3L 7s - Revision history

Furcht968 at 18:35, 3 April 2026

2026-04-03T18:35:36Z

← Older revision		Revision as of 18:35, 3 April 2026
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			{{Interwiki
			\|en=3L 7s
			\|es=
			\|de=
			\|ja=3L 7s
			}}
	{{Infobox MOS		{{Infobox MOS
	\| Name = sephiroid		\| Name = sephiroid

Lériendil: submajor -> demibuzzard

2026-02-08T16:01:43Z

submajor -> demibuzzard

← Older revision		Revision as of 16:01, 8 February 2026
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	== Scale tree ==		== Scale tree ==
	{{MOS tuning spectrum		{{MOS tuning spectrum
	\| 6/5 = [[~~Submajor (temperament)~~\|~~Submajor~~]]		\| 6/5 = [[Buzzardsmic clan#Demibuzzard\|Demibuzzard]]
	\| 13/8 = Unnamed golden tuning		\| 13/8 = Unnamed golden tuning
	\| 5/2 = [[Sephiroth]]		\| 5/2 = [[Sephiroth]]

Yourmusic Productions: Fix formatting.

2025-08-25T01:27:47Z

Fix formatting.

← Older revision		Revision as of 01:27, 25 August 2025
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	This MOS can represent tempered-flat chains of the 13th harmonic, which approximates phi (~833 cents).		This MOS can represent tempered-flat chains of the 13th harmonic, which approximates phi (~833 cents).

	With sephiroid scales with a soft-of-basic step ratio (around {nowrap\|L:s {{=}} 3:2}}, or 23edo), the 17th and 21st harmonics are tempered toward most accurately, which together are a stable harmony. This is the major chord of the modi sephiratorum.		With sephiroid scales with a soft-of-basic step ratio (around {{nowrap\|L:s {{=}} 3:2}}, or 23edo), the 17th and 21st harmonics are tempered toward most accurately, which together are a stable harmony. This is the major chord of the modi sephiratorum.

	Scales approaching an equalized step ratio ({{nowrap\|L:s {{=}} 1:1}}, or [[10edo]]) contain a 13th harmonic that's nearly perfect. [[121edo]] seems to be the first to 'accurately' represent the comma{{Clarify}}. Scales approaching a collapsed step ratio ({{nowrap\|L:s {{=}} 1:0}}, or [[3edo]]) have the comma [[65/64]] liable to be tempered out, thus equating [[8/5]] and [[13/8]]. Edos include [[13edo]], [[16edo]], [[19edo]], [[22edo]], [[29edo]], and others.		Scales approaching an equalized step ratio ({{nowrap\|L:s {{=}} 1:1}}, or [[10edo]]) contain a 13th harmonic that's nearly perfect. [[121edo]] seems to be the first to 'accurately' represent the comma{{Clarify}}. Scales approaching a collapsed step ratio ({{nowrap\|L:s {{=}} 1:0}}, or [[3edo]]) have the comma [[65/64]] liable to be tempered out, thus equating [[8/5]] and [[13/8]]. Edos include [[13edo]], [[16edo]], [[19edo]], [[22edo]], [[29edo]], and others.

ArrowHead294 at 18:59, 3 March 2025

2025-03-03T18:59:37Z

← Older revision		Revision as of 18:59, 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}}

	=== Proposed Names ===		=== Proposed Names ===

FloraC: /* Scale tree */ review

2025-03-03T13:24:25Z

Scale tree: review

← Older revision		Revision as of 13:24, 3 March 2025
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	== Scale tree ==		== Scale tree ==
	{{MOS tuning spectrum		{{MOS tuning spectrum
	\| 11/3 = ~~Muggles~~		\| 6/5 = [[Submajor (temperament)\|Submajor]]
	\| ~~4/1 = Magic/horcrux~~		\| 13/8 = Unnamed golden tuning
	\| ~~9/2 = Magic/witchcraft~~		\| 5/2 = [[Sephiroth]]
	~~\| 5/1 = Magic/telepathy~~
	~~\| 6~~/1 = ~~Würschmidt ↓~~
	\| 5/2 = Sephiroth
	\| 13/5 = Golden sephiroth		\| 13/5 = Golden sephiroth
	\| 6/5 = ~~Submajor~~		\| 11/3 = [[Muggles]]
	\| 13/8 = ~~Unnamed golden tuning~~		\| 4/1 = [[Magic]] / horcrux
			\| 9/2 = Magic / witchcraft / necromancy
			\| 5/1 = Magic / telepathy
			\| 6/1 = [[Würschmidt]] ↓
	}}		}}

ArrowHead294 at 21:59, 2 March 2025

2025-03-02T21:59:45Z

← Older revision		Revision as of 21:59, 2 March 2025
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	== Scale properties ==		== Scale properties ==
	{{TAMNAMS use}}		{{TAMNAMS use}}
	{{MOS data~~\|debug=1~~}}		{{MOS data}}

	=== Proposed Names ===		=== Proposed Names ===

ArrowHead294 at 21:58, 2 March 2025

2025-03-02T21:58:14Z

← Older revision		Revision as of 21:58, 2 March 2025
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	== Scale properties ==		== Scale properties ==
	{{TAMNAMS use}}		{{TAMNAMS use}}
	{{MOS data}}		{{MOS data\|debug=1}}

	=== Proposed Names ===		=== Proposed Names ===

ArrowHead294 at 21:57, 2 March 2025

2025-03-02T21:57:05Z

← Older revision		Revision as of 21:57, 2 March 2025
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	This MOS can represent tempered-flat chains of the 13th harmonic, which approximates phi (~833 cents).		This MOS can represent tempered-flat chains of the 13th harmonic, which approximates phi (~833 cents).

