Aberschismic: Difference between revisions
From Xenharmonic Reference
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== Supporting rank-2 temperaments == | == Supporting rank-2 temperaments == | ||
* 2.3.5.7[41 & 46]: [[Rodan]] | * 2.3.5.7[41 & 46]: [[Rodan]] | ||
* 2.3.5.7[41 & 48]: [[Tetracot#Extensions|Monkey]] | |||
* 2.3.5.7[41 & 53]: [[Garibaldi]] | * 2.3.5.7[41 & 53]: [[Garibaldi]] | ||
* 2.3.5.7[41 & 58]: [[Hemififths]] | * 2.3.5.7[41 & 58]: [[Hemififths]] | ||
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* 2.3.5.7[53 & 58]: [[Buzzard]] | * 2.3.5.7[53 & 58]: [[Buzzard]] | ||
* 2.3.5.7[87 & 99]: [[Misty]] | * 2.3.5.7[87 & 99]: [[Misty]] | ||
== Extensions == | == Extensions == | ||
* Prime 11 may be added by tempering out either 385/384 (thus equating 36/35 with 33/32; this is called Akea) or 896/891 (thus equating 81/64 with 14/11; this is called Pele). | * Prime 11 may be added by tempering out either 385/384 (thus equating 36/35 with 33/32; this is called Akea) or 896/891 (thus equating 81/64 with 14/11; this is called Pele). | ||
Revision as of 22:22, 3 April 2026
Hemifamity or Aberschismic, 2.3.5.7[41 & 46 & 53], is a 7-limit rank-3 temperament that tempers out 5120/5103 (known as the hemifamiton or the aberschisma), which manifests in several different ways:
- equates the 3-spine prime commas for 5 and 7, 81/80 and 64/63
- equates the limma 256/243 with 21/20
- equates the apotome 2187/2048 with 15/14
- equates the Pythagorean augmented fourth 729/512 with 10/7
- splits 36/35 into two equal parts each representing the "comma" 81/80 ~ 64/63
Structural theory
Aberschismic may be notated with diatonic notation and a comma symbol representing 81/80 ~ 64/63.
Supporting edos
Comma resolution
The following edos map both 81/80 and 64/63 to one edostep: 41edo, 46edo, 48edo, 53edo, 58edo.
Half-comma resolution
The following edos map both 81/80 and 64/63 to two edosteps: 87edo, 94edo, 99edo, 111edo.
Third-comma resolution
The following edos map both 81/80 and 64/63 to three edosteps: 128edo, 133edo, 135edo, 140edo, 145edo, 147edo, 152edo, 157edo.
Supporting rank-2 temperaments
- 2.3.5.7[41 & 46]: Rodan
- 2.3.5.7[41 & 48]: Monkey
- 2.3.5.7[41 & 53]: Garibaldi
- 2.3.5.7[41 & 58]: Hemififths
- 2.3.5.7[46 & 53]: Amity
- 2.3.5.7[46 & 58]: Septimal Diaschismic
- 2.3.5.7[53 & 58]: Buzzard
- 2.3.5.7[87 & 99]: Misty
Extensions
- Prime 11 may be added by tempering out either 385/384 (thus equating 36/35 with 33/32; this is called Akea) or 896/891 (thus equating 81/64 with 14/11; this is called Pele).
- Prime 13 may be added by tempering out 4096/4095 (which is the square-superparticular S64); this is the most efficient extension that adds prime 13 and is supported by edos as big as 140edo.
List of patent vals
- Main article: Hemifamity/Patent vals
