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.

[[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's the way the numbers fall. The Laka geometry happens to work reasonably well in the 13-limit but not so well in the 17-limit. There isn't one obvious 17-limit extension and none of them are competitive with other 17-limit temperaments.

</blockquote>

—[[Graham Breed]]<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101682.html#101776 Yahoo! Tuning Group | ''Laka 17-limit minimax planar temperament'']</ref>

It corresponds to the fact that [[41edo|41et]] and [[53edo|53et]] tune the 13-limit quite well but fail at the 17-limit. As such, laka 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. This again is related to the fact that 41et and 53et are good in the said subgroup.

See [[Hemifamity family #Laka]] for technical details.

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File:Lattice Laka19.png|2.3.5.7.11.13.19 subgroup laka

</gallery>

These lattices show laka as generated by ~2, ~3/2, and ~7/4 for a direct comparison with pele.

== Chords ==

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[[Category:Temperaments]]

[[Category:Laka| ]]

[[Category:Hemifamity family]]

[[Category:Swetismic temperaments]]

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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.
+[[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.
+<blockquote>
+It's the way the numbers fall. The Laka geometry happens to work reasonably well in the 13-limit but not so well in the 17-limit. There isn't one obvious 17-limit extension and none of them are competitive with other 17-limit temperaments.
+</blockquote>
+—[[Graham Breed]]<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101682.html#101776 Yahoo! Tuning Group | ''Laka 17-limit minimax planar temperament'']</ref>
+It corresponds to the fact that [[41edo|41et]] and [[53edo|53et]] tune the 13-limit quite well but fail at the 17-limit. As such, laka 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. This again is related to the fact that 41et and 53et are good in the said subgroup.
 See [[Hemifamity family #Laka]] for technical details.
@@ Line 10: / Line 17: @@
 File:Lattice Laka19.png|2.3.5.7.11.13.19 subgroup laka
 </gallery>
+These lattices show laka as generated by ~2, ~3/2, and ~7/4 for a direct comparison with pele.
 == Chords ==
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 [[Category:Temperaments]]
+[[Category:Laka| ]] <!-- main article -->
 [[Category:Hemifamity family]]
 [[Category:Swetismic temperaments]]