Laka - Revision history

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.

FloraC: Rework on intro for readability. Move the discussion on the 17-limit extension to the hemifamity family

2025-04-19T14:42:17Z

Rework on intro for readability. Move the discussion on the 17-limit extension to the hemifamity family

← Older revision		Revision as of 14:42, 19 April 2025
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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.~~		'''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.

	[[~~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.		See [[Hemifamity family #Laka]] for technical details.
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	<gallery>		<gallery>
	File:Lattice Laka.png\|13-limit laka		File:Lattice Laka.png\|13-limit laka
	File:Lattice Laka19.png\|2.3.5.7.11.13.19 subgroup laka		File:Lattice Laka19.png\|2.3.5.7.11.13.19-subgroup laka
	</gallery>		</gallery>

FloraC: +section for footnotes

2024-01-21T16:32:42Z

+section for footnotes

← Older revision		Revision as of 16:32, 21 January 2024
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	== Scales ==		== Scales ==
	* [[Dekany laka]] – a transversal scale		* [[Dekany laka]] – a transversal scale

			== Notes ==

	[[Category:Temperaments]]		[[Category:Temperaments]]