5L 5s - Revision history

Fredg999: Interwiki

2026-07-19T06:25:11Z

Interwiki

← Older revision		Revision as of 06:25, 19 July 2026
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			{{Interwiki
			\| de =
			\| en = 5L 5s
			\| es = Escala Blackwood
			\| ja =
			}}
	{{Infobox MOS		{{Infobox MOS
	\| Name = pentawood		\| Name = pentawood

FloraC: Style

2026-06-28T11:08:30Z

Style

← Older revision		Revision as of 11:08, 28 June 2026
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	{{MOS intro}}		{{MOS intro}}

	There is only one significant [[harmonic entropy]] minimum with this ~~MOS~~ pattern: [[~~limmic temperaments#5-limit_.28blackwood.29\|~~blackwood]], in which intervals of the prime numbers [[3/1\|3]] and [[7/1\|7]] are all represented using steps of [[~~5edo\|~~5edo]], and the generator reaches intervals of [[5/1\|5]], such as [[6/5]], [[5/4]], and [[7/5]].		There is only one significant [[harmonic entropy]] minimum with this mos pattern: [[blackwood]], in which intervals of the prime numbers [[3/1\|3]] and [[7/1\|7]] are all represented using steps of [[5edo]], and the generator reaches intervals of [[5/1\|5]], such as [[6/5]], [[5/4]], and [[7/5]].

	In addition to the true ~~MOS~~ form (LsLsLsLsLs and sLsLsLsLsL), there are 6 near-~~MOS~~ forms, which are also single-alteration [[~~MODMOS~~]]~~ses~~ – LLssLsLsLs, LLssLLssLs, LLsLssLsLs, LLsLssLLss, LLsLsLssLs, LLsLsLsLss – in which the period and its multiples (intervals of 2, 4, 6, and 8 mossteps) have more than two varieties. These forms are proper if the bright generator is less than ~~160¢~~.		In addition to the true mos form (LsLsLsLsLs and sLsLsLsLsL), there are 6 near-mos forms, which are also single-alteration [[modmos]] scales – LLssLsLsLs, LLssLLssLs, LLsLssLsLs, LLsLssLLss, LLsLsLssLs, LLsLsLsLss – in which the period and its multiples (intervals of 2, 4, 6, and 8 mossteps) have more than two varieties. These forms are proper if the bright generator is less than 160{{c}}.

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

Overthink: standardize layout

2026-06-02T04:18:21Z

standardize layout

← Older revision		Revision as of 04:18, 2 June 2026
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	In addition to the true MOS form (LsLsLsLsLs and sLsLsLsLsL), there are 6 near-MOS forms, which are also single-alteration [[MODMOS]]ses – LLssLsLsLs, LLssLLssLs, LLsLssLsLs, LLsLssLLss, LLsLsLssLs, LLsLsLsLss – in which the period and its multiples (intervals of 2, 4, 6, and 8 mossteps) have more than two varieties. These forms are proper if the bright generator is less than 160¢.		In addition to the true MOS form (LsLsLsLsLs and sLsLsLsLsL), there are 6 near-MOS forms, which are also single-alteration [[MODMOS]]ses – LLssLsLsLs, LLssLLssLs, LLsLssLsLs, LLsLssLLss, LLsLsLssLs, LLsLsLsLss – in which the period and its multiples (intervals of 2, 4, 6, and 8 mossteps) have more than two varieties. These forms are proper if the bright generator is less than 160¢.

	== Intervals ==		== Scale properties ==
			{{TAMNAMS use}}

			=== Intervals ===
	{{MOS intervals}}		{{MOS intervals}}

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

	== Scale tree ==		=== Scale tree ===
	{{MOS tuning spectrum		{{MOS tuning spectrum
	\| 6/5 = [[Qintosec]] ↑		\| 6/5 = [[Qintosec]] ↑

Overthink: links; mention modmos

2026-05-03T01:35:13Z

links; mention modmos

← Older revision		Revision as of 01:35, 3 May 2026
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	{{MOS intro}}		{{MOS intro}}

