Aberschismic temperaments: Difference between revisions

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The hemifamity temperaments temper out the hemifamity comma, {{monzo| 10 -6 1 -1 }} = [[5120/5103]], dividing an exact or approximate septimal quartertone, [[36/35]] into two equal steps, each representing [[81/80]]~[[64/63]], the syntonic comma or the septimal comma. Therefore, classical and septimal intervals are found by the same circle of fifths inflected by the syntonic~septimal comma to the opposite sides. In addition we may identify [[10/7]] by the augmented fourth and [[50/49]] by the [[Pythagorean comma]].

Belonging to it and considered below are undecental, leapday, mystery, quanic, septiquarter, countriton and ~~ketchup~~. Other hemifamity temperaments are:

Belonging to it and considered below are undecental, leapday, mystery, quanic, septiquarter, countriton, ketchup, and artoneutral. Other hemifamity temperaments are:

* ''[[Dominant]]'' → [[Meantone family #Dominant|Meantone family]]

* ''[[Dominant]]'' → [[Meantone family #Dominant|Meantone family]] (+36/35, the 12 & 17c temperament, generated by the fifth with 5/4 mapped to the M3)

: +36/35, the 12 & 17c temperament, generated by the fifth with 5/4 mapped to the M3.

* [[Garibaldi]] → [[Schismatic family #Garibaldi|Schismatic family]] (+225/224, the 41 & 53 temperament, generated by the fifth with 5/4 mapped to the d4)

* [[Garibaldi]] → [[Schismatic family #Garibaldi|Schismatic family]]

* ''[[Kwai]]'' → [[Mirkwai clan #Kwai|Mirkwai clan]] (+16875/16807, the 41 & 70 temperament, generated by the fifth with 5/4 mapped to the 4A7 aka m3 + 3 Pyth. commas)

: +225/224, the 41 & 53 temperament, generated by the fifth with 5/4 mapped to the d4.

* ''[[Diaschismic]]'' → [[Diaschismic family #Diaschismic|Diaschismic family]] (+126/125, the 46 & 58 temperament, generated by the fifth and using a semioctave period)

* ''[[Kwai]]'' → [[Mirkwai clan #Kwai|Mirkwai clan]]

* [[Hemififths]] → [[Breedsmic temperaments #Hemififths|Breedsmic temperaments]] (+2401/2400, the 41 & 58 temperament, fifth sliced into two and 5/4 mapped to the hemififth + Pyth. comma)

: +16875/16807, the 41 & 70 temperament, generated by the fifth with 5/4 mapped to the 4A7 aka m3 + 3 Pyth. commas.

* [[Rodan]] → [[Gamelismic clan #Rodan|Gamelismic clan]] (+245/243, the 41 & 46 temperament, fifth sliced into three as does slendric)

* ''[[Diaschismic]]'' → [[Diaschismic family #Diaschismic|Diaschismic family]]

* ''[[Trimot]]'' → [[Tricot family #Trimot|Tricot family]] (+2430/2401, the 53 & 70 temperament, twelfth sliced into three as does tricot)

: +126/125, the 46 & 58 temperament, generated by the fifth and using a semioctave period.

* ''[[Monkey]]'' → [[Tetracot family #Monkey|Tetracot family]] (+875/864, the 34 & 41 temperament, fifth sliced into four as does tetracot)

* [[Hemififths]] → [[Breedsmic temperaments #Hemififths|Breedsmic temperaments]]

* [[Buzzard]] → [[Vulture family #Buzzard|Vulture family]] (+1728/1715, the 53 & 58 temperament, twelfth sliced into four as does vulture)

: +2401/2400, the 41 & 58 temperament, fifth sliced into two and 5/4 mapped to the hemififth + Pyth. comma.

