Tour of regular temperaments: Difference between revisions

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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]].

=== Laru clan (P8, P5) ===

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

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

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This clan tempers out the Latriru comma, {{Monzo|-9 11 0 -3}} = 177147/175616. Generator = ~112/81 = ~566¢. Three 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 ~~temperaments~~|Stearnsmic or Latribiru clan]] (P8/2, P4/3)===

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

~~Stearnsmic temperaments~~ temper out the stearnsma, {{Monzo|1 10 0 -6}} = 118098/117649. The period is ~486/343 = ~600¢. The generator is ~9/7 = ~434¢, or alternatively one period minus ~9/7, which equals ~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.

This clan temper out the stearnsma, {{Monzo|1 10 0 -6}} = 118098/117649. The period is ~486/343 = ~600¢. The generator is ~9/7 = ~434¢, or alternatively one period minus ~9/7, which equals ~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.

=== Laquadru clan (P8, P11/4) ===

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This clan tempers out the Saquadru comma, {{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.

=== [[Cloudy comma|Laquinzo clan]] (P8/5, P5) ===

=== [[Cloudy comma|Cloudy or Laquinzo clan]] (P8/5, P5) ===

This clan tempers out the [[cloudy comma]] ~~(Laquinzo)~~, {{Monzo|-14 0 0 5}} = 16807/16384. Five ~8/7 periods equals an 8ve, and four periods equals ~7/4. 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.

This clan tempers out the [[cloudy comma]], {{Monzo|-14 0 0 5}} = 16807/16384. Five ~8/7 periods equals an 8ve, and four periods equals ~7/4. 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.

=== Quinru clan (P8, P5/5) ===

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 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]].
-=== Laru clan (P8, P5) ===
+=== [[Harrison's comma|Harrison or Laru clan]] (P8, P5) ===
 This clan tempers out the Laru comma, {{Monzo|-13 10 0 -1}} =  59049/57344. It equates 7/4 to an augmented 6th. Its best downward extension is [[Meantone family|septimal meantone]].
@@ Line 210: / Line 210: @@
 This clan tempers out the Latriru comma, {{Monzo|-9 11 0 -3}} = 177147/175616. Generator = ~112/81 = ~566¢. Three 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 temperaments|Stearnsmic or Latribiru clan]] (P8/2, P4/3)===
+===[[Stearnsmic clan|Stearnsmic or Latribiru clan]] (P8/2, P4/3)===
-Stearnsmic temperaments temper out the stearnsma, {{Monzo|1 10 0 -6}} = 118098/117649. The period is ~486/343 = ~600¢. The generator is ~9/7 = ~434¢, or alternatively one period minus ~9/7, which equals ~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.
+This clan temper out the stearnsma, {{Monzo|1 10 0 -6}} = 118098/117649. The period is ~486/343 = ~600¢. The generator is ~9/7 = ~434¢, or alternatively one period minus ~9/7, which equals ~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.
 === Laquadru clan (P8, P11/4) ===
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 This clan tempers out the Saquadru comma, {{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.
-=== [[Cloudy comma|Laquinzo clan]] (P8/5, P5) ===
+=== [[Cloudy comma|Cloudy or Laquinzo clan]] (P8/5, P5) ===
-This clan tempers out the [[cloudy comma]] (Laquinzo), {{Monzo|-14 0 0 5}} = 16807/16384. Five ~8/7 periods equals an 8ve, and four periods equals ~7/4. 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.
+This clan tempers out the [[cloudy comma]], {{Monzo|-14 0 0 5}} = 16807/16384. Five ~8/7 periods equals an 8ve, and four periods equals ~7/4. 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.
 === Quinru clan (P8, P5/5) ===