Lemba - Revision history

FloraC: + mos

2026-02-25T05:59:21Z

+ mos

← Older revision		Revision as of 05:59, 25 February 2026
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	\| Mapping = 2; 3 -1 -1 5 1		\| Mapping = 2; 3 -1 -1 5 1
	\| Generators = 8/7 \| Generators tuning = 231.2 \| Optimization method = CWE		\| Generators = 8/7 \| Generators tuning = 231.2 \| Optimization method = CWE
	\| MOS scales = [[4L 2s]], [[6L 4s]]		\| MOS scales = [[4L 2s]], [[6L 4s]], [[10L 6s]]
	\| Odd limit 1 = 9 \| Mistuning 1 = 17.5 \| Complexity 1 = 16		\| Odd limit 1 = 9 \| Mistuning 1 = 17.5 \| Complexity 1 = 16
	\| Odd limit 2 = 13 \| Mistuning 2 = 21.5 \| Complexity 2 = 16		\| Odd limit 2 = 13 \| Mistuning 2 = 21.5 \| Complexity 2 = 16

FloraC: + infobox, paragraphing & misc. cleanup

2026-02-25T05:58:25Z

+ infobox, paragraphing & misc. cleanup

← Older revision		Revision as of 05:58, 25 February 2026
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	<!-- ~~interwiki~~ -->		{{Interwiki
	[[~~de:Slendrisch#Lemba\|Lemba~~]]		\| en = Lemba
	'''Lemba''' is a [[regular temperament]] which is a natural extension of the [[jubilismic clan]] and a member of the [[gamelismic clan]]. This means that the perfect fifth of [[~]][[3/2]] is split into three equal parts, each approximating [[8/7]]. It also means the period is half an octave, and repeats precisely a tritone apart, tempering out [[50/49]]. A generator plus a period comes very close to the [[golden ratio]] phi, which means ratios in the sequence 8:13:21:34:55 etc. are also well approximated, and any one of these can be made just by choosing a suitable [[eigenmonzo]] (unchanged interval). The combination of these factors means many composite ratios in the 2.3.5.7.13.17 subgroup are both well approximated and accessible with a relatively small gamut, giving you a strong selection of chords to choose from. Its main weaknesses are that ratios of 5 and 13 are conflated by the tempering out of [[65/64]], favoring 13 in the better tunings, so traditional major and minor chords are strongly neutral flavoured (supraminor and submajor), and ratios involving 11 are not approximated at all until you have a large gamut. It forms [[mos scale]]s that are always double a fibonacci sequence number, at 4, 6, 10, 16, 26, etc, which means L/s ratios remain well mixed and clearly distinct many iterations down. Related temperaments include [[Gamelismic clan #Baladic\|baladic]], which discards the 5 and 11 to improve the accuracy of the 2.3.7.13.17 subgroup, and is very accurate in all of these except the 13, or [[echidnic]], which has a slightly sharper generator that sacrifices the precision of 7 and logarithmic phi to map most other intervals in a more accurate but complex way.		\| de = Slendrisch #Lemba
			\| es =
			\| ja =
			}}
			{{Infobox regtemp
			\| Title = Lemba
			\| Subgroups = 2.3.5.7, 2.3.5.7.11, 2.3.5.7.11.13
			\| Comma basis = [[50/49]], [[525/512]] (7-limit);<br>[[45/44]], [[50/49]], [[385/384]] (11-limit);<br>[[45/44]], [[50/49]], [[65/64]], [[78/77]]<br>(13-limit)
			\| Edo join 1 = 10 \| Edo join 2 = 16
			\| Mapping = 2; 3 -1 -1 5 1
			\| Generators = 8/7 \| Generators tuning = 231.2 \| Optimization method = CWE
			\| MOS scales = [[4L 2s]], [[6L 4s]]
			\| Odd limit 1 = 9 \| Mistuning 1 = 17.5 \| Complexity 1 = 16
			\| Odd limit 2 = 13 \| Mistuning 2 = 21.5 \| Complexity 2 = 16
			}}
			'''Lemba''' is a [[regular temperament]] which is a natural [[extension]] of the [[jubilismic clan]] and a member of the [[gamelismic clan]]. This means that the perfect fifth of [[~]][[3/2]] is split into three equal parts, each approximating [[8/7]]. It also means the period is half an octave, and repeats precisely a tritone apart, tempering out [[50/49]]. A generator plus a period comes very close to the [[golden ratio]] phi, which means ratios in the sequence 8:13:21:34:55 etc. are also well approximated, and any one of these can be made just by choosing a suitable [[eigenmonzo]] (unchanged interval). The combination of these factors means many composite ratios in the 2.3.5.7.13.17 subgroup are both well approximated and accessible with a relatively small gamut, giving you a strong selection of chords to choose from. Its main weaknesses are that ratios of 5 and 13 are conflated by the tempering out of [[65/64]], favoring 13 in the better tunings, so traditional major and minor chords are strongly neutral flavoured (supraminor and submajor), and ratios involving 11 are not approximated at all until you have a large gamut. It forms [[mos scale]]s that are always double a fibonacci sequence number, at 4, 6, 10, 16, 26, etc, which means L/s ratios remain well mixed and clearly distinct many iterations down.

