3L 2s (8/5-equivalent) - Revision history

CompactStar: Why is there a 14/9-repeating temperament??

2023-05-23T02:16:25Z

Why is there a 14/9-repeating temperament??

← Older revision		Revision as of 02:16, 23 May 2023
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	[[Optimal ET sequence]]: 5ed8/5, 8ed8/5, 13ed8/5		[[Optimal ET sequence]]: 5ed8/5, 8ed8/5, 13ed8/5
	~~==='''Aeolianic-Superpyth'''===~~
	~~[[Subgroup]]: 14/9.4/3.3/2~~

	~~[[Comma]] list: [[64/63]]~~

	~~[[POL2]] generator: ~7/6 = 276.0795~~

	~~[[Mapping]]: [{{val\|1 1 2}}, {{val\|0 -1 -3}}]~~

	~~[[Optimal ET sequence]]: 3ed14/9, 11ed14/9, 14ed14/9~~

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

CompactStar at 02:14, 23 May 2023

2023-05-23T02:14:30Z

← Older revision		Revision as of 02:14, 23 May 2023
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	[[Basic]] 3L 2s<8/5> is in [[8ed8/5]], which is a very good minor sixth-based equal tuning similar to [[12edo]].		[[Basic]] 3L 2s<8/5> is in [[8ed8/5]], which is a very good minor sixth-based equal tuning similar to [[12edo]].
	==Notation==		==Notation==
	There are 2 main ways to notate ~~the diatonic~~ scale. One method uses a simple sixth repeating notation consisting of 5 naturals (La, Si, Do, Re, Mi). Given that 1-7/6-3/2 is minor sixth-equivalent to a tone cluster of 1-16/15-7/6, it may be more convenient to notate these diatonic scales as repeating at the double sixth (diminished eleventh~tenth), however it does make navigating the [[Generator\|genchain]] harder. This way, 3/2 is its own pitch class, distinct from 16\15. Notating this way produces a tenth which is the Dorian mode of Annapolis[6L 4s] or Oriole[6L 4s]. Since there are exactly 10 naturals in double sixth notation, Greek numerals 1-10 may be used.		There are 2 main ways to notate this scale. One method uses a simple sixth repeating notation consisting of 5 naturals (La, Si, Do, Re, Mi). Given that 1-7/6-3/2 is minor sixth-equivalent to a tone cluster of 1-16/15-7/6, it may be more convenient to notate these diatonic scales as repeating at the double sixth (diminished eleventh~tenth), however it does make navigating the [[Generator\|genchain]] harder. This way, 3/2 is its own pitch class, distinct from 16\15. Notating this way produces a tenth which is the Dorian mode of Annapolis[6L 4s] or Oriole[6L 4s]. Since there are exactly 10 naturals in double sixth notation, Greek numerals 1-10 may be used.
	{\| class="wikitable"		{\| class="wikitable"
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CompactStar at 02:14, 23 May 2023

2023-05-23T02:14:07Z

← Older revision		Revision as of 02:14, 23 May 2023
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	The generator range is 240 to 342.9 cents, placing it on the [[6/5\|diatonic minor third]], usually representing a minor third of some type (like [[6/5]]). The bright (chroma-positive) generator is, however, its minor sixth complement (480 to 514.3 cents).		The generator range is 240 to 342.9 cents, placing it on the [[6/5\|diatonic minor third]], usually representing a minor third of some type (like [[6/5]]). The bright (chroma-positive) generator is, however, its minor sixth complement (480 to 514.3 cents).

	Because this is a minor sixth-repeating ~~equivalent of diatonic~~, each tone has an 8/5 minor sixth above it. The scale has one major chord, one minor chord and three diminished chords. This ~~diatonic~~ also has two diminished 7th chords, making it a warped melodic minor scale.		Because this is a minor sixth-repeating scale, each tone has an 8/5 minor sixth above it. The scale has one major chord, one minor chord and three diminished chords. This scale also has two diminished 7th chords, making it a warped melodic minor scale.