* [[Misty]] → [[Misty family #Misty|Misty family]] (+3136/3125, the 12 & 99 temperament, generated by the fifth and using a 1/3-octave period)

* [[Rodan]] → [[Gamelismic clan #Rodan|Gamelismic clan]]

* ''[[Supers]]'' → [[Stearnsmic clan #Supers|Stearnsmic clan]] (+118098/117649, the 36c & 58 temperament, fifth sliced into three and using a semioctave period)

: +245/243, the 41 & 46 temperament, fifth sliced into three as does slendric.

* ''[[Undim]]'' → [[Undim family #Septimal undim|Undim family]] (+390625/388962, the 12 & 140 temperament, generated by the fifth and using a 1/4-octave period)

* ''[[Trimot]]'' → [[Tricot family #Trimot|Tricot family]]

* ''[[Quinticosiennic]]'' → [[Quintaleap family #Quinticosiennic|Quintaleap family]] (+395136/390625, the 12 & 145 temperament, fourth sliced into five)

: +2430/2401, the 53 & 70 temperament, twelfth sliced into three as does tricot.

* ''[[Quintakwai]]'' → [[Quindromeda family #Quintakwai|Quindromeda family]] (+9765625/9680832, the 12 & 181 temperament, fourth sliced into five)

* ''[[Monkey]]'' → [[Tetracot family #Monkey|Tetracot family]]

* [[Amity]] → [[Amity family #Septimal amity|Amity family]] (+4375/4374, the 46 & 53 temperament, eleventh sliced into five)

: +875/864, the 34 & 41 temperament, fifth sliced into four as does tetracot.

* ''[[Countercata]]'' → [[Kleismic family #Countercata|Kleismic family]] (+15625/15552, the 34 & 53 temperament, twelfth sliced into six as does hanson)

* [[Buzzard]] → [[Vulture family #Buzzard|Vulture family]]

* ''[[Warrior]]'' → [[Sensipent family #Warrior|Sensipent family]] (+78732/78125, the 46 & 65d temperament, 6th harmonic sliced into seven as does sensi)

: +1728/1715, the 53 & 58 temperament, twelfth sliced into four as does vulture.

* ''[[Alphaquarter]]'' → [[Escapade family #Alphaquarter|Escapade family]] (+29360128/29296875, the 65d & 87 temperament, fourth sliced into nine as does escapade)

* [[Misty]] → [[Misty family #Misty|Misty family]]

: +3136/3125, the 12 & 99 temperament, generated by the fifth and using a 1/3-octave period.

* ''[[Supers]]'' → [[Stearnsmic clan #Supers|Stearnsmic clan]]

: +118098/117649, the 36c & 58 temperament, fifth sliced into three and using a semioctave period.

* ''[[Undim]]'' → [[Undim family #Septimal undim|Undim family]]

: +390625/388962, the 12 & 140 temperament, generated by the fifth and using a 1/4-octave period.

* ''[[Quinticosiennic]]'' → [[Quintaleap family #Quinticosiennic|Quintaleap family]]

: +395136/390625, the 12 & 145 temperament, fourth sliced into five.

* ''[[Quintakwai]]'' → [[Quindromeda family #Quintakwai|Quindromeda family]]

: +9765625/9680832, the 12 & 181 temperament, fourth sliced into five.

* [[Amity]] → [[Amity family #Septimal amity|Amity family]]

: +4375/4374, the 46 & 53 temperament, eleventh sliced into five.

* ''[[Countercata]]'' → [[Kleismic family #Countercata|Kleismic family]]

: +15625/15552, the 34 & 53 temperament, twelfth sliced into six as does hanson.

* ''[[Warrior]]'' → [[Sensipent family #Warrior|Sensipent family]]

: +78732/78125, the 46 & 65d temperament, 6th harmonic sliced into seven as does sensi.

* ''[[Alphaquarter]]'' → [[Escapade family #Alphaquarter|Escapade family]]

: +29360128/29296875, the 65d & 87 temperament, fourth sliced into nine as does escapade.

