Tour of regular temperaments: Difference between revisions

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===[[Gamelismic clan|Gamelismic or Latrizo clan]] (P8, P5/3)===

This clan tempers out the gamelisma, {{Monzo|-10 1 0 3}} = 1029/1024. Three ~8/7 generators equals a 5th. 7/4 is equated to an 8ve minus a generator. A particularly noteworthy member of the gamelismic clan is miracle, but other members include valentine, unidec, mothra, rodan, and hemithirds. Miracle temperament divides the fifth into 6 equal steps, thus it's a weak extension. Its 21-note scale called "blackjack" and 31-note scale called "canasta" have some useful properties. It is the most efficient 11-limit temperament for many purposes, with a tuning close to 72-EDO.

This clan tempers out the gamelisma, {{Monzo|-10 1 0 3}} = 1029/1024. Three ~8/7 generators equals a 5th. 7/4 is equated to an 8ve minus a generator. Five generators is slightly flat of 2/1, making this a [[cluster temperament]]. See also Sawa and Lasepzo.

A particularly noteworthy member of the gamelismic clan is miracle, but other members include valentine, unidec, mothra, rodan, and hemithirds. Miracle temperament divides the fifth into 6 equal steps, thus it's a weak extension. Its 21-note scale called "blackjack" and 31-note scale called "canasta" have some useful properties. It is the most efficient 11-limit temperament for many purposes, with a tuning close to 72-EDO.

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

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=== Saquinzo clan (P8, P12/5) ===

This clan tempers out the Saquinzo comma, {{Monzo|5 -12 0 5}} = 537824/531441. 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.

=== Lasepzo clan (P8, P11/7) ===

This clan tempers out the Lasepzo comma [-18 -1 0 7> = 823543/786432. Its generator is ~8/7. Six generators equals ~7/3, and seven generators equals ~8/3. Three generators is ~30¢ sharp of 3/2, and five generators is ~15¢ sharp of 2/1, making this a [[cluster temperament]]. See also Sawa and Latrizo.

=== Sepru clan (P8, P12/7) ===

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 ===[[Gamelismic clan|Gamelismic or Latrizo clan]] (P8, P5/3)===
-This clan tempers out the gamelisma, {{Monzo|-10 1 0 3}} = 1029/1024. Three ~8/7 generators equals a 5th. 7/4 is equated to an 8ve minus a generator. A particularly noteworthy member of the gamelismic clan is miracle, but other members include valentine, unidec, mothra, rodan, and hemithirds. Miracle temperament divides the fifth into 6 equal steps, thus it's a weak extension. Its 21-note scale called "blackjack" and 31-note scale called "canasta" have some useful properties. It is the most efficient 11-limit temperament for many purposes, with a tuning close to 72-EDO.
+This clan tempers out the gamelisma, {{Monzo|-10 1 0 3}} = 1029/1024. Three ~8/7 generators equals a 5th. 7/4 is equated to an 8ve minus a generator. Five generators is slightly flat of 2/1, making this a [[cluster temperament]]. See also Sawa and Lasepzo.
+A particularly noteworthy member of the gamelismic clan is miracle, but other members include valentine, unidec, mothra, rodan, and hemithirds. Miracle temperament divides the fifth into 6 equal steps, thus it's a weak extension. Its 21-note scale called "blackjack" and 31-note scale called "canasta" have some useful properties. It is the most efficient 11-limit temperament for many purposes, with a tuning close to 72-EDO.
 === Latriru clan (P8, P11/3) ===
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 === Saquinzo clan (P8, P12/5) ===
 This clan tempers out the Saquinzo comma, {{Monzo|5 -12 0 5}} = 537824/531441. 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.
+=== Lasepzo clan (P8, P11/7) ===
+This clan tempers out the Lasepzo comma [-18 -1 0 7> = 823543/786432. Its generator is ~8/7. Six generators equals ~7/3, and seven generators equals ~8/3. Three generators is ~30¢ sharp of 3/2, and five generators is ~15¢ sharp of 2/1, making this a [[cluster temperament]]. See also Sawa and Latrizo.
 === Sepru clan (P8, P12/7) ===