			Related temperaments include [[Gamelismic clan #Baladic\|baladic]], which discards the 5 and 11 to improve the accuracy of the 2.3.7.13.17 subgroup, and is very accurate in all of these except the 13, or [[echidnic]], which has a slightly sharper generator that sacrifices the precision of 7 and logarithmic phi to map most other intervals in a more accurate but complex way.

	The name is from [[Herman Miller]]'s conlang name for the temperament.		The name is from [[Herman Miller]]'s conlang name for the temperament.
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	* [https://sites.google.com/site/teamouse/lemba-gpo-test.mp3 ''GPO Lemb''a]		* [https://sites.google.com/site/teamouse/lemba-gpo-test.mp3 ''GPO Lemb''a]

	[[Billy Stiltner]]		; [[Billy Stiltner]]
	* [https://billystiltner.bandcamp.com/track/26lembaforxmt ''26lembaforxmt'']		* [https://billystiltner.bandcamp.com/track/26lembaforxmt ''26lembaforxmt'']

Hstraub at 17:26, 22 January 2026

2026-01-22T17:26:05Z

← Older revision		Revision as of 17:26, 22 January 2026
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	<!-- interwiki -->		<!-- interwiki -->
	[[de:Slendrisch#Lemba\|~~Slendrisch-~~Lemba]]		[[de:Slendrisch#Lemba\|Lemba]]
	'''Lemba''' is a [[regular temperament]] which is a natural extension of the [[jubilismic clan]] and a member of the [[gamelismic clan]]. This means that the perfect fifth of [[~]][[3/2]] is split into three equal parts, each approximating [[8/7]]. It also means the period is half an octave, and repeats precisely a tritone apart, tempering out [[50/49]]. A generator plus a period comes very close to the [[golden ratio]] phi, which means ratios in the sequence 8:13:21:34:55 etc. are also well approximated, and any one of these can be made just by choosing a suitable [[eigenmonzo]] (unchanged interval). The combination of these factors means many composite ratios in the 2.3.5.7.13.17 subgroup are both well approximated and accessible with a relatively small gamut, giving you a strong selection of chords to choose from. Its main weaknesses are that ratios of 5 and 13 are conflated by the tempering out of [[65/64]], favoring 13 in the better tunings, so traditional major and minor chords are strongly neutral flavoured (supraminor and submajor), and ratios involving 11 are not approximated at all until you have a large gamut. It forms [[mos scale]]s that are always double a fibonacci sequence number, at 4, 6, 10, 16, 26, etc, which means L/s ratios remain well mixed and clearly distinct many iterations down. Related temperaments include [[Gamelismic clan #Baladic\|baladic]], which discards the 5 and 11 to improve the accuracy of the 2.3.7.13.17 subgroup, and is very accurate in all of these except the 13, or [[echidnic]], which has a slightly sharper generator that sacrifices the precision of 7 and logarithmic phi to map most other intervals in a more accurate but complex way.		'''Lemba''' is a [[regular temperament]] which is a natural extension of the [[jubilismic clan]] and a member of the [[gamelismic clan]]. This means that the perfect fifth of [[~]][[3/2]] is split into three equal parts, each approximating [[8/7]]. It also means the period is half an octave, and repeats precisely a tritone apart, tempering out [[50/49]]. A generator plus a period comes very close to the [[golden ratio]] phi, which means ratios in the sequence 8:13:21:34:55 etc. are also well approximated, and any one of these can be made just by choosing a suitable [[eigenmonzo]] (unchanged interval). The combination of these factors means many composite ratios in the 2.3.5.7.13.17 subgroup are both well approximated and accessible with a relatively small gamut, giving you a strong selection of chords to choose from. Its main weaknesses are that ratios of 5 and 13 are conflated by the tempering out of [[65/64]], favoring 13 in the better tunings, so traditional major and minor chords are strongly neutral flavoured (supraminor and submajor), and ratios involving 11 are not approximated at all until you have a large gamut. It forms [[mos scale]]s that are always double a fibonacci sequence number, at 4, 6, 10, 16, 26, etc, which means L/s ratios remain well mixed and clearly distinct many iterations down. Related temperaments include [[Gamelismic clan #Baladic\|baladic]], which discards the 5 and 11 to improve the accuracy of the 2.3.7.13.17 subgroup, and is very accurate in all of these except the 13, or [[echidnic]], which has a slightly sharper generator that sacrifices the precision of 7 and logarithmic phi to map most other intervals in a more accurate but complex way.