== Undecental ==

@@ Line 1: / Line 1: @@
 The hemifamity temperaments temper out the hemifamity comma, {{monzo| 10 -6 1 -1 }} = [[5120/5103]], dividing an exact or approximate septimal quartertone, [[36/35]] into two equal steps, each representing [[81/80]]~[[64/63]], the syntonic comma or the septimal comma. Therefore, classical and septimal intervals are found by the same circle of fifths inflected by the syntonic~septimal comma to the opposite sides. In addition we may identify [[10/7]] by the augmented fourth and [[50/49]] by the [[Pythagorean comma]].
-Belonging to it and considered below are undecental, leapday, mystery, quanic, septiquarter, countriton and ketchup. Other hemifamity temperaments are:
+Belonging to it and considered below are undecental, leapday, mystery, quanic, septiquarter, countriton, ketchup, and artoneutral. Other hemifamity temperaments are:
-* ''[[Dominant]]'' → [[Meantone family #Dominant|Meantone family]]
+* ''[[Dominant]]'' → [[Meantone family #Dominant|Meantone family]] (+36/35, the 12 & 17c temperament, generated by the fifth with 5/4 mapped to the M3)
-: +36/35, the 12 & 17c temperament, generated by the fifth with 5/4 mapped to the M3.
+* [[Garibaldi]] → [[Schismatic family #Garibaldi|Schismatic family]] (+225/224, the 41 & 53 temperament, generated by the fifth with 5/4 mapped to the d4)
-* [[Garibaldi]] → [[Schismatic family #Garibaldi|Schismatic family]]
+* ''[[Kwai]]'' → [[Mirkwai clan #Kwai|Mirkwai clan]] (+16875/16807, the 41 & 70 temperament, generated by the fifth with 5/4 mapped to the 4A7 aka m3 + 3 Pyth. commas)
-: +225/224, the 41 & 53 temperament, generated by the fifth with 5/4 mapped to the d4.
+* ''[[Diaschismic]]'' → [[Diaschismic family #Diaschismic|Diaschismic family]] (+126/125, the 46 & 58 temperament, generated by the fifth and using a semioctave period)
-* ''[[Kwai]]'' → [[Mirkwai clan #Kwai|Mirkwai clan]]
+* [[Hemififths]] → [[Breedsmic temperaments #Hemififths|Breedsmic temperaments]] (+2401/2400, the 41 & 58 temperament, fifth sliced into two and 5/4 mapped to the hemififth + Pyth. comma)
-: +16875/16807, the 41 & 70 temperament, generated by the fifth with 5/4 mapped to the 4A7 aka m3 + 3 Pyth. commas.
+* [[Rodan]] → [[Gamelismic clan #Rodan|Gamelismic clan]] (+245/243, the 41 & 46 temperament, fifth sliced into three as does slendric)
-* ''[[Diaschismic]]'' → [[Diaschismic family #Diaschismic|Diaschismic family]]
+* ''[[Trimot]]'' → [[Tricot family #Trimot|Tricot family]] (+2430/2401, the 53 & 70 temperament, twelfth sliced into three as does tricot)
-: +126/125, the 46 & 58 temperament, generated by the fifth and using a semioctave period.
+* ''[[Monkey]]'' → [[Tetracot family #Monkey|Tetracot family]] (+875/864, the 34 & 41 temperament, fifth sliced into four as does tetracot)
-* [[Hemififths]] → [[Breedsmic temperaments #Hemififths|Breedsmic temperaments]]
+* [[Buzzard]] → [[Vulture family #Buzzard|Vulture family]] (+1728/1715, the 53 & 58 temperament, twelfth sliced into four as does vulture)
-: +2401/2400, the 41 & 58 temperament, fifth sliced into two and 5/4 mapped to the hemififth + Pyth. comma.
+* [[Misty]] → [[Misty family #Misty|Misty family]] (+3136/3125, the 12 & 99 temperament, generated by the fifth and using a 1/3-octave period)
