Laka - Revision history

FloraC: Rework

2026-07-26T07:00:48Z

Rework

← Older revision		Revision as of 07:00, 26 July 2026
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	\| Odd limit 2 = 13-limit 21 \| Mistuning 2 = 3.20 \| Complexity 2 = ?		\| Odd limit 2 = 13-limit 21 \| Mistuning 2 = 3.20 \| Complexity 2 = ?
	}}		}}
	'''~~Laka~~''' ~~is a~~ [[rank-3 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]]~~.		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♯).

	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.		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.

	See [[~~Hemifamity~~ family #Laka]] for technical ~~details~~.		See [[Aberschismic family #Laka]] for technical data.

	== Interval lattice ==		== Interval lattice ==

FloraC: + infobox

2026-07-24T15:51:29Z

+ infobox

← Older revision		Revision as of 15:51, 24 July 2026
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			{{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 = ?
			}}
	'''Laka''' is a [[rank-3 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]].		'''Laka''' is a [[rank-3 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]].

FloraC: Text replacement - "rank-3 temperament" to "rank-3 temperament"

2026-06-08T08:36:19Z

Text replacement - "rank-3 temperament" to "rank-3 temperament"

← Older revision		Revision as of 08:36, 8 June 2026
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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]].		'''Laka''' is a [[rank-3 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]].

	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.		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.

FloraC: Text replacement - "Category:Hemifamity family" to "Category:Aberschismic family"

2026-06-06T12:41:19Z

Text replacement - "Category:Hemifamity family" to "Category:Aberschismic family"

← Older revision		Revision as of 12:41, 6 June 2026
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	[[Category:Laka\| ]] <!-- main article -->		[[Category:Laka\| ]] <!-- main article -->
	[[Category:Rank-3 temperaments]]		[[Category:Rank-3 temperaments]]
	[[Category:~~Hemifamity~~ family]]		[[Category:Aberschismic family]]
	[[Category:Swetismic temperaments]]		[[Category:Swetismic temperaments]]

FloraC: /* Chords */ -> chords and harmony

2025-10-22T07:13:37Z

Chords: -> chords and harmony

← Older revision		Revision as of 07:13, 22 October 2025
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	These lattices show laka as generated by ~2, ~3/2, and ~7/4 for a direct comparison with pele.		These lattices show laka as generated by ~2, ~3/2, and ~7/4 for a direct comparison with pele.

	== Chords ==		== 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]].		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]].

FloraC: /* Tunings */

2025-10-22T07:12:34Z

Tunings

← Older revision		Revision as of 07:12, 22 October 2025
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	\|-		\|-
	! Tenney		! Tenney
	\| CTE: ~3/2 = 702.5133, ~5/4 = 385.5563{{c}}		\| CTE: ~3/2 = 702.5133{{c}}, ~5/4 = 385.5563{{c}}
	\| CWE: ~3/2 = 702.6175, ~5/4 = 386.4170{{c}}		\| CWE: ~3/2 = 702.6175{{c}}, ~5/4 = 386.4170{{c}}
	\| POTE: ~3/2 = 702.6640, ~5/4 = 386.8005{{c}}		\| POTE: ~3/2 = 702.6640{{c}}, ~5/4 = 386.8005{{c}}
	\|}		\|}

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	\|-		\|-
	! Tenney		! Tenney
	\| CTE: ~3/2 = 702.4078, ~5/4 = 385.5405{{c}}		\| CTE: ~3/2 = 702.4078{{c}}, ~5/4 = 385.5405{{c}}
	\| CWE: ~3/2 = 702.5780, ~5/4 = 386.7718{{c}}		\| CWE: ~3/2 = 702.5780{{c}}, ~5/4 = 386.7718{{c}}
	\| POTE: ~3/2 = 702.6464, ~5/4 = 387.2662{{c}}		\| POTE: ~3/2 = 702.6464{{c}}, ~5/4 = 387.2662{{c}}
	\|}		\|}

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	\|-		\|-
	! Tenney		! Tenney
	\| CTE: ~3/2 = 702.4062, ~5/4 = 385.5254{{c}}		\| CTE: ~3/2 = 702.4062{{c}}, ~5/4 = 385.5254{{c}}
	\| CWE: ~3/2 = 702.5613, ~5/4 = 386.6230{{c}}		\| CWE: ~3/2 = 702.5613{{c}}, ~5/4 = 386.6230{{c}}
	\| POTE: ~3/2 = 702.6221, ~5/4 = 387.0532{{c}}		\| POTE: ~3/2 = 702.6221{{c}}, ~5/4 = 387.0532{{c}}
	\|}		\|}

FloraC: + basic tunings

2025-10-22T07:07:42Z

+ basic tunings

@@ Line 19: / Line 19: @@
 * [[Dekany laka]] – a transversal scale
-== Notes ==
+== Tunings ==
 [[Category:Laka| ]] <!-- main article -->

FloraC: - parent category

2025-04-29T09:53:34Z

- parent category

← Older revision		Revision as of 09:53, 29 April 2025
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	== Notes ==		== Notes ==

	~~[[Category:Temperaments]]~~
	[[Category:Laka\| ]] <!-- main article -->		[[Category:Laka\| ]] <!-- main article -->
	[[Category:Rank-3 temperaments]]		[[Category:Rank-3 temperaments]]
	[[Category:Hemifamity family]]		[[Category:Hemifamity family]]
	[[Category:Swetismic temperaments]]		[[Category:Swetismic temperaments]]

Lériendil at 23:11, 19 April 2025

2025-04-19T23:11:09Z

← Older revision		Revision as of 23:11, 19 April 2025
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	[[Category:Temperaments]]		[[Category:Temperaments]]
	[[Category:Laka\| ]] <!-- main article -->		[[Category:Laka\| ]] <!-- main article -->
			[[Category:Rank-3 temperaments]]
	[[Category:Hemifamity family]]		[[Category:Hemifamity family]]
	[[Category:Swetismic temperaments]]		[[Category:Swetismic temperaments]]

FloraC: Address the no-17 19-limit extension

2025-04-19T15:19:35Z

Address the no-17 19-limit extension

← Older revision		Revision as of 15:19, 19 April 2025
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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]]. The canonical [[extension]] to the [[13-limit]] ~~tempers~~ out [[352/351]], [[640/637]], [[729/728]] and [[847/845]], and ~~to the~~ no-17 [[19-limit]], [[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.		'''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]].

			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.

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