Tour of regular temperaments: Difference between revisions

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===[[Porcupine family|Porcupine or Triyo family]] (P8, P4/3)===

The porcupine family tempers out {{Monzo|1 -5 3}} = [[250/243]], the difference between three 10/9's (1000/729) and 4/3, known as the maximal diesis or porcupine comma. It subdivides the fourth into three equal parts, each taken as an approximated 10/9, of which two approximate 6/5. It also manifests itself as the difference between three 6/5's and 16/9, as the difference between 10/9 and 27/25, and as the difference between 81/80 and 25/24. 5/4 is equated to 1 octave minus 5 generators. Some porcupine temperaments include [[15edo]], [[22edo]], [[37edo]], and [[59edo]]. An important 7-limit extension also tempers out 64/63.

~~===[[Laconic family|Laconic or Latrigubi family]] (P8, P5/3)===~~

This low-accuracy family of temperaments tempers out the laconic comma, {{Monzo|-4 7 -3}} (2187/2000), which is the difference between three 10/9's and one 3/2. The generator is ~10/9 = ~230¢. 5/4 is equated to 7 generators minus 1 octave. Laconic is supported by [[16edo]], [[21edo]], and [[37edo]] (using the 37b mapping), among others. An obvious 7-limit interpretation of the generator is ~8/7, which leads to Gamelismic aka Latrizo.

===[[Tricot family|Tricot or Quadsatriyo family]] (P8, P11/3)===

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===[[Vulture family|Vulture or Sasa-quadyo family]] (P8, P12/4)===

This tempers out the [[vulture comma]], {{Monzo|24 -21 4}}. Its generator is ~320/243 = ~475¢, four of which make ~3/1. 5/4 is equated to 21 generators minus 8 octaves. An obvious 7-limit interpretation of the generator is 21/16, which makes Saquadru.

~~===[[Comic family|Comic or Saquadyobi family]] (P8/2, M2/4)===~~

This tempers out the comic comma, {{Monzo|13 -14 4}} = 5120000/4782969. Its generator is ~81/80 = 55¢. 5/4 is equated to 7 generators. An obvious 11-limit interpretation of the generator is 33/32, which makes Laquadlo.

===[[Pental family|Pental or Trila-quingu family]] (P8/5, P5)===

This tempers out the pental comma, 847288609443/838860800000 = {{Monzo|-28 25 -5}}. The period is 59049/51200, and 5 periods make an octave. The generator is a 5th, or equivalently, 3/5 of an 8ve minus a 5th. This alternate generator is only about 18¢, thus the scales have a very lopsided L/s ratio. 5/4 is equated to 2/5 of an octave minus 5 of these 18¢ generators. An obvious 7-limit interpretation of the generator is 8/7, which leads to Laquinzo.

===[[Ripple family|Ripple or Quingu family]] (P8, P4/5)===

This tempers out the ripple comma, 6561/6250 = {{Monzo| -1 8 -5 }}, which equates a stack of four [[10/9]]'s with [[8/5]]. As one might expect, [[12edo]] is about as accurate as it can be.

===[[Amity family|Amity or Saquinyo family]] (P8, P11/5)===

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 ===[[Porcupine family|Porcupine or Triyo family]] (P8, P4/3)===
 The porcupine family tempers out {{Monzo|1 -5 3}} = [[250/243]], the difference between three 10/9's (1000/729) and 4/3, known as the maximal diesis or porcupine comma. It subdivides the fourth into three equal parts, each taken as an approximated 10/9, of which two approximate 6/5. It also manifests itself as the difference between three 6/5's and 16/9, as the difference between 10/9 and 27/25, and as the difference between 81/80 and 25/24. 5/4 is equated to 1 octave minus 5 generators. Some porcupine temperaments include [[15edo]], [[22edo]], [[37edo]], and [[59edo]]. An important 7-limit extension also tempers out 64/63.
-===[[Laconic family|Laconic or Latrigubi family]] (P8, P5/3)===
-This low-accuracy family of temperaments tempers out the laconic comma, {{Monzo|-4 7 -3}} (2187/2000), which is the difference between three 10/9's and one 3/2. The generator is ~10/9 = ~230¢. 5/4 is equated to 7 generators minus 1 octave. Laconic is supported by [[16edo]], [[21edo]], and [[37edo]] (using the 37b mapping), among others. An obvious 7-limit interpretation of the generator is ~8/7, which leads to Gamelismic aka Latrizo.
 ===[[Tricot family|Tricot or Quadsatriyo family]] (P8, P11/3)===
@@ Line 101: / Line 98: @@
 ===[[Vulture family|Vulture or Sasa-quadyo family]] (P8, P12/4)===
 This tempers out the [[vulture comma]], {{Monzo|24 -21 4}}. Its generator is ~320/243 = ~475¢, four of which make ~3/1. 5/4 is equated to 21 generators minus 8 octaves. An obvious 7-limit interpretation of the generator is 21/16, which makes Saquadru.
-===[[Comic family|Comic or Saquadyobi family]] (P8/2, M2/4)===
-This tempers out the comic comma, {{Monzo|13 -14 4}} = 5120000/4782969. Its generator is ~81/80 = 55¢. 5/4 is equated to 7 generators. An obvious 11-limit interpretation of the generator is 33/32, which makes Laquadlo.
 ===[[Pental family|Pental or Trila-quingu family]] (P8/5, P5)===
 This tempers out the pental comma, 847288609443/838860800000 = {{Monzo|-28 25 -5}}. The period is 59049/51200, and 5 periods make an octave. The generator is a 5th, or equivalently, 3/5 of an 8ve minus a 5th. This alternate generator is only about 18¢, thus the scales have a very lopsided L/s ratio.  5/4 is equated to 2/5 of an octave minus 5 of these 18¢ generators. An obvious 7-limit interpretation of the generator is 8/7, which leads to Laquinzo.
+===[[Ripple family|Ripple or Quingu family]] (P8, P4/5)===
+This tempers out the ripple comma, 6561/6250 = {{Monzo| -1 8 -5 }}, which equates a stack of four [[10/9]]'s with [[8/5]]. As one might expect, [[12edo]] is about as accurate as it can be.
 ===[[Amity family|Amity or Saquinyo family]] (P8, P11/5)===