Hemimean clan: Difference between revisions

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The '''hemimean clan'''~~, tempering~~ out the no-threes hemimean comma [[3136/3125]], contains the temperaments hemithirds, misty, and semisept, considered below, as well as [[Meantone family #Septimal meantone|septimal meantone]], [[Archytas clan #Passion|passion]], [[Augmented family #Hexe|hexe]], [[Würschmidt family #Hemiwürschmidt|hemiwürschmidt]], [[Ragismic microtemperaments #Parakleismic|parakleismic]], [[Kleismic family #Clyde|clyde]], [[Schismatic family #Bischismic|bischismic]], and [[Sycamore family #Sycamore|sycamore]] considered elsewhere.

The '''hemimean clan''' tempers out the no-threes hemimean comma [[3136/3125]].

= Didacus =

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== Extensions ==

Full 7-limit [[extension]]s of didacus, in general, split the [[syntonic comma]] into two, each for [[126/125]]~[[225/224]], as 3136/3125 = (126/125)/(225/224). These include hemithirds, misty, semisept, sengagen, subpental, arch, and emka, considered below, as well as [[Meantone family #Septimal meantone|septimal meantone]], [[Archytas clan #Passion|passion]], [[Augmented family #Hexe|hexe]], [[Würschmidt family #Hemiwürschmidt|hemiwürschmidt]], [[Ragismic microtemperaments #Parakleismic|parakleismic]], [[Kleismic family #Clyde|clyde]], [[Schismatic family #Bischismic|bischismic]], and [[Sycamore family #Sycamore|sycamore]] considered elsewhere.

A notable subgroup extension of didacus is [[Chromatic pairs #Roulette|roulette]].

= Hemithirds =

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-The '''hemimean clan''', tempering out the no-threes hemimean comma [[3136/3125]], contains the temperaments hemithirds, misty, and semisept, considered below, as well as [[Meantone family #Septimal meantone|septimal meantone]], [[Archytas clan #Passion|passion]], [[Augmented family #Hexe|hexe]], [[Würschmidt family #Hemiwürschmidt|hemiwürschmidt]], [[Ragismic microtemperaments #Parakleismic|parakleismic]], [[Kleismic family #Clyde|clyde]], [[Schismatic family #Bischismic|bischismic]], and [[Sycamore family #Sycamore|sycamore]] considered elsewhere.
+The '''hemimean clan''' tempers out the no-threes hemimean comma [[3136/3125]].
 = Didacus =
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 {{Val list|legend=1| 6, 19, 25, 31, 99, 130, 161, 353, 514c }}
+== Extensions ==
+Full 7-limit [[extension]]s of didacus, in general, split the [[syntonic comma]] into two, each for [[126/125]]~[[225/224]], as 3136/3125 = (126/125)/(225/224). These include hemithirds, misty, semisept, sengagen, subpental, arch, and emka, considered below, as well as [[Meantone family #Septimal meantone|septimal meantone]], [[Archytas clan #Passion|passion]], [[Augmented family #Hexe|hexe]], [[Würschmidt family #Hemiwürschmidt|hemiwürschmidt]], [[Ragismic microtemperaments #Parakleismic|parakleismic]], [[Kleismic family #Clyde|clyde]], [[Schismatic family #Bischismic|bischismic]], and [[Sycamore family #Sycamore|sycamore]] considered elsewhere.
+A notable subgroup extension of didacus is [[Chromatic pairs #Roulette|roulette]].
 = Hemithirds =