Tour of regular temperaments: Difference between revisions

Line 87:

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, ~~P12~~/3)===

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

The tricot family tempers out the [[Tricot|tricot comma]], {{Monzo|39 -29 3}}. The generator is ~13/9 = ~~~634¢~~, or ~18/13 = ~~~566¢~~. Three generators of ~13/9 ~~equals a compound 5th~~ of ~3/1.

The tricot family tempers out the [[Tricot|tricot comma]], {{Monzo|39 -29 3}}. The generator is ~59049/40960 = [-13 10 -1> = 633¢, or its octave inverse ~81920/59049 = 567¢. Three of the latter generators equals a compound 4th of ~8/3. 5/4 is equated to 14 octaves minus 29 of these generators. An obvious 7-limit interpretation of the generator is 81/56 = 639¢, a much simpler ratio which leads to the [[Tour of Regular Temperaments#Latriru clan (P8, P11/3)|Latriru clan]]. An obvious 13-limit interpretation is 13/9 = 637¢, an even simpler ratio implying the [[Tour of Regular Temperaments#Satritho clan (P8, P11/3)|Satritho clan]].

===[[Dimipent family|Dimipent or Quadgu family]] (P8/4, P5)===

@@ Line 87: / Line 87: @@
 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, P12/3)===
+===[[Tricot family|Tricot or Quadsatriyo family]] (P8, P11/3)===
-The tricot family tempers out the [[Tricot|tricot comma]], {{Monzo|39 -29 3}}. The generator is ~13/9 = ~634¢, or ~18/13 = ~566¢. Three generators of ~13/9 equals a compound 5th of ~3/1.
+The tricot family tempers out the [[Tricot|tricot comma]], {{Monzo|39 -29 3}}. The generator is ~59049/40960 = [-13 10 -1> = 633¢, or its octave inverse ~81920/59049 = 567¢. Three of the latter generators equals a compound 4th of ~8/3. 5/4 is equated to 14 octaves minus 29 of these generators. An obvious 7-limit interpretation of the generator is 81/56 = 639¢, a much simpler ratio which leads to the [[Tour of Regular Temperaments#Latriru clan (P8, P11/3)|Latriru clan]]. An obvious 13-limit interpretation is 13/9 = 637¢, an even simpler ratio implying the [[Tour of Regular Temperaments#Satritho clan (P8, P11/3)|Satritho clan]].
 ===[[Dimipent family|Dimipent or Quadgu family]] (P8/4, P5)===