Aberschismic: Difference between revisions
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* 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). | ||
* Prime 13 may be added by tempering out 4096/4095; this is the most efficient extension that adds prime 13 and is supported by edos as big as [[140edo]]. | * Prime 13 may be added by tempering out 4096/4095; 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]]'' | |||
{{navbox regtemp}} | {{navbox regtemp}} | ||
{{Cat|Temperaments}} | {{Cat|Temperaments}} | ||
Revision as of 22:11, 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
Supporting rank-2 temperaments
- 2.3.5.7[41 & 46]: Rodan
- 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; 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