-* [[Rodan]] → [[Gamelismic clan #Rodan|Gamelismic clan]]
+* ''[[Supers]]'' → [[Stearnsmic clan #Supers|Stearnsmic clan]] (+118098/117649, the 36c & 58 temperament, fifth sliced into three and using a semioctave period)
-: +245/243, the 41 & 46 temperament, fifth sliced into three as does slendric.
+* ''[[Undim]]'' → [[Undim family #Septimal undim|Undim family]] (+390625/388962, the 12 & 140 temperament, generated by the fifth and using a 1/4-octave period)
-* ''[[Trimot]]'' → [[Tricot family #Trimot|Tricot family]]
+* ''[[Quinticosiennic]]'' → [[Quintaleap family #Quinticosiennic|Quintaleap family]] (+395136/390625, the 12 & 145 temperament, fourth sliced into five)
-: +2430/2401, the 53 & 70 temperament, twelfth sliced into three as does tricot.
+* ''[[Quintakwai]]'' → [[Quindromeda family #Quintakwai|Quindromeda family]] (+9765625/9680832, the 12 & 181 temperament, fourth sliced into five)
-* ''[[Monkey]]'' → [[Tetracot family #Monkey|Tetracot family]]
+* [[Amity]] → [[Amity family #Septimal amity|Amity family]] (+4375/4374, the 46 & 53 temperament, eleventh sliced into five)
-: +875/864, the 34 & 41 temperament, fifth sliced into four as does tetracot.
+* ''[[Countercata]]'' → [[Kleismic family #Countercata|Kleismic family]] (+15625/15552, the 34 & 53 temperament, twelfth sliced into six as does hanson)
-* [[Buzzard]] → [[Vulture family #Buzzard|Vulture family]]
+* ''[[Warrior]]'' → [[Sensipent family #Warrior|Sensipent family]] (+78732/78125, the 46 & 65d temperament, 6th harmonic sliced into seven as does sensi)
-: +1728/1715, the 53 & 58 temperament, twelfth sliced into four as does vulture.
+* ''[[Alphaquarter]]'' → [[Escapade family #Alphaquarter|Escapade family]] (+29360128/29296875, the 65d & 87 temperament, fourth sliced into nine as does escapade)
-* [[Misty]] → [[Misty family #Misty|Misty family]]
-: +3136/3125, the 12 & 99 temperament, generated by the fifth and using a 1/3-octave period.
-* ''[[Supers]]'' → [[Stearnsmic clan #Supers|Stearnsmic clan]]
-: +118098/117649, the 36c & 58 temperament, fifth sliced into three and using a semioctave period.
-* ''[[Undim]]'' → [[Undim family #Septimal undim|Undim family]]
-: +390625/388962, the 12 & 140 temperament, generated by the fifth and using a 1/4-octave period.
-* ''[[Quinticosiennic]]'' → [[Quintaleap family #Quinticosiennic|Quintaleap family]]
-: +395136/390625, the 12 & 145 temperament, fourth sliced into five.
-* ''[[Quintakwai]]'' → [[Quindromeda family #Quintakwai|Quindromeda family]]
-: +9765625/9680832, the 12 & 181 temperament, fourth sliced into five.
-* [[Amity]] → [[Amity family #Septimal amity|Amity family]]
-: +4375/4374, the 46 & 53 temperament, eleventh sliced into five.
-* ''[[Countercata]]'' → [[Kleismic family #Countercata|Kleismic family]]
-: +15625/15552, the 34 & 53 temperament, twelfth sliced into six as does hanson.
-* ''[[Warrior]]'' → [[Sensipent family #Warrior|Sensipent family]]
-: +78732/78125, the 46 & 65d temperament, 6th harmonic sliced into seven as does sensi.
-* ''[[Alphaquarter]]'' → [[Escapade family #Alphaquarter|Escapade family]]
-: +29360128/29296875, the 65d & 87 temperament, fourth sliced into nine as does escapade.
 == Undecental ==