Tour of regular temperaments: Difference between revisions

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=== [[Negri|Negri or Laquadyo family]] (P8, P4/4) ===

This tempers out the [[negri comma]], [-14 3 4>. Its generator is ~16/15 , four of which make ~4/3. 5/4 is equated to 3 generators.

This tempers out the [[negri comma]], [-14 3 4>. Its generator is ~16/15, four of which make ~4/3. 5/4 is equated to 3 generators.

===[[Tetracot family|Tetracot or Saquadyo family]] (P8, P5/4)===

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=== Latriru clan (P8, P11/3) ===

This clan tempers out [-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 7~~-limit~~ interpretation of the generator is 7/5, leading to the [[Liese]] temperament, which is a weak extension of Meantone.

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

Stearnsmic temperaments temper out the stearnsma, [1 10 0 -6> = 118098/117649. The period is ~486/343 = ~600¢. The generator is ~9/7 = ~434¢, or ~~alternately~~ 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.

Stearnsmic temperaments temper out the stearnsma, [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.

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

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=== [[Rastmic temperaments|Rastmic or Neutral or Lulu clan]] (P8, P5/2) ===

This 2.3.11 clan tempers out 243/242 = [-1 5 0 0 -2>. Its generator is ~11/9. Two generators equals ~3/2. 11/8 is equated to 5 generators minus an octave. This clan includes as a strong extension the [[Dicot]] temperament, which is in the Dicot family.

=== Laquadlo clan (P8/2, M2/4) ===

This 2.3.11 clan tempers out [-17 2 0 0 4>. Its half-ocave period is ~363/256, and its generator is ~33/32. Four generators equals ~9/8. 3/2 is equated to a period plus 2 generators, and 11/8 is equated to a period minus a generator. This clan includes as a strong extension the Comic aka Saquadyobi temperament, which is in the Comic family.

=== [[Hemif|Hemif or Thuthu clan]] (P8, P5/2) ===

This 2.3.13 clan tempers out 512/507 = [9 -1 0 0 0 -2>. Its generator is ~16/13. Two generators equals ~3/2. 13/8 is equated to 1 octave minus 1 generator. This clan includes as a strong extension the [[Dicot]] temperament, which is in the Dicot family.

=== Satritho clan (P8, P11/3) ===

This 2.3.13 clan tempers out 512/507 = [0 -7 0 0 0 3>. Its generator is ~18/13. Three generators equals ~8/3. 13/8 is equated to 7 generators minus three octaves. This clan is related to the Latriru clan.

== 2.5.7 Clans ==

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 === [[Negri|Negri or Laquadyo family]] (P8, P4/4) ===
-This tempers out the [[negri comma]], [-14 3 4&gt;. Its generator is ~16/15 , four of which make ~4/3. 5/4 is equated to 3 generators.
+This tempers out the [[negri comma]], [-14 3 4&gt;. Its generator is ~16/15, four of which make ~4/3. 5/4 is equated to 3 generators.
 ===[[Tetracot family|Tetracot or Saquadyo family]] (P8, P5/4)===
@@ Line 193: / Line 193: @@
 === Latriru clan (P8, P11/3) ===
-This clan tempers out [-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 7-limit interpretation of the generator is 7/5, leading to the [[Liese]] temperament, which is a weak extension of Meantone.
+This clan tempers out [-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|Stearnsmic or Latribiru clan]] (P8/2, P4/3)===
-Stearnsmic temperaments temper out the stearnsma, [1 10 0 -6&gt; = 118098/117649. The period is ~486/343 = ~600¢. The generator is ~9/7 = ~434¢, or alternately 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.
+Stearnsmic temperaments temper out the stearnsma, [1 10 0 -6&gt; = 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.
 === Laquadru clan (P8, P11/4) ===
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 === [[Rastmic temperaments|Rastmic or Neutral or Lulu clan]] (P8, P5/2) ===
 This 2.3.11 clan tempers out 243/242 = [-1 5 0 0 -2>. Its generator is ~11/9. Two generators equals ~3/2. 11/8 is equated to 5 generators minus an octave. This clan includes as a strong extension the [[Dicot]] temperament, which is in the Dicot family.
+=== Laquadlo clan (P8/2, M2/4) ===
+This 2.3.11 clan tempers out [-17 2 0 0 4>. Its half-ocave period is ~363/256, and its generator is ~33/32. Four generators equals ~9/8. 3/2 is equated to a period plus 2 generators, and 11/8 is equated to a period minus a generator. This clan includes as a strong extension the Comic aka Saquadyobi temperament, which is in the Comic family.
 === [[Hemif|Hemif or Thuthu clan]] (P8, P5/2) ===
 This 2.3.13 clan tempers out 512/507 = [9 -1 0 0 0 -2>. Its generator is ~16/13. Two generators equals ~3/2. 13/8 is equated to 1 octave minus 1 generator. This clan includes as a strong extension the [[Dicot]] temperament, which is in the Dicot family.
+=== Satritho clan (P8, P11/3) ===
+This 2.3.13 clan tempers out 512/507 = [0 -7 0 0 0 3>. Its generator is ~18/13. Three generators equals ~8/3. 13/8 is equated to 7 generators minus three octaves. This clan is related to the Latriru clan.
 == 2.5.7 Clans ==