Laka: Difference between revisions
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# | '''Laka''' is a [[rank-3 temperament|rank-3]] [[regular temperament|temperament]] generated by a perfect fifth of [[~]][[3/2]] and a step for the [[81/80|syntonic]]~[[64/63|septimal comma]] to reach the interval classes of [[5/1|5]], [[7/1|7]], and higher [[prime harmonic|primes]]. Using an arrow to represent this comma step, we have [[5/4]] at the down major third (C–vE), [[7/4]] at the down minor seventh (C–vBb), and [[11/8]] at the up augmented third (C–^E#), [[tempering out]] [[540/539]], which makes it a member of [[swetismic temperaments]]. | ||
[[Category: | The canonical [[extension]] to the [[13-limit]] finds [[13/8]] at the up augmented fifth (C–^G#), tempering out [[352/351]], [[640/637]], [[729/728]] and [[847/845]], and a no-17 [[19-limit]] extension is available by recognizing [[19/16]] at the down augmented second (C–vD#), tempering out [[400/399]], [[456/455]] and [[495/494]]. 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. | ||
[[Category: | |||
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> | |||
These lattices show laka as generated by ~2, ~3/2, and ~7/4 for a direct comparison with pele. | |||
== Chords and harmony == | |||
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 | |||
== Tunings == | |||
{| class="wikitable mw-collapsible mw-collapsed" | |||
|+ style="font-size: 105%; white-space: nowrap;" | 11-limit norm-based tunings | |||
|- | |||
! rowspan="2" | | |||
! colspan="3" | Euclidean | |||
|- | |||
! Constrained | |||
! Constrained & skewed | |||
! Destretched | |||
|- | |||
! Tenney | |||
| CTE: ~3/2 = 702.5133{{c}}, ~5/4 = 385.5563{{c}} | |||
| CWE: ~3/2 = 702.6175{{c}}, ~5/4 = 386.4170{{c}} | |||
| POTE: ~3/2 = 702.6640{{c}}, ~5/4 = 386.8005{{c}} | |||
|} | |||
{| class="wikitable mw-collapsible mw-collapsed" | |||
|+ style="font-size: 105%; white-space: nowrap;" | 13-limit norm-based tunings | |||
|- | |||
! rowspan="2" | | |||
! colspan="3" | Euclidean | |||
|- | |||
! Constrained | |||
! Constrained & skewed | |||
! Destretched | |||
|- | |||
! Tenney | |||
| CTE: ~3/2 = 702.4078{{c}}, ~5/4 = 385.5405{{c}} | |||
| CWE: ~3/2 = 702.5780{{c}}, ~5/4 = 386.7718{{c}} | |||
| POTE: ~3/2 = 702.6464{{c}}, ~5/4 = 387.2662{{c}} | |||
|} | |||
{| class="wikitable mw-collapsible mw-collapsed" | |||
|+ style="font-size: 105%; white-space: nowrap;" | No-17 19-limit norm-based tunings | |||
|- | |||
! rowspan="2" | | |||
! colspan="3" | Euclidean | |||
|- | |||
! Constrained | |||
! Constrained & skewed | |||
! Destretched | |||
|- | |||
! Tenney | |||
| CTE: ~3/2 = 702.4062{{c}}, ~5/4 = 385.5254{{c}} | |||
| CWE: ~3/2 = 702.5613{{c}}, ~5/4 = 386.6230{{c}} | |||
| POTE: ~3/2 = 702.6221{{c}}, ~5/4 = 387.0532{{c}} | |||
|} | |||
[[Category:Laka| ]] <!-- main article --> | |||
[[Category:Rank-3 temperaments]] | |||
[[Category:Aberschismic family]] | |||
[[Category:Swetismic temperaments]] | [[Category:Swetismic temperaments]] | ||