	With sephiroid scales with a soft-of-basic step ratio (around L:s = 3:2, or 23edo), the 17th and 21st harmonics are tempered toward most accurately, which together are a stable harmony. This is the major chord of the modi sephiratorum.		With sephiroid scales with a soft-of-basic step ratio (around {nowrap\|L:s {{=}} 3:2}}, or 23edo), the 17th and 21st harmonics are tempered toward most accurately, which together are a stable harmony. This is the major chord of the modi sephiratorum.

	Scales approaching an equalized step ratio (L:s = 1:1, or [[10edo]]) contain a 13th harmonic that's nearly perfect. [[121edo]] seems to be the first to 'accurately' represent the comma{{Clarify}}. Scales approaching a collapsed step ratio (L:s = 1:0, or [[3edo]]) have the comma [[65/64]] liable to be tempered out, thus equating [[8/5]] and [[13/8]]. Edos include [[13edo]], [[16edo]], [[19edo]], [[22edo]], [[29edo]], and others.		Scales approaching an equalized step ratio ({{nowrap\|L:s {{=}} 1:1}}, or [[10edo]]) contain a 13th harmonic that's nearly perfect. [[121edo]] seems to be the first to 'accurately' represent the comma{{Clarify}}. Scales approaching a collapsed step ratio ({{nowrap\|L:s {{=}} 1:0}}, or [[3edo]]) have the comma [[65/64]] liable to be tempered out, thus equating [[8/5]] and [[13/8]]. Edos include [[13edo]], [[16edo]], [[19edo]], [[22edo]], [[29edo]], and others.

	Harmonically, the arrangement forming a chord (degrees 0, 1, 4, 7, 10){{Clarify}} is symmetrical – not ascending but rather descending, and so reminiscent of ancient Greek practice. These scales, and their truncated heptatonic forms referenced below, are strikingly linear in several ways and so seem suited to a similar outlook as traditional western music (modality, baroque tonality, classical tonality, etc. progressing to today) but with higher harmonics.		Harmonically, the arrangement forming a chord (degrees 0, 1, 4, 7, 10){{Clarify}} is symmetrical – not ascending but rather descending, and so reminiscent of ancient Greek practice. These scales, and their truncated heptatonic forms referenced below, are strikingly linear in several ways and so seem suited to a similar outlook as traditional western music (modality, baroque tonality, classical tonality, etc. progressing to today) but with higher harmonics.

ArrowHead294 at 17:55, 28 February 2025

2025-02-28T17:55:39Z

← Older revision		Revision as of 17:55, 28 February 2025
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	== Scale tree ==		== Scale tree ==
	{{~~Scale tree~~\|~~Comments=~~11/3: Muggles; 4/1: Magic/horcrux; 9/2: Magic/witchcraft; 5/1: Magic/telepathy; 6/1~~: Würschmidt↓~~; 5/2: Sephiroth; 13/5: Golden sephiroth; 6/5: Submajor; 13/8: Unnamed golden tuning}}		{{MOS tuning spectrum
			\| 11/3 = Muggles
			\| 4/1 = Magic/horcrux
			\| 9/2 = Magic/witchcraft
			\| 5/1 = Magic/telepathy
			\| 6/1 = Würschmidt ↓
			\| 5/2 = Sephiroth
			\| 13/5 = Golden sephiroth
			\| 6/5 = Submajor
			\| 13/8 = Unnamed golden tuning
			}}

	== External links ==		== External links ==

	* [https://ia800703.us.archive.org/12/items/TractatumDeModiSephiratorum/ModiSephiratorum.pdf Tractatum de Modi Sephiratorum] by Kosmorsky		* [https://ia800703.us.archive.org/12/items/TractatumDeModiSephiratorum/ModiSephiratorum.pdf Tractatum de Modi Sephiratorum] by Kosmorsky

	[[Category:10-tone scales]]		[[Category:10-tone scales]]

ArrowHead294 at 17:52, 28 February 2025

2025-02-28T17:52:48Z

@@ Line 8: / Line 8: @@
 | Pattern = LssLssLsss
 }}
 {{MOS intro}}
-==Name==
+== Name ==
 [[TAMNAMS]] suggests the temperament-agnostic name '''sephiroid''' for this scale, in reference to Kosmorsky's ''Tracatum de Modi Sephiratorum.''
-==Intervals==
+== Scale properties ==
-:''This article assumes [[TAMNAMS]] for naming step ratios, mossteps, and mosdegrees.''
+{{TAMNAMS use}}
-{{MOS intervals|MOS Prefix=seph}}
+{{MOS data}}
 ==Theory==
 === The ''modi sephiratorum'' ===
 This MOS can represent tempered-flat chains of the 13th harmonic, which approximates phi (~833 cents).
@@ Line 27: / Line 43: @@
 There are MODMOS as well, but Kosmorsky has not explored them yet, as "there's enough undiscovered harmonic resources already in these to last me a while!" Taking this approach to the 13th harmonic also yields heptatonic MOS with similar properties: [[3L 4s|4s+3L "mish"]] in the form of modes of ssLsLsL "led".
 == Scale tree ==