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 | 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 | Belonging to it and considered below are undecental, leapday, mystery, quanic and ketchup. Other hemifamity temperaments are: | ||
* ''[[Dominant]]'' | * ''[[Dominant]]'' → [[Meantone family #Dominant|Meantone family]] | ||
* ''[[ | : +36/35, the 12 & 17c temperament, generated by the fifth with 5/4 mapped to the M3. | ||
* [[ | * [[Garibaldi]] → [[Schismatic family #Garibaldi|Schismatic family]] | ||
* [[Rodan]] | : +225/224, the 41 & 53 temperament, generated by the fifth with 5/4 mapped to the d4. | ||
* ''[[Monkey]]'' | * ''[[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. | ||
* ''[[Diaschismic]]'' → [[Diaschismic family #Diaschismic|Diaschismic family]] | |||
* [[Misty]] | : +126/125, the 46 & 58 temperament, generated by the fifth and using a semioctave period. | ||
* [[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. | ||
* ''[[ | * [[Rodan]] → [[Gamelismic clan #Rodan|Gamelismic clan]] | ||
* ''[[ | : +245/243, the 41 & 46 temperament, fifth sliced into three as does slendric. | ||
* ''[[ | * ''[[Monkey]]'' → [[Tetracot family #Monkey|Tetracot family]] | ||
* | : +875/864, the 34 & 41 temperament, fifth sliced into four as does tetracot. | ||
* ''[[ | * [[Buzzard]] → [[Vulture family #Buzzard|Vulture family]] | ||
* ''[[ | : +1728/1715, the 53 & 58 temperament, twelfth sliced into four as does vulture. | ||
* ''[[Alphaquarter]]'' | * [[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 == | == Undecental == | ||