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| ===[[Mirkwai clan|Mirkwai or Quinru-aquadyo Noca clan]] (P12, WM7/4)=== | | ===[[Mirkwai clan|Mirkwai or Quinru-aquadyo Noca clan]] (P12, WM7/4)=== |
| This 3.5.7 clan tempers out the mirkwai comma, [0 3 4 -5> = 16875/16807, a no-twos comma. Four generators = a major 14th = 27/7. | | This 3.5.7 clan tempers out the mirkwai comma, [0 3 4 -5> = 16875/16807, a no-twos comma. Four generators = a major 14th = 27/7. |
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| =Temperaments for a given comma=
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| ===[[Septisemi temperaments|Septisemi or Zogu temperaments]] (P8, P5, ^1)===
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| These are very low complexity temperaments tempering out the minor septimal semitone, [[21/20]] and hence equating 5/3 with 7/4. ^1 = 81/80.
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| ===[[Wizmic microtemperaments|Wizmic or Quinzo-ayoyo microtemperaments]] (P8, P5, vm7/2)===
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| A wizmic temperament is one which tempers out the wizma, [ -6 -8 2 5 > = 420175/419904. vm7 = 7/4.
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| ===[[Greenwoodmic temperaments|Greenwoodmic or Ruruyo temperaments]] (P8, P5, ^1)===
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| These temper out the greenwoodma, [-3 4 1 -2> = 405/392. ^1 = 64/63.
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| ===[[Avicennmic temperaments|Avicennmic or Zoyoyo temperaments]] (P8, P5, ^1)===
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| These temper out the avicennma, [-9 1 2 1> = 525/512, also known as Avicenna's enharmonic diesis. ^1 = 81/80.
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| ===[[Garischismic temperaments|Garischismic or Sasaru temperaments]] (P8, P5, ^1)===
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| A garischismic temperament is one which tempers out the garischisma, [25 -14 0 -1> = 33554432/33480783. ^1 = 81/80.
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| ===[[Stearnsmic temperaments|Stearnsmic or Latribiru temperaments]] (P8/2, P4/3, ^1)===
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| Stearnsmic temperaments temper out the stearnsma, [1 10 0 -6> = 118098/117649. ^1 = 81/80.
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| ===[[Cataharry temperaments|Cataharry or Labirugu temperaments]] (P8, P12/2, ^1)===
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| Cataharry temperaments temper out the cataharry comma, [-4 9 -2 -2> = 19683/19600. ^1 = 81/80.
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| ===''[[Mint temperaments|Mint or Rugu temperaments]] (P8, P5, ^1)''===
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| ''These are low complexity, high error temperaments tempering out the septimal quarter-tone, [[36/35]].''
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| ===''[[Keemic temperaments|Keemic or Zotriyo temperaments]] (P8, P5, ^1)''===
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| ''These temper out the keema, [-5 -3 3 1> = 875/864.''
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| ===''[[Starling temperaments|Starling or Zotrigu temperaments]] (P8, P5, ^1)''===
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| ''These temper out [1 2 -3 1> = [[126/125]], the septimal semicomma or starling comma the difference between three 6/5s plus one 7/6, and an octave), and include myna, sensi, valentine, casablanca and nusecond temperaments, not to mention meantone, keemun, muggles and opossum.''
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| ===''[[Marvel temperaments|Marvel or Ruyoyo temperaments]] (P8, P5, ^1)''===
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| ''These temper out [-5 2 2 -1> = [[225/224]], the marvel comma.''
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| ===''[[Orwellismic temperaments|Orwellismic or Satriru-agu temperaments]] (P8, P5, ^1)''===
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| ''These temper out [6 3 -1 -3> = 1728/1715, the orwellisma.''
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| ===[[Octagar temperaments|''Octagar or Rurutriyo temperaments'']]===
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| ''Octagar temperaments temper out the octagar comma, [5 -4 3 -2> = 4000/3969.''
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| ===''[[Hemifamity temperaments|Hemifamity or Saruyo temperaments]] (P8, P5, ^1)''===
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| ''Hemifamity temperaments temper out the hemifamity comma, [10 -6 1 -1> = 5120/5103.''
