Tour of regular temperaments: Difference between revisions

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===[[Mirkwai clan|Mirkwai or Quinru-aquadyo Noca clan]] (P12, cM7/4)===

This 3.5.7 clan tempers out the mirkwai comma, {{Monzo|0 3 4 -5}} = 16875/16807. The generator is ~7/5, and four generators equals a compound major 7th = ~27/7.

== Rank-two temperaments defined by a 2.3.5.7 (yaza) comma ==

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

===[[Marvel temperaments|Marvel or Ruyoyo 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.

===[[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]]===

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

===[[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.

===[[Keemic temperaments|Keemic or Zotriyo temperaments]]===

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

===[[Orwellismic temperaments|Orwellismic or Triru-agu temperaments]]===

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

===[[Nuwell temperaments|Nuwell or Quadru-ayo temperaments]] (P8, P5, ^1)===

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]] (P8, P5, ^1)===

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]]===

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]] (P8, P5, ^1)===

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]] (P8, P4/2, ^1)===

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

===[[Landscape microtemperaments|Landscape or Trizogugu temperaments]] (P8/3, P5, ^1)===

Lanscape rank-two temperaments temper out the lanscape comma, {{Monzo|-4 6 -6 3}} = 250047/250000.

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

===[[Wizmic microtemperaments|Wizmic or Quinzo-ayoyo temperaments]]===

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

===[[Canousmic temperaments|Canousmic or Saquadzo-atriyo temperaments]]===

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

=Rank-3 temperaments=

@@ Line 269: / Line 269: @@
 ===[[Mirkwai clan|Mirkwai or Quinru-aquadyo Noca clan]] (P12, cM7/4)===
 This 3.5.7 clan tempers out the mirkwai comma, {{Monzo|0 3 4 -5}} = 16875/16807. The generator is ~7/5, and four generators equals a compound major 7th = ~27/7.
+== Rank-two temperaments defined by a 2.3.5.7 (yaza) comma ==
+These are defined by a full 7-limit (or yaza) comma.
+===[[Marvel temperaments|Marvel or Ruyoyo 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.
+===[[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]]===
+These temper out the greenwoodma, {{Monzo|-3 4 1 -2}} = 405/392.
+===[[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.
+===[[Keemic temperaments|Keemic or Zotriyo temperaments]]===
+Keemic rank-two temperaments temper out the keema, {{Monzo|-5 -3 3 1}} = 875/864.
+===[[Orwellismic temperaments|Orwellismic or Triru-agu temperaments]]===
+Orwellismic rank-two temperaments temper out orwellisma, {{Monzo|6 3 -1 -3}} = 1728/1715.
+===[[Nuwell temperaments|Nuwell or Quadru-ayo temperaments]] (P8, P5, ^1)===
+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]] (P8, P5, ^1)===
+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]]===
+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]] (P8, P5, ^1)===
+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]] (P8, P4/2, ^1)===
+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 rank-two temperaments temper out the mirwomo comma, {{Monzo|-15 3 2 2}} = 33075/32768.
+===[[Landscape microtemperaments|Landscape or Trizogugu temperaments]] (P8/3, P5, ^1)===
+Lanscape rank-two temperaments temper out the lanscape comma, {{Monzo|-4 6 -6 3}} = 250047/250000.
+===[[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 rank-two temperaments temper out the octagar comma, {{Monzo|5 -4 3 -2}} = 4000/3969.
+===[[Wizmic microtemperaments|Wizmic or Quinzo-ayoyo temperaments]]===
+Wizmic rank-two temperaments temper out the wizma, {{Monzo|-6 -8 2 5}} = 420175/419904.
+===[[Canousmic temperaments|Canousmic or Saquadzo-atriyo temperaments]]===
+Canousmic rank-two temperaments temper out the canousma, {{Monzo|4 -14 3 4}} = 4802000/4782969.
 =Rank-3 temperaments=