Hstraub: Link to German

2026-01-22T17:25:33Z

Link to German

← Older revision		Revision as of 17:25, 22 January 2026
Line 1:		Line 1:
			<!-- interwiki -->
			[[de:Slendrisch#Lemba\|Slendrisch-Lemba]]
	'''Lemba''' is a [[regular temperament]] which is a natural extension of the [[jubilismic clan]] and a member of the [[gamelismic clan]]. This means that the perfect fifth of [[~]][[3/2]] is split into three equal parts, each approximating [[8/7]]. It also means the period is half an octave, and repeats precisely a tritone apart, tempering out [[50/49]]. A generator plus a period comes very close to the [[golden ratio]] phi, which means ratios in the sequence 8:13:21:34:55 etc. are also well approximated, and any one of these can be made just by choosing a suitable [[eigenmonzo]] (unchanged interval). The combination of these factors means many composite ratios in the 2.3.5.7.13.17 subgroup are both well approximated and accessible with a relatively small gamut, giving you a strong selection of chords to choose from. Its main weaknesses are that ratios of 5 and 13 are conflated by the tempering out of [[65/64]], favoring 13 in the better tunings, so traditional major and minor chords are strongly neutral flavoured (supraminor and submajor), and ratios involving 11 are not approximated at all until you have a large gamut. It forms [[mos scale]]s that are always double a fibonacci sequence number, at 4, 6, 10, 16, 26, etc, which means L/s ratios remain well mixed and clearly distinct many iterations down. Related temperaments include [[Gamelismic clan #Baladic\|baladic]], which discards the 5 and 11 to improve the accuracy of the 2.3.7.13.17 subgroup, and is very accurate in all of these except the 13, or [[echidnic]], which has a slightly sharper generator that sacrifices the precision of 7 and logarithmic phi to map most other intervals in a more accurate but complex way.		'''Lemba''' is a [[regular temperament]] which is a natural extension of the [[jubilismic clan]] and a member of the [[gamelismic clan]]. This means that the perfect fifth of [[~]][[3/2]] is split into three equal parts, each approximating [[8/7]]. It also means the period is half an octave, and repeats precisely a tritone apart, tempering out [[50/49]]. A generator plus a period comes very close to the [[golden ratio]] phi, which means ratios in the sequence 8:13:21:34:55 etc. are also well approximated, and any one of these can be made just by choosing a suitable [[eigenmonzo]] (unchanged interval). The combination of these factors means many composite ratios in the 2.3.5.7.13.17 subgroup are both well approximated and accessible with a relatively small gamut, giving you a strong selection of chords to choose from. Its main weaknesses are that ratios of 5 and 13 are conflated by the tempering out of [[65/64]], favoring 13 in the better tunings, so traditional major and minor chords are strongly neutral flavoured (supraminor and submajor), and ratios involving 11 are not approximated at all until you have a large gamut. It forms [[mos scale]]s that are always double a fibonacci sequence number, at 4, 6, 10, 16, 26, etc, which means L/s ratios remain well mixed and clearly distinct many iterations down. Related temperaments include [[Gamelismic clan #Baladic\|baladic]], which discards the 5 and 11 to improve the accuracy of the 2.3.7.13.17 subgroup, and is very accurate in all of these except the 13, or [[echidnic]], which has a slightly sharper generator that sacrifices the precision of 7 and logarithmic phi to map most other intervals in a more accurate but complex way.

