Tour of regular temperaments: Difference between revisions

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]].

This clan tempers out the Laru comma {{Monzo|-13 10 0 -1}} =  50.7¢. It equates 7/4 to an augmented 6th. Its best downward extension is [[Meantone family|Septimal Meantone]].

This clan tempers out the Laruru comma {{Monzo|-7 8 0 -2}} = 78¢. 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 Diaschismatic or Sagugu temperament and the Jubalismic or Biruyo temperament.

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]].

This clan tempers out the Sasa-zozo comma {{Monzo|15 -13 0 2}} = 12.2¢, and includes as a strong extension the [[Hemififths]] temperament. 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, {{Monzo|-1 6 0 -3}} = 105¢, 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|Augmented or Trigu]] temperament.

This clan tempers out the Trizo comma, {{Monzo|-2 -4 0 3}} = 99¢, 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 Latriru comma {{Monzo|-9 11 0 -3}} = 15.0¢. 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 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|Porcupine or Triyo]] temperament, as does equating the period to ~7/5.

This clan tempers out the Laquadru comma {{Monzo|-3 9 0 -4}} = 42.3¢. 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 Saquadru comma {{Monzo|16 -3 0 -4}} = 18.8¢. 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.

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

This clan tempers out the Laquinzo comma {{Monzo|-14 0 0 5}} = 44¢. 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 Quinru comma {{Monzo|3 7 0 -5}} = 70¢. 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.  

This clan tempers out the Saquinzo comma {{Monzo|5 -12 0 5}} = 20.7¢. Its generator is ~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.

This clan tempers out the Sepru comma {{Monzo|7 8 0 -7}} = 33.8¢. 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.