2L 8s - Revision history

FloraC: Cleanup

2025-08-03T11:45:49Z

Cleanup

← Older revision		Revision as of 11:45, 3 August 2025
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	{{MOS intro}}		{{MOS intro}}
	2L 8s is the ~~MOS~~ pattern of the decatonic scale of [[~~Paul_Erlich\|~~Paul Erlich]] and others.		2L 8s is the mos pattern of the decatonic scale of [[Paul Erlich]] and others.

	The only significant harmonic entropy minimum that is [[~~Rothenberg_propriety~~\|proper]] is the decatonic scale itself ([[~~Diaschismic_family\|pajara~~]][10]), in which the period is 7/5~10/7 (tempered to be the same interval), one generator down from that makes [[4/3]], and another generator down makes [[5/4]]. More than a few people think this is a beautiful scale that deserves a lot of investigation and use, with some going so far as to say it's the next step up from the diatonic scale that preserves the most desirable features of diatonic melody and harmony. Paul Erlich's original paper on this scale can be found ~~at either of these links~~:		The only significant harmonic entropy minimum that is [[Rothenberg propriety\|Rothenberg proper]] is the decatonic scale itself ([[Pajara]][10]), in which the period is [[7/5]][[~]][[10/7]] (tempered to be the same interval), one generator down from that makes [[4/3]], and another generator down makes [[5/4]]. More than a few people think this is a beautiful scale that deserves a lot of investigation and use, with some going so far as to say it is the next step up from the [[5L 2s\|diatonic]] scale that preserves the most desirable features of diatonic melody and harmony. Paul Erlich's original paper on this scale can be found here: [http://sethares.engr.wisc.edu/paperspdf/Erlich-22.pdf ''Tuning, Tonality, and Twenty-Two-Tone Temperament''] ([http://www.lumma.org/tuning/erlich/ alt link]).

	~~http:~~/~~/sethares.engr.wisc.edu/paperspdf/Erlich-22~~.~~pdf~~		Improper harmonic entropy minima include [[injera]] (which is similar to pajara except that 5/4 is now four generators ''up'' and no periods) and [[shrutar]] (which is basically pajara with the generator divided in two).

	~~http://www.lumma.org/tuning/erlich/~~		In addition to the true mos form, LssssLssss, these scales also exist in a near-mos form, LsssssLsss, in which the period is the only interval class with more than two flavors. In the case of the decatonic scale, LssssLssss is called the ''symmetric'' scale and LsssssLsss is called the ''pentachordal'' scale (because it has two identical [[pentachord]]s in the same way that the diatonic scale has two identical [[tetrachord]]s).

	Improper harmonic entropy minima include [[Meantone_family#Injera\|injera]] (which is similar to pajara except that 5/4 is now four generators '''up''' and no periods) and [[Diaschismic_family#Shrutar\|shrutar]] (which is basically pajara with the generator divided in two).

	In addition to the true ~~MOS~~ form, LssssLssss, these scales also exist in a near-~~MOS~~ form, LsssssLsss, in which the period is the only interval class with more than two flavors. In the case of the decatonic scale, LssssLssss is called the "symmetric" scale and LsssssLsss is called the "pentachordal" scale (because it has two identical ~~"pentachords"~~ in the same way that the diatonic scale has two identical ~~tetrachords~~).

	== Scale properties ==		== Scale properties ==

ArrowHead294 at 18:57, 3 March 2025

2025-03-03T18:57:02Z

← Older revision		Revision as of 18:57, 3 March 2025
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	== Scale properties ==		== Scale properties ==
	{{TAMNAMS use}}		{{TAMNAMS use}}
	{{MOS ~~data~~}}
			=== Intervals ===
			{{MOS intervals}}

			=== Generator chain ===
			{{MOS genchain}}

			=== Modes ===
			{{MOS mode degrees}}

	== Scale tree ==		== Scale tree ==

ArrowHead294 at 17:29, 28 February 2025

2025-02-28T17:29:37Z

← Older revision		Revision as of 17:29, 28 February 2025
Line 22:		Line 22:
	In addition to the true MOS form, LssssLssss, these scales also exist in a near-MOS form, LsssssLsss, in which the period is the only interval class with more than two flavors. In the case of the decatonic scale, LssssLssss is called the "symmetric" scale and LsssssLsss is called the "pentachordal" scale (because it has two identical "pentachords" in the same way that the diatonic scale has two identical tetrachords).		In addition to the true MOS form, LssssLssss, these scales also exist in a near-MOS form, LsssssLsss, in which the period is the only interval class with more than two flavors. In the case of the decatonic scale, LssssLssss is called the "symmetric" scale and LsssssLsss is called the "pentachordal" scale (because it has two identical "pentachords" in the same way that the diatonic scale has two identical tetrachords).

