Hemifamity family: Difference between revisions
m Spell 1\1 in decimal, note the badness metric being used, and misc. cleanup |
Move the discussion on 17-limit extensions of laka here |
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== Laka == | == Laka == | ||
{{Main| Laka }} | {{Main| Laka }} | ||
Laka can be described as the {{nowrap| 41 & 53 & 58 }} temperament, tempering out [[540/539]]. [[Gene Ward Smith]] considered it to be a [[17-limit]] temperament, assigning †442/441 ({{nowrap| 41g & 53 & 58 }}) as the main extension. It should be noted that {{nowrap| 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 makes most sense as a 2.3.5.7.11.13.19-[[subgroup]] temperament, omitting harmonic 17, as the 19 is accurate and easily available in a 24-tone scale. | |||
[[Subgroup]]: 2.3.5.7.11 | [[Subgroup]]: 2.3.5.7.11 | ||
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Badness (Smith): 0.781 × 10<sup>-3</sup> | Badness (Smith): 0.781 × 10<sup>-3</sup> | ||
== Notes == | |||
[[Category:Temperament families]] | [[Category:Temperament families]] | ||