	The name is from [[Herman Miller]]'s conlang name for the temperament.		The name is from [[Herman Miller]]'s conlang name for the temperament.

	See [[Jubilismic clan #Lemba]] for more technical data.		See [[Jubilismic clan #Lemba]] for more technical data.

	== Interval chain ==		== Interval chain ==

FloraC: Text replacement - "Prime-optimized" to "Norm-based"

2025-09-12T14:08:43Z

Text replacement - "Prime-optimized" to "Norm-based"

← Older revision		Revision as of 14:08, 12 September 2025
Line 75:		Line 75:

	== Tunings ==		== Tunings ==
	=== ~~Prime~~-~~optimized~~ tunings ===		=== Norm-based tunings ===
	{\| class="wikitable mw-collapsible mw-collapsed"		{\| class="wikitable mw-collapsible mw-collapsed"
	\|+ style="font-size: 105%; white-space: nowrap;" \| 7-limit norm-based tunings		\|+ style="font-size: 105%; white-space: nowrap;" \| 7-limit norm-based tunings

FloraC: Text replacement - "prime-optimized" to "norm-based"

2025-09-12T14:06:23Z

Text replacement - "prime-optimized" to "norm-based"

← Older revision		Revision as of 14:06, 12 September 2025
Line 77:		Line 77:
	=== Prime-optimized tunings ===		=== Prime-optimized tunings ===
	{\| class="wikitable mw-collapsible mw-collapsed"		{\| class="wikitable mw-collapsible mw-collapsed"
	\|+ style="font-size: 105%; white-space: nowrap;" \| 7-limit ~~prime~~-~~optimized~~ tunings		\|+ style="font-size: 105%; white-space: nowrap;" \| 7-limit norm-based tunings
	\|-		\|-
	! rowspan="2" \|		! rowspan="2" \|
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	{\| class="wikitable mw-collapsible mw-collapsed"		{\| class="wikitable mw-collapsible mw-collapsed"
	\|+ style="font-size: 105%; white-space: nowrap;" \| 11-limit ~~prime~~-~~optimized~~ tunings		\|+ style="font-size: 105%; white-space: nowrap;" \| 11-limit norm-based tunings
	\|-		\|-
	! rowspan="2" \|		! rowspan="2" \|
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	{\| class="wikitable mw-collapsible mw-collapsed"		{\| class="wikitable mw-collapsible mw-collapsed"
	\|+ style="font-size: 105%; white-space: nowrap;" \| 13-limit ~~prime~~-~~optimized~~ tunings		\|+ style="font-size: 105%; white-space: nowrap;" \| 13-limit norm-based tunings
	\|-		\|-
	! rowspan="2" \|		! rowspan="2" \|

Yourmusic Productions: Add music.