	== ~~Intervals~~ ==		== Scale properties ==
	{{MOS ~~intervals~~}}		{{TAMNAMS use}}
			{{MOS data}}

	== ~~Modes~~ ==		== Scale tree ==
	{{MOS ~~mode degrees~~}}		{{MOS tuning spectrum
			\| 6/5 = [[Semimiracle]] ↑
			\| 3/2 = [[Pajara]]
			\| 8/5 = [[Keen]]
			\| 12/7 = [[Srutal]]
			\| 9/5 = [[Diaschismic]]
			\| 9/4 = [[Bimeantone]]
			\| 5/2 = [[Injera]]
			\| 9/2 = [[Vishnu]] (incomplete)
			\| 6/1 = [[Shrutar]], [[teff]]/[[pombe]] (incomplete) ↓
			}}

	~~== Scale tree ==~~
	~~{{Scale tree\|Comments=6/5: [[Semimiracle]] ↑;~~
	~~3/2: [[Pajara]];~~
	~~8/5: [[Keen]];~~
	~~12/7: [[Srutal]];~~
	~~9/5: [[Diaschismic]];~~
	~~9/4: [[Bimeantone]];~~
	~~5/2: [[Injera]];~~
	~~9/2: [[Vishnu]] (incomplete);~~
	~~6/1: [[Shrutar]], [[teff]]/[[pombe]] (incomplete)↓}}~~
	[[Category:jaric]]		[[Category:jaric]]
	[[Category:10-tone scales]]		[[Category:10-tone scales]]

Ganaram inukshuk: drop unused notation; add mos intervals

2024-07-29T11:23:43Z

drop unused notation; add mos intervals

← Older revision		Revision as of 11:23, 29 July 2024
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	In addition to the true MOS form, LssssLssss, these scales also exist in a near-MOS form, LsssssLsss, in which the period is the only interval class with more than two flavors. In the case of the decatonic scale, LssssLssss is called the "symmetric" scale and LsssssLsss is called the "pentachordal" scale (because it has two identical "pentachords" in the same way that the diatonic scale has two identical tetrachords).		In addition to the true MOS form, LssssLssss, these scales also exist in a near-MOS form, LsssssLsss, in which the period is the only interval class with more than two flavors. In the case of the decatonic scale, LssssLssss is called the "symmetric" scale and LsssssLsss is called the "pentachordal" scale (because it has two identical "pentachords" in the same way that the diatonic scale has two identical tetrachords).

	== ~~Notation~~ ==		== Intervals ==
	The notation used in this article is ssLssssLss = JKLMNOPQRSJ unless specified otherwise. We denote raising and lowering by a chroma (L − s) by & "amp" and @ "at". (Mnemonics: & "and" means additional pitch. @ "at" rhymes with "flat".)		{{MOS intervals}}

	~~Thus the 12edo gamut is as follows:~~

	~~'''J''' '''K''' '''L''' L& '''M''' '''N''' '''O''' '''P''' '''Q''' Q& '''R''' '''S''' '''J'''~~

	== Modes ==		== Modes ==

Nick Vuci: /* Modes */ added MOS mode degrees template

2024-07-24T23:08:31Z

Modes: added MOS mode degrees template

← Older revision		Revision as of 23:08, 24 July 2024
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	== Modes ==		== Modes ==
	*8\|0(2) LssssLssss, J-K&-L&-M-N-O-P&-Q&-R-S-J		{{MOS mode degrees}}
	*6\|2(2) sLssssLsss, J-K-L&-M-N-O-P-Q&-R-S-J
	*4\|4(2) ssLssssLss, J-K-L-M-N-O-P-Q-R-S-J
	*2\|6(2) sssLssssLs, J-K-L-M@-N-O-P-Q-R@-S-J
	*0\|8(2) ssssLssssL, J-K-L-M@-N@-O-P-Q-R@-S@-J