	[[Basic]] ~~diatonic~~ is in [[8ed8/5]], which is a very good minor sixth-based equal tuning similar to [[12edo]].		[[Basic]] 3L 2s<8/5> is in [[8ed8/5]], which is a very good minor sixth-based equal tuning similar to [[12edo]].
	==Notation==		==Notation==
	There are 2 main ways to notate the diatonic scale. One method uses a simple sixth repeating notation consisting of 5 naturals (La, Si, Do, Re, Mi). Given that 1-7/6-3/2 is minor sixth-equivalent to a tone cluster of 1-16/15-7/6, it may be more convenient to notate these diatonic scales as repeating at the double sixth (diminished eleventh~tenth), however it does make navigating the [[Generator\|genchain]] harder. This way, 3/2 is its own pitch class, distinct from 16\15. Notating this way produces a tenth which is the Dorian mode of Annapolis[6L 4s] or Oriole[6L 4s]. Since there are exactly 10 naturals in double sixth notation, Greek numerals 1-10 may be used.		There are 2 main ways to notate the diatonic scale. One method uses a simple sixth repeating notation consisting of 5 naturals (La, Si, Do, Re, Mi). Given that 1-7/6-3/2 is minor sixth-equivalent to a tone cluster of 1-16/15-7/6, it may be more convenient to notate these diatonic scales as repeating at the double sixth (diminished eleventh~tenth), however it does make navigating the [[Generator\|genchain]] harder. This way, 3/2 is its own pitch class, distinct from 16\15. Notating this way produces a tenth which is the Dorian mode of Annapolis[6L 4s] or Oriole[6L 4s]. Since there are exactly 10 naturals in double sixth notation, Greek numerals 1-10 may be used.

CompactStar: CompactStar moved page User:Moremajorthanmajor/3L 2s (8/5-equivalent) to 3L 2s (8/5-equivalent) over redirect: This page is mostly OK now that "sextave" thing is resolved

2023-05-23T02:12:34Z

CompactStar moved page User:Moremajorthanmajor/3L 2s (8/5-equivalent) to 3L 2s (8/5-equivalent) over redirect: This page is mostly OK now that "sextave" thing is resolved

← Older revision	Revision as of 02:12, 23 May 2023
(No difference)

CompactStar: Sextave replaced with sixth (which makes sense in both this scale and actual diatonic)

2023-05-23T02:12:09Z

Sextave replaced with sixth (which makes sense in both this scale and actual diatonic)

← Older revision		Revision as of 02:12, 23 May 2023
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	{{Infobox MOS\|		{{Infobox MOS}}
	~~Pattern=LLsLs\|~~
	~~Equave=8/5\|~~
	~~Name=\|~~
	~~Equalized=3\|~~
	~~Collapsed=2\|~~
	~~nLargeSteps=3\|~~
	~~nSmallSteps=2~~}}

	'''3L 2s<8/5>''' ~~(sometimes called '''diatonic'''),~~ is a minor sixth-repeating MOS scale. The notation "<8/5>" means the period of the MOS is 8/5, disambiguating it from octave-repeating [[3L 2s]]~~. The name of the period interval is called the '''sextave''' (by analogy to the [[tritave]])~~.		'''3L 2s<8/5>''' is a minor sixth-repeating MOS scale. The notation "<8/5>" means the period of the MOS is 8/5, disambiguating it from octave-repeating [[3L 2s]].

	The generator range is 240 to 342.9 cents, placing it on the [[6/5\|diatonic minor third]], usually representing a minor third of some type (like [[6/5]]). The bright (chroma-positive) generator is, however, its minor sixth complement (480 to 514.3 cents).		The generator range is 240 to 342.9 cents, placing it on the [[6/5\|diatonic minor third]], usually representing a minor third of some type (like [[6/5]]). The bright (chroma-positive) generator is, however, its minor sixth complement (480 to 514.3 cents).

	Because this ~~diatonic~~ is a minor sixth-repeating ~~scale~~, each tone has an 8/5 minor sixth above it. The scale has one major chord, one minor chord and three diminished chords. This diatonic also has two diminished 7th chords, making it a warped melodic minor scale.		Because this is a minor sixth-repeating equivalent of diatonic, each tone has an 8/5 minor sixth above it. The scale has one major chord, one minor chord and three diminished chords. This diatonic also has two diminished 7th chords, making it a warped melodic minor scale.