	There is only one significant [[harmonic entropy]] minimum with this MOS pattern: [[limmic temperaments#5-limit_.28blackwood.29\|blackwood]], in which intervals of the prime numbers 3 and 7 are all represented using steps of [[5edo\|5edo]], and the generator reaches intervals of 5 ~~like~~ 6/5, 5/4, or 7/5.		There is only one significant [[harmonic entropy]] minimum with this MOS pattern: [[limmic temperaments#5-limit_.28blackwood.29\|blackwood]], in which intervals of the prime numbers [[3/1\|3]] and [[7/1\|7]] are all represented using steps of [[5edo\|5edo]], and the generator reaches intervals of [[5/1\|5]], such as [[6/5]], [[5/4]], and [[7/5]].

	In addition to the true MOS form (LsLsLsLsLs and sLsLsLsLsL), there are 6 near-MOS forms – LLssLsLsLs, LLssLLssLs, LLsLssLsLs, LLsLssLLss, LLsLsLssLs, LLsLsLsLss – in which the period and its multiples (intervals of 2, 4, 6, and 8 mossteps) have more than two varieties. These forms are proper if the bright generator is less than 160¢.		In addition to the true MOS form (LsLsLsLsLs and sLsLsLsLsL), there are 6 near-MOS forms, which are also single-alteration [[MODMOS]]ses – LLssLsLsLs, LLssLLssLs, LLsLssLsLs, LLsLssLLss, LLsLsLssLs, LLsLsLsLss – in which the period and its multiples (intervals of 2, 4, 6, and 8 mossteps) have more than two varieties. These forms are proper if the bright generator is less than 160¢.

	== Intervals ==		== Intervals ==
	{{MOS intervals}}		{{MOS intervals}}

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

Overthink: /* Scale tree */ cent values for golden tunings

2026-05-03T01:22:15Z

Scale tree: cent values for golden tunings

← Older revision		Revision as of 01:22, 3 May 2026
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	\| 6/5 = [[Qintosec]] ↑		\| 6/5 = [[Qintosec]] ↑
	\| 7/5 = [[Warlock]]		\| 7/5 = [[Warlock]]
	\| 13/8 = Unnamed golden tuning		\| 13/8 = Unnamed golden tuning (148.328{{c}})
	\| 7/4 = [[Quinkee]]		\| 7/4 = [[Quinkee]]
	\| 2/1 = [[Blackwood]] (optimal around here)		\| 2/1 = [[Blackwood]] (optimal around here)
	\| 9/4 = [[Trisedodge]]		\| 9/4 = [[Trisedodge]]
	\| 13/5 = Unnamed golden tuning		\| 13/5 = Unnamed golden tuning (173.666{{c}})
	\| 6/1 = [[Cloudtone]] ↓		\| 6/1 = [[Cloudtone]] ↓
	}}		}}

Overthink: /* Scale tree */ links

2026-05-03T01:19:52Z

Scale tree: links

← Older revision		Revision as of 01:19, 3 May 2026
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	== Scale tree ==		== Scale tree ==
	{{MOS tuning spectrum		{{MOS tuning spectrum
	\| 6/5 = Qintosec ↑		\| 6/5 = [[Qintosec]] ↑
	\| 7/5 = Warlock		\| 7/5 = [[Warlock]]
	\| 13/8 = Unnamed golden tuning		\| 13/8 = Unnamed golden tuning
	\| 7/4 = Quinkee		\| 7/4 = [[Quinkee]]
	\| 2/1 = Blackwood (optimal around here)		\| 2/1 = [[Blackwood]] (optimal around here)
	\| 9/4 = Trisedodge		\| 9/4 = [[Trisedodge]]
	\| 13/5 = Unnamed golden tuning		\| 13/5 = Unnamed golden tuning
	\| 6/1 = Cloudtone ↓		\| 6/1 = [[Cloudtone]] ↓
	}}		}}

	[[Category:Pentawood\| ]]		[[Category:Pentawood\| ]] <!-- main article -->
	[[Category:10-tone scales]]		[[Category:10-tone scales]]
	~~<!-- main article -->~~

