Laka: Difference between revisions
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'''Laka''' is the [[Rank-3 temperament|rank-3]] [[temperament]] [[tempering out]] [[540/539]] and [[5120/5103]], with the canonical [[extension]] to the [[13-limit]] tempering out [[352/351]], [[640/637]], [[729/728]] and [[847/845]]. The [[lattice]] structure is very comparable to that of [[pele]], but it is more complex as many of the simple divisive ratios are further away from the origin. | |||
[[Gene Ward Smith]] considered laka to be a [[17-limit]] temperament, assigning †442/441 (41g & 53 & 58) as the main extension. It should be noted that 41 & 53g & 58 also makes for a possible extension. It makes the most sense as a 2.3.5.7.11.13.19 [[subgroup]] temperament, omitting [[harmonic]] [[17/1|17]], as [[19/1|19]] is easily available in a 24-tone scale, shown in the lattice below. | |||
See [[Hemifamity family #Laka]] for technical details. | |||
== Interval lattice == | |||
<gallery> | |||
File:Lattice Laka.png|13-limit laka | |||
File:Lattice Laka19.png|2.3.5.7.11.13.19 subgroup laka | |||
</gallery> | |||
== Chords == | |||
Laka enables [[essentially tempered chord]]s of [[swetismic chords|swetismic]] in the [[11-odd-limit]], in addition to [[major minthmic chords|major minthmic]], [[huntmic chords|huntmic]], [[squbemic chords|squbemic]] and [[cuthbert chords|cuthbert]] in the [[13-odd-limit]]. | |||
== Scales == | |||
* [[Dekany laka]] – a transversal scale | |||
[[Category:Temperaments]] | [[Category:Temperaments]] | ||
[[Category:Hemifamity family]] | [[Category:Hemifamity family]] | ||
[[Category:Swetismic temperaments]] | [[Category:Swetismic temperaments]] | ||
Revision as of 15:47, 21 January 2024
Laka is the rank-3 temperament tempering out 540/539 and 5120/5103, with the canonical extension to the 13-limit tempering out 352/351, 640/637, 729/728 and 847/845. The lattice structure is very comparable to that of pele, but it is more complex as many of the simple divisive ratios are further away from the origin.
Gene Ward Smith considered laka to be a 17-limit temperament, assigning †442/441 (41g & 53 & 58) as the main extension. It should be noted that 41 & 53g & 58 also makes for a possible extension. It makes the most sense as a 2.3.5.7.11.13.19 subgroup temperament, omitting harmonic 17, as 19 is easily available in a 24-tone scale, shown in the lattice below.
See Hemifamity family #Laka for technical details.
Interval lattice
-
13-limit laka -
2.3.5.7.11.13.19 subgroup laka
Chords
Laka enables essentially tempered chords of swetismic in the 11-odd-limit, in addition to major minthmic, huntmic, squbemic and cuthbert in the 13-odd-limit.
Scales
- Dekany laka – a transversal scale