 -2}} = 19683/19600.
===[[Breedsmic temperaments|Breedsmic or Bizozogu temperaments]]===
Breedsmic rank-two temperaments temper out the breedsma, {{Monzo|-5 -1 -2 4}} = 2401/2400.


===[[Mirwomo temperaments|Mirwomo or Labizoyo temperaments]]===
===[[Mirwomo temperaments|Mirwomo or Labizoyo temperaments]]===
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The trimyna rank-two temperaments temper out the trimyna comma, {{Monzo|-4 1 -5 5}} = 50421/50000.
The trimyna rank-two temperaments temper out the trimyna comma, {{Monzo|-4 1 -5 5}} = 50421/50000.


===[[Landscape microtemperaments|Landscape or Trizogugu temperaments]]===
===[[Starling temperaments|Starling or Zotrigu temperaments]]===
Lanscape rank-two temperaments temper out the lanscape comma, {{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.
Starling rank-two temperaments temper out the septimal semicomma or starling comma {{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.
 
===[[Dimcomp temperaments|Dimcomp or Quadruyoyo temperaments]]===
Dimcomp rank-two temperaments temper out the dimcomp comma, {{Monzo|-1 -4 8 -4}} = 390625/388962.
 
===[[Sengic temperaments|Sengic or Trizo-agugu temperaments]]===
Sengic rank-two temperaments temper out the senga, {{Monzo|1 -3 -2 3}} = 686/675.
 
===[[Porwell temperaments|Porwell or Sarurutrigu temperaments]]===
Porwell rank-two temperaments temper out the porwell comma, {{Monzo|11 1 -3 -2}} = 6144/6125.


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


===[[Secanticorn temperaments|Secanticorn or Laruquingu temperaments]]===
===[[Orwellismic temperaments|Orwellismic or Triru-agu temperaments]]===
Secanticorn rank-two temperaments temper out the ''secanticornisma'' (named by [[User:Xenllium|Xenllium]]), {{monzo|-3 11 -5 -1}} = 177147/175000.
Orwellismic rank-two temperaments temper out orwellisma, {{Monzo|6 3 -1 -3}} = 1728/1715.
 
===[[Mistismic temperaments|Mistismic or sazoquadgu temperaments]]===
Mistismic rank-two temperaments temper out the ''mistisma'' (named by [[User:Xenllium|Xenllium]]), {{Monzo|16 -6 -4 1}} = 458752/455625.


===[[Varunismic temperaments|Varunismic or Labizogugu temperaments]]===
===[[Varunismic temperaments|Varunismic or Labizogugu temperaments]]===
Varunismic rank-two temperaments temper out the varunisma, {{monzo|-9 8 -4 2}} = 321489/320000.
Varunismic rank-two temperaments temper out the varunisma, {{monzo|-9 8 -4 2}} = 321489/320000.


===[[Wizmic microtemperaments|Wizmic or Quinzo-ayoyo temperaments]]===
===[[Marvel temperaments|Marvel or Ruyoyo temperaments]]===
Wizmic rank-two temperaments temper out the wizma, {{Monzo|-6 -8 2 5}} = 420175/419904.
Marvel rank-two temperaments temper out {{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 temperaments|Dimcomp or Quadruyoyo temperaments]]===
Dimcomp rank-two temperaments temper out the dimcomp comma, {{Monzo|-1 -4 8 -4}} = 390625/388962.


===[[Mistismic temperaments|Mistismic or sazoquadgu temperaments]]===
===[[Cataharry temperaments|Cataharry or Labirugu temperaments]]===
Mistismic rank-two temperaments temper out the ''mistisma'' (named by [[User:Xenllium|Xenllium]]), {{Monzo|16 -6 -4 1}} = 458752/455625.
Cataharry rank-two temperaments temper out the cataharry comma, {{Monzo|-4 9 -2 -2}} = 19683/19600.


