Aberschismic: Difference between revisions
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{{Interwiki | |||
| en = Aberschismic | |||
| de = Aberrschismisch | |||
| es = | |||
| ja = | |||
| ko = 애버스키스믹 (음률) | |||
}} | |||
{{Infobox regtemp | |||
| Title = Aberschismic | |||
| Subgroups = 2.3.5.7 | |||
| Comma basis = [[5120/5103]] | |||
| Edo join 1 = 12 | Edo join 2 = 41 | Edo join 3 = 46 | |||
| Mapping = 1; 1 0 -6; 0 1 1 | |||
| Generators = 3/2; 5/4 | Generators tuning = 702.8; 386.5 | |||
| Optimization method = CWE | |||
| Odd limit 1 = 9 | Mistuning 1 = 1.44 | Complexity 1 = ? | |||
}} | |||
'''Aberschismic''' (formerly ''hemifamity'') is a [[rank-3 temperament]] that equates the syntonic comma of [[81/80]] with the septimal comma of [[64/63]], bisecting their sum, the septimal quartertone of [[36/35]], and [[tempering out|tempering out]] their difference, the [[aberschisma]]. This reduces the two [[formal comma]]s required for [[7-limit]] [[JI]] to one generic comma step, and classical and septimal intervals are found on the same [[chain of fifths]] inflected by this step to the opposite sides. In addition, [[10/7]] is identified with the diatonic augmented fourth (C–F♯), and [[50/49]] is identified with the [[Pythagorean comma]] (C–B♯′). Because of this, aberschismic favors a slightly sharp [[3/2|perfect fifth]], in contrast to simpler temperaments like [[marvel]] or [[starling]]. | |||
[[Category: | Aberschismic is the head of the [[aberschismic family]]; notable [[11-limit]] [[extension]]s include [[pele]] (41 & 46 & 58), [[laka]] (41 & 53 & 58), [[akea]] (41 & 46 & 53), and [[lono]] (46 & 53 & 58). | ||
This article concerns the basic 7-limit temperament, aberschismic itself. | |||
The temperament's name was derived from [[Tristan Bay]]'s name for the corresponding comma, ''aberschisma'', proposed in 2024 and officialized in 2026. The former name ''hemifamity'' was a contraction of ''[[hemififths]]'' and ''[[amity]]'', two of the [[support]]ing rank-2 temperaments. | |||
See [[Aberschismic family #Aberschismic]] for technical data. | |||
== Interval lattice == | |||
[[File:Lattice Aberschismic.png|960px]] | |||
== Notation == | |||
Aberschismic is easily notated with [[chain-of-fifths notation]] with an extra pair of accidental for the generic comma step. As an example, we can use up and down arrows (^/v) for the comma step. Note that this comma step does ''not'' represent the [[Pythagorean comma]], unless it is further tempered to [[cassandra]]. Aberschismic can therefore be seen cassandra with the Pythagorean comma decoupled from the generic comma step. | |||
{| class="wikitable center-1 center-3" | |||
|+Nomenclature of selected intervals | |||
! Ratio | |||
! Name | |||
! Example<br>on C | |||
|- | |||
| 3/2 | |||
| Perfect fifth | |||
| C–G | |||
|- | |||
| 5/4 | |||
| Down major third | |||
| C–vE | |||
|- | |||
| 7/4 | |||
| Down minor seventh | |||
| C–vB♭ | |||
|} | |||
== Tunings == | |||
[[Edo]] tunings where the comma step is one step wide and all [[9-odd-limit]] intervals are distinct include [[41edo|41]], [[46edo|46]], [[53edo|53]], and [[58edo|58]]. Sums of these edos tend to give more accurate tunings. | |||
{| class="wikitable center-all left-5 mw-collapsible mw-collapsed" | |||
|+ style="font-size: 105%; white-space: nowrap;" | Target tunings | |||
|- | |||
! rowspan="2" | Target | |||
! colspan="2" | Minimax | |||
|- | |||
! Generators | |||
! Eigenmonzo basis | |||
|- | |||
| 7-odd-limit | |||
| ~3/2 = 702.7775{{c}}, ~5/4 = 386.3137{{c}} | |||
| 2.5.7/3 | |||
|- | |||
| 9-odd-limit | |||
| ~3/2 = 702.6747{{c}}, ~5/4 = 386.3137{{c}} | |||
| 2.5.9/7 | |||
|} | |||
{| class="wikitable mw-collapsible mw-collapsed" | |||
|+ style="font-size: 105%; white-space: nowrap;" | Norm-based tunings | |||
|- | |||
! rowspan="2" | | |||
! colspan="3" | Euclidean | |||
|- | |||
! Constrained | |||
! Constrained & skewed | |||
! Destretched | |||
|- | |||
! Tenney | |||
| CTE: ~3/2 = 702.7918{{c}}, ~5/4 = 386.0144{{c}} | |||
| CWE: ~3/2 = 700.8166{{c}}, ~5/4 = 386.5465{{c}} | |||
| POTE: ~3/2 = 702.8292{{c}}, ~5/4 = 386.8177{{c}} | |||
|} | |||
== Music == | |||
; [[Gene Ward Smith]] | |||
* ''Choraled'' (archived 2010) – [http://www.archive.org/details/Choraled details] | [http://www.archive.org/download/Choraled/Genewardsmith-Choraled.mp3 play] | |||
; [[Chris Vaisvil]] | |||
* [https://web.archive.org/web/20201127015604/http://clones.soonlabel.com/public/micro/hemifamity27/hemifamity27-IF-20100917.mp3 ''Hemifamity27''] | |||
[[Category:Aberschismic| ]] <!-- main article --> | |||
[[Category:Rank-3 temperaments]] | [[Category:Rank-3 temperaments]] | ||
[[Category:Aberschismic family]] | [[Category:Aberschismic family]] | ||