2025-08-17T09:03:45Z

Add music.

← Older revision		Revision as of 09:03, 17 August 2025
Line 381:		Line 381:
	* [https://sites.google.com/site/teamouse/LembaGalatsia.mp3 ''Lemba Galatsia'']		* [https://sites.google.com/site/teamouse/LembaGalatsia.mp3 ''Lemba Galatsia'']
	* [https://sites.google.com/site/teamouse/lemba-gpo-test.mp3 ''GPO Lemb''a]		* [https://sites.google.com/site/teamouse/lemba-gpo-test.mp3 ''GPO Lemb''a]

			[[Billy Stiltner]]
			* [https://billystiltner.bandcamp.com/track/26lembaforxmt ''26lembaforxmt'']

	== Notes ==		== Notes ==

FloraC: /* Interval chain */ + another missing ratio

2025-07-21T15:47:36Z

Interval chain: + another missing ratio

← Older revision		Revision as of 15:47, 21 July 2025
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	\| 6		\| 6
	\| 187.0		\| 187.0
	\| '''9/8'''		\| '''9/8''', 11/10
	\| 787.0		\| 787.0
	\| 11/7		\| 11/7

FloraC: /* Tunings */ + tuning ranges

2025-07-21T15:45:02Z

Tunings: + tuning ranges

← Older revision		Revision as of 15:45, 21 July 2025
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	\|		\|
	\| 225.000		\| 225.000
	\|		\| Lower bound of 7-odd-limit diamond monotone
	\|-		\|-
	\|		\|
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	\|		\|
	\| 230.769		\| 230.769
	\|		\| Lower bound of 9-odd-limit diamond monotone<br>11- and 13-odd-limit diamond monotone (singleton)
	\|-		\|-
	\|		\|
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	\| 239.814		\| 239.814
	\|		\|
			\|-
			\| 2\10
			\|
			\| 240.000
			\| Upper bound of 7- and 9-odd-limit diamond monotone
	\|-		\|-
	\|		\|

FloraC: /* Tunings */ move the target tunings that don't correspond to significant eigenintervals out of the tuning spectra. Simplify the ratios. Note vals

2025-07-21T15:31:55Z

Tunings: move the target tunings that don't correspond to significant eigenintervals out of the tuning spectra. Simplify the ratios. Note vals

Show changes

← Older revision		Revision as of 14:06, 12 September 2025
Line 77:		Line 77:
	=== Prime-optimized tunings ===		=== Prime-optimized tunings ===
	{\| class="wikitable mw-collapsible mw-collapsed"		{\| class="wikitable mw-collapsible mw-collapsed"
	\|+ style="font-size: 105%; white-space: nowrap;" \| 7-limit ~~prime~~-~~optimized~~ tunings		\|+ style="font-size: 105%; white-space: nowrap;" \| 7-limit norm-based tunings
	\|-		\|-
	! rowspan="2" \|		! rowspan="2" \|
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	{\| class="wikitable mw-collapsible mw-collapsed"		{\| class="wikitable mw-collapsible mw-collapsed"
	\|+ style="font-size: 105%; white-space: nowrap;" \| 11-limit ~~prime~~-~~optimized~~ tunings		\|+ style="font-size: 105%; white-space: nowrap;" \| 11-limit norm-based tunings
	\|-		\|-
	! rowspan="2" \|		! rowspan="2" \|
Line 109:		Line 109:

	{\| class="wikitable mw-collapsible mw-collapsed"		{\| class="wikitable mw-collapsible mw-collapsed"
	\|+ style="font-size: 105%; white-space: nowrap;" \| 13-limit ~~prime~~-~~optimized~~ tunings		\|+ style="font-size: 105%; white-space: nowrap;" \| 13-limit norm-based tunings
	\|-		\|-
	! rowspan="2" \|		! rowspan="2" \|