	== Scale tree ==		== Scale tree ==

Ganaram inukshuk: /* Scale tree */ Add scale tree template, transferred entries (except for golden tunings)

2024-04-24T19:00:35Z

Scale tree: Add scale tree template, transferred entries (except for golden tunings)

@@ Line 37: / Line 37: @@
 == Scale tree ==
-Generator ranges:
+{{Scale tree|Comments=6/5: [[Semimiracle]] ↑;
-* Chroma-positive generator: 480 cents (4\10) to 600 cents (1\2)
+/2: [[Pajara]];
-* Chroma-negative generator: 0 cents (0\2) to 120 cents (1\10)
+/5: [[Keen]];
+/7: [[Srutal]];
-{| class="wikitable center-all"
+/5: [[Diaschismic]];
-! colspan="6" rowspan="2" | Generator
+/4: [[Bimeantone]];
-! colspan="2" | Cents
+/2: [[Injera]];
-! rowspan="2" | L
+/2: [[Vishnu]] (incomplete);
-! rowspan="2" | s
+/1: [[Shrutar]], [[teff]]/[[pombe]] (incomplete)↓}}
 [[Category:jaric]]
 [[Category:10-tone scales]]

Ganaram inukshuk at 00:54, 1 June 2023

2023-06-01T00:54:49Z

← Older revision		Revision as of 00:54, 1 June 2023
Line 9:		Line 9:
	}}		}}

	~~'''~~2L 8s~~'''~~ is the MOS pattern of the decatonic scale of [[Paul_Erlich\|Paul Erlich]] and others.		{{MOS intro}}
			2L 8s is the MOS pattern of the decatonic scale of [[Paul_Erlich\|Paul Erlich]] and others.

	The only significant harmonic entropy minimum that is [[Rothenberg_propriety\|proper]] is the decatonic scale itself ([[Diaschismic_family\|pajara]][10]), in which the period is 7/5~10/7 (tempered to be the same interval), one generator down from that makes [[4/3]], and another generator down makes [[5/4]]. More than a few people think this is a beautiful scale that deserves a lot of investigation and use, with some going so far as to say it's the next step up from the diatonic scale that preserves the most desirable features of diatonic melody and harmony. Paul Erlich's original paper on this scale can be found at either of these links:		The only significant harmonic entropy minimum that is [[Rothenberg_propriety\|proper]] is the decatonic scale itself ([[Diaschismic_family\|pajara]][10]), in which the period is 7/5~10/7 (tempered to be the same interval), one generator down from that makes [[4/3]], and another generator down makes [[5/4]]. More than a few people think this is a beautiful scale that deserves a lot of investigation and use, with some going so far as to say it's the next step up from the diatonic scale that preserves the most desirable features of diatonic melody and harmony. Paul Erlich's original paper on this scale can be found at either of these links:

Yourmusic Productions: formatting

2023-03-23T14:37:58Z

formatting

Yourmusic Productions: /* Scale tree */ Fix math error.

2023-03-23T14:29:28Z

Scale tree: Fix math error.

← Older revision		Revision as of 14:29, 23 March 2023
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	Thus the 12edo gamut is as follows:		Thus the 12edo gamut is as follows:

	'''J''' '''K''' '''L''' L&/M@ '''M''' '''N''' '''O''' '''P''' '''Q''' Q&/R@ '''R''' '''S''' '''J'''		'''J''' '''K''' '''L''' L&/[[/cdn-cgi/l/email-protection\|[email protected]]] '''M''' '''N''' '''O''' '''P''' '''Q''' Q&/[[/cdn-cgi/l/email-protection\|[email protected]]] '''R''' '''S''' '''J'''

	== Modes ==		== Modes ==
Line 32:		Line 32:
	* 6\|2(2) sLssssLsss, J-K-L&-M-N-O-P-Q&-R-S-J		* 6\|2(2) sLssssLsss, J-K-L&-M-N-O-P-Q&-R-S-J
	* 4\|4(2) ssLssssLss, J-K-L-M-N-O-P-Q-R-S-J		* 4\|4(2) ssLssssLss, J-K-L-M-N-O-P-Q-R-S-J
	* 2\|6(2) sssLssssLs, J-K-~~L-M@-N-O-P-Q-R~~@-S-J		* 2\|6(2) sssLssssLs, [[/cdn-cgi/l/email-protection\|[email protected]]]@-S-J
	* 0\|8(2) ssssLssssL, J-K-~~L-M~~@-N@-~~O-P-Q-R@-S~~@-J		* 0\|8(2) ssssLssssL, [[/cdn-cgi/l/email-protection\|[email protected]]]@[[/cdn-cgi/l/email-protection\|[email protected]]]@-J