FloraC: Blacksmith -> blackwood

2025-09-12T08:51:56Z

Blacksmith -> blackwood

← Older revision		Revision as of 08:51, 12 September 2025
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	\| 13/8 = Unnamed golden tuning		\| 13/8 = Unnamed golden tuning
	\| 7/4 = Quinkee		\| 7/4 = Quinkee
	\| 2/1 = ~~Blacksmith is~~ optimal around here		\| 2/1 = Blackwood (optimal around here)
	\| 9/4 = Trisedodge		\| 9/4 = Trisedodge
	\| 13/5 = Unnamed golden tuning		\| 13/5 = Unnamed golden tuning

ArrowHead294: /* Scale tree */

2025-03-13T13:19:15Z

Scale tree

← Older revision		Revision as of 13:19, 13 March 2025
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	\| 13/5 = Unnamed golden tuning		\| 13/5 = Unnamed golden tuning
	\| 6/1 = Cloudtone ↓		\| 6/1 = Cloudtone ↓
	\|}		}}

	[[Category:Pentawood\| ]]		[[Category:Pentawood\| ]]
	[[Category:10-tone scales]]		[[Category:10-tone scales]]
	<!-- main article -->		<!-- main article -->

ArrowHead294: /* Scale tree */ Adopt MOS tuning spectrum template and merge in comments

2025-03-13T13:19:08Z

Scale tree: Adopt MOS tuning spectrum template and merge in comments

@@ Line 20: / Line 20: @@
 {{MOS mode degrees}}
-==Scale tree==
+== Scale tree ==
-{| class="wikitable center-all"
+{{MOS tuning spectrum
-! colspan="6" rowspan="2" |Generator
+| 6/5 = Qintosec&nbsp;↑
-! colspan="2" |Cents
+| 7/5 = Warlock
-! rowspan="2" | L
+| 13/8 = Unnamed golden tuning
-! rowspan="2" | s
+| 7/4 = Quinkee
-! rowspan="2" |L/s
+| 2/1 = Blacksmith is optimal around here
-! rowspan="2" |Comments
+| 9/4 = Trisedodge
-|-
+| 13/5 = Unnamed golden tuning
-!Chroma-positive
+| 6/1 = Cloudtone&nbsp;↓
 |}

BudjarnLambeth: == Intervals == {{MOS intervals}}

2024-12-16T00:42:20Z

== Intervals == {{MOS intervals}}

← Older revision		Revision as of 00:42, 16 December 2024
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	}}		}}
	{{MOS intro}}		{{MOS intro}}

	There is only one significant [[harmonic entropy]] minimum with this MOS pattern: [[limmic temperaments#5-limit_.28blackwood.29\|blackwood]], in which intervals of the prime numbers 3 and 7 are all represented using steps of [[5edo\|5edo]], and the generator reaches intervals of 5 like 6/5, 5/4, or 7/5.		There is only one significant [[harmonic entropy]] minimum with this MOS pattern: [[limmic temperaments#5-limit_.28blackwood.29\|blackwood]], in which intervals of the prime numbers 3 and 7 are all represented using steps of [[5edo\|5edo]], and the generator reaches intervals of 5 like 6/5, 5/4, or 7/5.

	In addition to the true MOS form (LsLsLsLsLs and sLsLsLsLsL), there are 6 near-MOS forms – LLssLsLsLs, LLssLLssLs, LLsLssLsLs, LLsLssLLss, LLsLsLssLs, LLsLsLsLss – in which the period and its multiples (intervals of 2, 4, 6, and 8 mossteps) have more than two varieties. These forms are proper if the bright generator is less than 160¢.		In addition to the true MOS form (LsLsLsLsLs and sLsLsLsLsL), there are 6 near-MOS forms – LLssLsLsLs, LLssLLssLs, LLsLssLsLs, LLsLssLLss, LLsLsLssLs, LLsLsLsLss – in which the period and its multiples (intervals of 2, 4, 6, and 8 mossteps) have more than two varieties. These forms are proper if the bright generator is less than 160¢.

			== Intervals ==
			{{MOS intervals}}

	==Modes==		==Modes==