Hemifamity: Difference between revisions
From Xenharmonic Reference
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== Supporting edos == | == Supporting edos == | ||
=== Comma resolution === | === Comma resolution === | ||
[[41edo]], [[46edo]], [[48edo]], [[53edo]], [[58edo]] | The following edos map both 81/80 and 64/63 to one edostep: [[41edo]], [[46edo]], [[48edo]], [[53edo]], [[58edo]]. | ||
=== Half-comma resolution === | === Half-comma resolution === | ||
[[87edo]], [[94edo]], [[99edo]], [[111edo]] | The following edos map both 81/80 and 64/63 to two edosteps: [[87edo]], [[94edo]], [[99edo]], [[111edo]]. | ||
=== Third-comma resolution === | === Third-comma resolution === | ||
[[128edo]], [[133edo]], [[135edo]], [[140edo]], [[145edo]], [[147edo]], [[152edo]], [[157edo]] | 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 == | == Supporting rank-2 temperaments == | ||
* 2.3.5.7[41 & 46]: [[Rodan]] | * 2.3.5.7[41 & 46]: [[Rodan]] | ||
Revision as of 22:21, 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 & 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
| View • Talk • EditRegular temperaments | |
|---|---|
| Rank-2 | |
| Acot | Blackwood (1/5-octave) • Whitewood (1/7-octave) • Compton (1/12-octave) |
| Monocot | Meantone • Schismic • Leapday • Archy |
| Complexity 2 | Diaschismic (diploid monocot) • Pajara (diploid monocot) • Injera (diploid monocot) • Rastmatic (dicot) • Mohajira (dicot) • Intertridecimal (dicot) • Interseptimal (alpha-dicot) |
| Complexity 3 | Augmented (triploid) • Misty (triploid) • Slendric (tricot) • Porcupine (omega-tricot) |
| Complexity 4 | Diminished (tetraploid) • Tetracot (tetracot) • Buzzard (alpha-tetracot) • Squares (beta-tetracot) • Negri (omega-tetracot) |
| Complexity 5-6 | Magic (alpha-pentacot) • Amity (gamma-pentacot) • Kleismic (alpha-hexacot) • Miracle (hexacot) |
| Higher complexity | Orwell (alpha-heptacot) • Sensi (beta-heptacot) • Octacot (octacot) • Wurschmidt (beta-octacot) • Valentine (enneacot) • Ammonite (epsilon-enneacot) • Myna (beta-decacot) • Ennealimmal (enneaploid dicot) |
| Straddle-3 | A-Team (alter-tricot) • Machine (alter-monocot) |
| No-3 | Trismegistus (alpha-triseph) • Orgone (trimech) • Didacus (diseph) |
| No-octaves | Sensamagic (monogem) |
| Exotemperament | Dicot • Mavila • Father |
| Higher-rank | |
| Rank-3 | Hemifamity • Marvel • Parapyth |