	== Scale tree ==		== Scale tree ==
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	\| \|\| \|\| \|\| \|\| \|\| 31\76 \|\| 489.474 \|\| 110.526 \|\| 10 \|\| 7 \|\| 1.429 \|\|		\| \|\| \|\| \|\| \|\| \|\| 31\76 \|\| 489.474 \|\| 110.526 \|\| 10 \|\| 7 \|\| 1.429 \|\|
	\|-		\|-
	\| \|\| \|\| 9\22 \|\| \|\| \|\| \|\| 490.909 \|\| ~~107~~.~~692~~ \|\| 3 \|\| 2 \|\| 1.500 \|\| [[Pajara]]		\| \|\| \|\| 9\22 \|\| \|\| \|\| \|\| 490.909 \|\| 109.090 \|\| 3 \|\| 2 \|\| 1.500 \|\| [[Pajara]]
	\|-		\|-
	\| \|\| \|\| \|\| \|\| \|\| 32\78 \|\| 492.308 \|\| ~~131~~.~~250~~ \|\| 11 \|\| 7 \|\| 1.571 \|\|		\| \|\| \|\| \|\| \|\| \|\| 32\78 \|\| 492.308 \|\| 107.692 \|\| 11 \|\| 7 \|\| 1.571 \|\|
	\|-		\|-
	\| \|\| \|\| \|\| \|\| 23\56 \|\| \|\| 492.857 \|\| 107.143 \|\| 8 \|\| 5 \|\| 1.600 \|\| [[Keen]]		\| \|\| \|\| \|\| \|\| 23\56 \|\| \|\| 492.857 \|\| 107.143 \|\| 8 \|\| 5 \|\| 1.600 \|\| [[Keen]]

Inthar at 18:10, 17 August 2022

2022-08-17T18:10:27Z

← Older revision		Revision as of 18:10, 17 August 2022
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	\| nSmallSteps = 8		\| nSmallSteps = 8
	\| Equalized = 1		\| Equalized = 1
	\| ~~Paucitonic~~ = 0		\| Collapsed = 0
	\| Pattern = ssLssssLss		\| Pattern = ssLssssLss
	\| Name = jaric		\| Name = jaric

← Older revision		Revision as of 14:37, 23 March 2023
Line 26:		Line 26:
	Thus the 12edo gamut is as follows:		Thus the 12edo gamut is as follows:

	'''J''' '''K''' '''L''' L&~~/[[/cdn-cgi/l/email-protection\|[email protected]]]~~ '''M''' '''N''' '''O''' '''P''' '''Q''' Q&~~/[[/cdn-cgi/l/email-protection\|[email protected]]]~~ '''R''' '''S''' '''J'''		'''J''' '''K''' '''L''' L& '''M''' '''N''' '''O''' '''P''' '''Q''' Q& '''R''' '''S''' '''J'''

	== Modes ==		== Modes ==
	* 8\|0(2) LssssLssss, J-K&-L&-M-N-O-P&-Q&-R-S-J		*8\|0(2) LssssLssss, J-K&-L&-M-N-O-P&-Q&-R-S-J
	* 6\|2(2) sLssssLsss, J-K-L&-M-N-O-P-Q&-R-S-J		*6\|2(2) sLssssLsss, J-K-L&-M-N-O-P-Q&-R-S-J
	* 4\|4(2) ssLssssLss, J-K-L-M-N-O-P-Q-R-S-J		*4\|4(2) ssLssssLss, J-K-L-M-N-O-P-Q-R-S-J
	* 2\|6(2) sssLssssLs, ~~[[/cdn~~-~~cgi/l/email~~-~~protection\|[email protected]]]~~@-S-J		*2\|6(2) sssLssssLs, J-K-L-M@-N-O-P-Q-R@-S-J
	* 0\|8(2) ssssLssssL, ~~[[/cdn~~-~~cgi/l/email~~-~~protection\|[email protected]]]~~@~~[[/cdn~~-~~cgi/l/email~~-~~protection\|[email protected]]]~~@-J		*0\|8(2) ssssLssssL, J-K-L-M@-N@-O-P-Q-R@-S@-J