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| ===''[[Porwell temperaments|Porwell or Sarurutrigu temperaments]]'' ===
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| ''Porwell temperaments temper out the porwell comma, [11 1 -3 -2> = 6144/6125.''
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| ===''[[Hemimage temperaments|Hemimage or Satrizo-agu temperaments]] (P8, P5, ^1)''===
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| ''Hemimage temperaments temper out the hemimage comma, [5 -7 -1 3> = 10976/10935.''
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| ===''[[Horwell temperaments|Horwell or Lazoquinyo temperaments]] (P8, P5, ^1)''===
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| ''Horwell temperaments temper out the horwell comma, [-16 1 5 1> = 65625/65536.''
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| ===''[[Breedsmic temperaments|Breedsmic or Bizozogu temperaments]] (P8, P5/2, /1)''===
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| ''A breedsmic temperament is one which tempers out the breedsma, [-5 -1 -2 4> = 2401/2400.''
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| ===''[[Ragismic microtemperaments|Ragismic or Zoquadyo microtemperaments]] (P8, P5, ^1)''===
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| ''A ragismic temperament is one which tempers out [-1 -7 4 1> = 4375/4374. These are not by any means all microtemperaments, but those which are not highly accurate are probably best discussed under another heading. Accurate ones include ennealimmal, supermajor, enneadecal, amity, mitonic, parakleismic, gamera and vishnu. Pontiac belongs on the list but falls under the schismatic family rubric.''
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| ===''[[Landscape microtemperaments|Landscape or Trizogugu microtemperaments]] (P8/3, P5, ^1)''===
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| ''A landscape temperament is one which tempers out [-4 6 -6 3> = 250047/250000.''
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| =Rank-3 temperaments= | | =Rank-3 temperaments= |
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| ===[[Mint family|Mint or Rugu family]] (P8, P5, ^1)=== | | ===[[Mint family|Mint or Rugu family]] (P8, P5, ^1)=== |
| The mint temperament is a low complexity, high error temperament, tempering out the septimal quarter-tone 36/35, identifying both 7/6 with 6/5 and 5/4 with 9/7. ^1 = 81/80 or 64/63. | | The mint temperament is a low complexity, high error temperament, tempering out the septimal quarter-tone 36/35, identifying both 7/6 with 6/5 and 5/4 with 9/7. ^1 = 81/80 or 64/63. |
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| | ===[[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. ^1 = 81/80. |
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| | ===[[Wizmic microtemperaments|Wizmic or Quinzo-ayoyo microtemperaments]] (P8, P5, vm7/2)=== |
| | A wizmic temperament is one which tempers out the wizma, [ -6 -8 2 5 > = 420175/419904. vm7 = 7/4. |
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| | ===[[Greenwoodmic temperaments|Greenwoodmic or Ruruyo temperaments]] (P8, P5, ^1)=== |
| | These temper out the greenwoodma, [-3 4 1 -2> = 405/392. ^1 = 64/63. |
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| | ===[[Avicennmic temperaments|Avicennmic or Zoyoyo temperaments]] (P8, P5, ^1)=== |
| | These temper out the avicennma, [-9 1 2 1> = 525/512, also known as Avicenna's enharmonic diesis. ^1 = 81/80. |
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| | ===[[Garischismic temperaments|Garischismic or Sasaru temperaments]] (P8, P5, ^1)=== |
| | A garischismic temperament is one which tempers out the garischisma, [25 -14 0 -1> = 33554432/33480783. ^1 = 81/80. |
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| | ===[[Stearnsmic temperaments|Stearnsmic or Latribiru temperaments]] (P8/2, P4/3, ^1)=== |
| | Stearnsmic temperaments temper out the stearnsma, [1 10 0 -6> = 118098/117649. ^1 = 81/80. |
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| | ===[[Cataharry temperaments|Cataharry or Labirugu temperaments]] (P8, P12/2, ^1)=== |
| | Cataharry temperaments temper out the cataharry comma, [-4 9 -2 -2> = 19683/19600. ^1 = 81/80. |
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| =[[Rank_four_temperaments|Rank-4 temperaments]]= | | =[[Rank_four_temperaments|Rank-4 temperaments]]= |