Laka: Difference between revisions

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-#redirect [[Hemifamity family #Laka]]
+{{Infobox regtemp
+| Title = Laka
+| Subgroups = 2.3.5.7.11; 2.3.5.7.11.13
+| Comma basis = [[540/539]], [[5120/5103]]; <br>[[352/351]], [[540/539]], [[729/728]]
+| Edo join 1 = 41 | Edo join 2 = 53 | Edo join 3 = 58
+| Mapping = 1; 1 0 -6 15 12; 0 1 1 -1 -1
+| Generators = 3/2; 5/4 | Generators tuning = 702.6; 386.8
+| Optimization method = CWE
+| Odd limit 1 = 11 | Mistuning 1 = 1.74 | Complexity 1 = ?
+| Odd limit 2 = 13-limit 21 | Mistuning 2 = 3.20 | Complexity 2 = ?
+}}
+The '''laka''' [[rank-3 temperament]] is one of the [[11-limit]] [[extension]]s of [[aberschismic]], inheriting the [[chain of fifths|chain-of-fifths-based]] structure and the generic comma step that results from equating the [[81/80|syntonic]] and [[64/63|septimal commas]]. It [[tempering out|tempers out]] [[540/539]], which makes it a member of [[swetismic temperaments]], and as a consequence, [[11/8]] is mapped to the comma-up augmented third (C–^E♯).
-[[Category:Temperaments]]
+The canonical [[extension]] to the [[13-limit]] maps [[13/11]] to the diatonic minor third, which is the exact mean of [[6/5]] and [[7/6]], and implies [[13/8]] is the comma-up augmented fifth (C–^G♯) and that [[352/351]], [[640/637]], [[729/728]] and [[847/845]] are tempered out. Additionally, a no-17 [[19-limit]] extension is available by recognizing [[19/16]] at the comma-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:Hemifamity family]]
+See [[Aberschismic family #Laka]] for technical data.
+== 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]]