	== Scale tree ==		== Scale tree ==
Line 53:		Line 53:
	\| 4\10 \|\| \|\| \|\| \|\| \|\| \|\| 480.000 \|\| 120.000 \|\| 1 \|\| 1 \|\| 1.000 \|\|		\| 4\10 \|\| \|\| \|\| \|\| \|\| \|\| 480.000 \|\| 120.000 \|\| 1 \|\| 1 \|\| 1.000 \|\|
	\|-		\|-
	\| \|\| \|\| \|\| \|\| \|\| 21\52 \|\| 484.615 \|\| 115.385 \|\| 6 \|\| 5 \|\| 1.200 \|\| [[Semimiracle]]↑		\| \|\| \|\| \|\| \|\| \|\| 21\52 \|\| 484.615 \|\| 115.385 \|\| 6 \|\| 5 \|\| 1.200 \|\| [[Gamelismic_clan#Semimiracle\|Semimiracle]]↑
	\|-		\|-
	\| \|\| \|\| \|\| \|\| 17\42 \|\| \|\| 485.714 \|\| 114.286 \|\| 5 \|\| 4 \|\| 1.250 \|\|		\| \|\| \|\| \|\| \|\| 17\42 \|\| \|\| 485.714 \|\| 114.286 \|\| 5 \|\| 4 \|\| 1.250 \|\|
Line 71:		Line 71:
	\| \|\| \|\| \|\| \|\| \|\| 32\78 \|\| 492.308 \|\| 107.692 \|\| 11 \|\| 7 \|\| 1.571 \|\|		\| \|\| \|\| \|\| \|\| \|\| 32\78 \|\| 492.308 \|\| 107.692 \|\| 11 \|\| 7 \|\| 1.571 \|\|
	\|-		\|-
	\| \|\| \|\| \|\| \|\| 23\56 \|\| \|\| 492.857 \|\| 107.143 \|\| 8 \|\| 5 \|\| 1.600 \|\| [[Keen]]		\| \|\| \|\| \|\| \|\| 23\56 \|\| \|\| 492.857 \|\| 107.143 \|\| 8 \|\| 5 \|\| 1.600 \|\| [[Diaschismic_family#Keen\|Keen]]
	\|-		\|-
	\| \|\| \|\| \|\| \|\| \|\| 37\90 \|\| 493.333 \|\| 106.667 \|\| 13 \|\| 8 \|\| 1.625 \|\| Golden pajaroid (493.2011¢)		\| \|\| \|\| \|\| \|\| \|\| 37\90 \|\| 493.333 \|\| 106.667 \|\| 13 \|\| 8 \|\| 1.625 \|\| Golden pajaroid (493.2011¢)
Line 109:		Line 109:
	\| \|\| \|\| \|\| 7\16 \|\| \|\| \|\| 525.000 \|\| 75.000 \|\| 4 \|\| 1 \|\| 4.000 \|\|		\| \|\| \|\| \|\| 7\16 \|\| \|\| \|\| 525.000 \|\| 75.000 \|\| 4 \|\| 1 \|\| 4.000 \|\|
	\|-		\|-
	\| \|\| \|\| \|\| \|\| \|\| 15\34 \|\| 529.412 \|\| 70.588 \|\| 9 \|\| 2 \|\| 4.500 \|\| [[~~Vishnuzmic~~]] (incomplete)		\| \|\| \|\| \|\| \|\| \|\| 15\34 \|\| 529.412 \|\| 70.588 \|\| 9 \|\| 2 \|\| 4.500 \|\| [[Vishnuzmic_family#Vishnu\|Vishnu]] (incomplete)
	\|-		\|-
	\| \|\| \|\| \|\| \|\| 8\18 \|\| \|\| 533.333 \|\| 66.667 \|\| 5 \|\| 1 \|\| 5.000 \|\|		\| \|\| \|\| \|\| \|\| 8\18 \|\| \|\| 533.333 \|\| 66.667 \|\| 5 \|\| 1 \|\| 5.000 \|\|