	[[Basic]] diatonic is in [[8ed8/5]], which is a very good minor sixth-based equal tuning similar to [[12edo]].		[[Basic]] diatonic is in [[8ed8/5]], which is a very good minor sixth-based equal tuning similar to [[12edo]].
	==Notation==		==Notation==
	There are 2 main ways to notate the diatonic scale. One method uses a simple ~~sextave (minor~~ sixth) repeating notation consisting of 5 naturals (La, Si, Do, Re, Mi). Given that 1-7/6-3/2 is minor sixth-equivalent to a tone cluster of 1-16/15-7/6, it may be more convenient to notate these diatonic scales as repeating at the double ~~sextave~~ (diminished eleventh~tenth), however it does make navigating the [[Generator\|genchain]] harder. This way, 3/2 is its own pitch class, distinct from 16\15. Notating this way produces a tenth which is the Dorian mode of Annapolis[6L 4s] or Oriole[6L 4s]. Since there are exactly 10 naturals in double ~~sextave~~ notation, Greek numerals 1-10 may be used.		There are 2 main ways to notate the diatonic scale. One method uses a simple sixth repeating notation consisting of 5 naturals (La, Si, Do, Re, Mi). Given that 1-7/6-3/2 is minor sixth-equivalent to a tone cluster of 1-16/15-7/6, it may be more convenient to notate these diatonic scales as repeating at the double sixth (diminished eleventh~tenth), however it does make navigating the [[Generator\|genchain]] harder. This way, 3/2 is its own pitch class, distinct from 16\15. Notating this way produces a tenth which is the Dorian mode of Annapolis[6L 4s] or Oriole[6L 4s]. Since there are exactly 10 naturals in double sixth notation, Greek numerals 1-10 may be used.
	{\| class="wikitable"		{\| class="wikitable"
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	{\| class="wikitable"		{\| class="wikitable"
	!Generators		!Generators
	!~~Sextave~~ notation		!Sixth notation
	!Interval category name		!Interval category name
	!Generators		!Generators
Line 1,031:		Line 1,024:
	\|0		\|0
	\|La		\|La
	\|~~sextave~~ (minor sixth)		\|perfect sixth (minor sixth)
	\|0		\|0
	\|La		\|La
Line 1,071:		Line 1,064:
	\| -5		\| -5
	\|Lab		\|Lab
	\|diminished ~~sextave~~		\|diminished sixth
	\|-		\|-
	\|6		\|6

Fredg999: Fredg999 moved page 3L 2s (8/5-equivalent) to User:Moremajorthanmajor/3L 2s (8/5-equivalent) over redirect: Page not ready for the main namespace

2023-05-20T05:22:30Z

Fredg999 moved page 3L 2s (8/5-equivalent) to User:Moremajorthanmajor/3L 2s (8/5-equivalent) over redirect: Page not ready for the main namespace

← Older revision	Revision as of 05:22, 20 May 2023
(No difference)

Moremajorthanmajor: Moremajorthanmajor moved page User:Moremajorthanmajor/3L 2s (8/5-equivalent) to 3L 2s (8/5-equivalent) over redirect

2023-05-19T02:59:44Z

Moremajorthanmajor moved page User:Moremajorthanmajor/3L 2s (8/5-equivalent) to 3L 2s (8/5-equivalent) over redirect

← Older revision	Revision as of 02:59, 19 May 2023
(No difference)

Moremajorthanmajor: Moremajorthanmajor moved page User:3L 2s (8/5-equivalent) to User:Moremajorthanmajor/3L 2s (8/5-equivalent) over redirect: revert

2023-05-19T02:59:23Z

Moremajorthanmajor moved page User:3L 2s (8/5-equivalent) to User:Moremajorthanmajor/3L 2s (8/5-equivalent) over redirect: revert

← Older revision	Revision as of 02:59, 19 May 2023
(No difference)

Moremajorthanmajor: Moremajorthanmajor moved page User:Moremajorthanmajor/3L 2s (8/5-equivalent) to User:3L 2s (8/5-equivalent)

2023-05-19T02:58:31Z

Moremajorthanmajor moved page User:Moremajorthanmajor/3L 2s (8/5-equivalent) to User:3L 2s (8/5-equivalent)

← Older revision	Revision as of 02:58, 19 May 2023
(No difference)

FloraC: FloraC moved page 3L 2s (8/5-equivalent) to User:Moremajorthanmajor/3L 2s (8/5-equivalent): Go back. Who calls this "diatonic"? And your use of "sextave" is even contradicting your own other articles

2023-05-18T07:31:40Z

FloraC moved page 3L 2s (8/5-equivalent) to User:Moremajorthanmajor/3L 2s (8/5-equivalent): Go back. Who calls this "diatonic"? And your use of "sextave" is even contradicting your own other articles

← Older revision	Revision as of 07:31, 18 May 2023
(No difference)