===[[Canousmic temperaments|Canousmic or Saquadzo-atriyo temperaments]]===
===[[Canousmic temperaments|Canousmic or Saquadzo-atriyo temperaments]]===
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===[[Triwellismic temperaments|Triwellismic or Tribizo-asepgu temperaments]]===
===[[Triwellismic temperaments|Triwellismic or Tribizo-asepgu temperaments]]===
Triwellismic rank-two temperaments temper out the ''triwellisma'' (named by [[User:Xenllium|Xenllium]]), {{Monzo|1 -1 -7 6}} = 235298/234375.
Triwellismic rank-two temperaments temper out the ''triwellisma'' (named by [[User:Xenllium|Xenllium]]), {{Monzo|1 -1 -7 6}} = 235298/234375.
===[[Hemimage temperaments|Hemimage or Satrizo-agu temperaments]]===
Hemimage rank-two temperaments temper out the hemimage comma, {{Monzo|5 -7 -1 3}} = 10976/10935.
===[[Hemifamity temperaments|Hemifamity or Saruyo temperaments]]===
Hemifamity rank-two temperaments temper out the hemifamity comma, {{Monzo|10 -6 1 -1}} = 5120/5103.
===[[Porwell temperaments|Porwell or Sarurutrigu temperaments]]===
Porwell rank-two temperaments temper out the porwell comma, {{Monzo|11 1 -3 -2}} = 6144/6125.
===[[Hemfiness temperaments|Hemfiness or Saquadru-atriyo temperaments]]===
Hemfiness rank-two temperaments temper out the ''hemfiness'' comma (named by [[User:Xenllium|Xenllium]]), {{Monzo|15 -5 3 -5}} = 4096000/4084101.


===[[Hewuermera temperaments|Hewuermera or Satribiru-agu temperaments]]===
===[[Hewuermera temperaments|Hewuermera or Satribiru-agu temperaments]]===
Hewuermera rank-two temperaments temper out the ''hewuermera'' comma (named by [[User:Xenllium|Xenllium]]), {{Monzo|16 2 -1 -6}} = 589824/588245.
Hewuermera rank-two temperaments temper out the ''hewuermera'' comma (named by [[User:Xenllium|Xenllium]]), {{Monzo|16 2 -1 -6}} = 589824/588245.
===[[Horwell temperaments|Horwell or Lazoquinyo temperaments]]===
Horwell rank-two temperaments temper out the horwell comma, {{Monzo|-16 1 5 1}} = 65625/65536.


===[[Metric microtemperaments|Metric or Latriru-asepyo temperaments]]===
===[[Metric microtemperaments|Metric or Latriru-asepyo temperaments]]===
Metric rank-two temperaments temper out the meter comma, {{Monzo|-11 2 7 -3}} = 703125/702464.
Metric rank-two temperaments temper out the meter comma, {{Monzo|-11 2 7 -3}} = 703125/702464.
===[[Wizmic microtemperaments|Wizmic or Quinzo-ayoyo temperaments]]===
Wizmic rank-two temperaments temper out the wizma, {{Monzo|-6 -8 2 5}} = 420175/419904.
===[[Supermatertismic temperaments|Supermatertismic or Lasepru-atritriyo temperaments]]===
Supermatertismic rank-two temperaments temper out the ''supermatertisma'' (named by [[User:Xenllium|Xenllium]]), {{Monzo|-6 3 9 -7}} = 52734375/52706752.
===[[Breedsmic temperaments|Breedsmic or Bizozogu temperaments]]===
Breedsmic rank-two temperaments temper out the breedsma, {{Monzo|-5 -1 -2 4}} = 2401/2400.
===[[Supermasesquartismic temperaments|Supermasesquartismic or Laquadbiru-aquinyo temperaments]]===
Supermasesquartismic rank-two temperaments temper out the ''supermasesquartisma'' (named by [[User:Xenllium|Xenllium]]), {{Monzo|-5 10 5 -8}} = 184528125/184473632.
===[[Ragismic microtemperaments|Ragismic or Zoquadyo microtemperaments]]===
Ragismic rank-two microtemperaments temper out the ragisma, {{Monzo|-1 -7 4 1}} = 4375/4374.


===[[Akjaysmic temperaments|Akjaysmic or Trisa-seprugu temperaments]]===
===[[Akjaysmic temperaments|Akjaysmic or Trisa-seprugu 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 Lawa family, ~3/2 is not equated with four-sevenths of an octave, resulting in small intervals.
===[[Landscape microtemperaments|Landscape or Trizogugu temperaments]]===
Lanscape rank-two temperaments temper out the lanscape comma, {{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.


= Rank-3 temperaments =
= Rank-3 temperaments =
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