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

Inthar at 12:02, 27 May 2023

2023-05-27T12:02:40Z

← Older revision		Revision as of 12:02, 27 May 2023
Line 1:		Line 1:
	{{Infobox MOS}}		{{Infobox MOS}}
	'''3L 2s<3/2>''' (sometimes called '''uranian'''), is a fifth-repeating MOS scale. The notation "<3/2>" means the period of the MOS is 3/2, disambiguating it from octave-repeating [[3L 2s]]. The name of the period interval is called the '''sesquitave''' (by analogy to the [[tritave]]). It is a [[Warped diatonic\|warped diatonic scale]] because it has one extra small step compared to the 3/2-equivalent version of diatonic ([[3L 1s (3/2-equivalent)\|3L 1s<3/2>]]): for example, the Ionian diatonic fifth LLsL can be distorted to the Oberonan mode LsLLs.		'''3L 2s<span class="Unicode">&lang;</span>3/2<span class="Unicode">&rang;</span>''' (sometimes called '''uranian'''), is a fifth-repeating MOS scale. The notation "<span class="Unicode">&lang;</span>3/2<span class="Unicode">&rang;</span>" means the period of the MOS is 3/2, disambiguating it from octave-repeating [[3L 2s]]. The name of the period interval is called the '''sesquitave''' (by analogy to the [[tritave]]). It is a [[Warped diatonic\|warped diatonic scale]] because it has one extra small step compared to the 3/2-equivalent version of diatonic ([[3L 1s (3/2-equivalent)\|3L 1s<span class="Unicode">&lang;</span>3/2<span class="Unicode">&rang;</span>]]): for example, the Ionian diatonic fifth LLsL can be distorted to the Oberonan mode LsLLs.

	The generator range is 234 to 280.8 cents, placing it in between the [[9/8\|diatonic major second]] and the [[6/5\|diatonic minor third]], usually representing a subminor third of some type (like [[7/6]]). The bright (chroma-positive) generator is, however, its fifth complement (468 to 421.2 cents).		The generator range is 234 to 280.8 cents, placing it in between the [[9/8\|diatonic major second]] and the [[6/5\|diatonic minor third]], usually representing a subminor third of some type (like [[7/6]]). The bright (chroma-positive) generator is, however, its fifth complement (468 to 421.2 cents).

Cmloegcmluin: "optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence

2023-05-07T19:01:37Z

"optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence

← Older revision		Revision as of 19:01, 7 May 2023
Line 675:		Line 675:
	[[Mapping]]: [{{val\|1 1 3}}, {{val\|0 1 -2}}]		[[Mapping]]: [{{val\|1 1 3}}, {{val\|0 1 -2}}]

	~~[[Vals]]:~~ {{~~val list~~\|8edf, 11edf, 13edf}}		{{Optimal ET sequence\|legend=1\|8edf, 11edf, 13edf}}
	====Semilupine====		====Semilupine====
	[[Subgroup]]: 3/2.7/4.5/2.11/4		[[Subgroup]]: 3/2.7/4.5/2.11/4
Line 685:		Line 685:
	[[Mapping]]: [{{val\|1 1 3 4}}, {{val\|0 1 -2 -4}}]		[[Mapping]]: [{{val\|1 1 3 4}}, {{val\|0 1 -2 -4}}]

	~~[[Vals]]:~~ {{~~val list~~\|8edf, 13edf}}		{{Optimal ET sequence\|legend=1\|8edf, 13edf}}
	====Hemilycan====		====Hemilycan====
	[[Subgroup]]: 3/2.7/4.5/2.11/4		[[Subgroup]]: 3/2.7/4.5/2.11/4
Line 695:		Line 695:
	[[Mapping]]: [{{val\|1 1 3 1}}, {{val\|0 1 -2 4}}]		[[Mapping]]: [{{val\|1 1 3 1}}, {{val\|0 1 -2 4}}]

	~~[[Vals]]:~~ {{~~val list~~\|8edf, 11edf}}		{{Optimal ET sequence\|legend=1\|8edf, 11edf}}

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

Inthar: Template now computes all table values automatically.

2023-04-02T01:34:00Z

Template now computes all table values automatically.

← Older revision		Revision as of 01:34, 2 April 2023
Line 1:		Line 1:
	{{Infobox MOS		{{Infobox MOS}}
	~~\| Equave = 3/2~~
	~~\| nLargeSteps = 3~~
	~~\| nSmallSteps = 2~~
	~~\| Equalized = 2~~
	~~\| Collapsed = 1~~
	~~\| Pattern = LLsLs~~
	}}
	'''3L 2s<3/2>''' (sometimes called '''uranian'''), is a fifth-repeating MOS scale. The notation "<3/2>" means the period of the MOS is 3/2, disambiguating it from octave-repeating [[3L 2s]]. The name of the period interval is called the '''sesquitave''' (by analogy to the [[tritave]]). It is a [[Warped diatonic\|warped diatonic scale]] because it has one extra small step compared to the 3/2-equivalent version of diatonic ([[3L 1s (3/2-equivalent)\|3L 1s<3/2>]]): for example, the Ionian diatonic fifth LLsL can be distorted to the Oberonan mode LsLLs.		'''3L 2s<3/2>''' (sometimes called '''uranian'''), is a fifth-repeating MOS scale. The notation "<3/2>" means the period of the MOS is 3/2, disambiguating it from octave-repeating [[3L 2s]]. The name of the period interval is called the '''sesquitave''' (by analogy to the [[tritave]]). It is a [[Warped diatonic\|warped diatonic scale]] because it has one extra small step compared to the 3/2-equivalent version of diatonic ([[3L 1s (3/2-equivalent)\|3L 1s<3/2>]]): for example, the Ionian diatonic fifth LLsL can be distorted to the Oberonan mode LsLLs.

Inthar at 14:42, 1 April 2023

2023-04-01T14:42:20Z

← Older revision		Revision as of 14:42, 1 April 2023
Line 7:		Line 7:
	\| Pattern = LLsLs		\| Pattern = LLsLs
	}}		}}
	'''3L 2s<3/2>''' (sometimes called '''uranian'''), is a fifth-repeating MOS scale. The notation "<3/2>" means the period of the MOS is 3/2, disambiguating it from octave-repeating [[3L 2s]]. The name of the period interval is called the '''sesquitave''' (by analogy to the [[tritave]]). It is a [[Warped diatonic\|warped diatonic scale]] because it has one extra small step compared to the 3/2-equivalent version diatonic ([[3L 1s (3/2-equivalent)\|3L 1s<3/2>]]): for example, the Ionian diatonic fifth LLsL can be distorted to the Oberonan mode LsLLs.		'''3L 2s<3/2>''' (sometimes called '''uranian'''), is a fifth-repeating MOS scale. The notation "<3/2>" means the period of the MOS is 3/2, disambiguating it from octave-repeating [[3L 2s]]. The name of the period interval is called the '''sesquitave''' (by analogy to the [[tritave]]). It is a [[Warped diatonic\|warped diatonic scale]] because it has one extra small step compared to the 3/2-equivalent version of diatonic ([[3L 1s (3/2-equivalent)\|3L 1s<3/2>]]): for example, the Ionian diatonic fifth LLsL can be distorted to the Oberonan mode LsLLs.

	The generator range is 234 to 280.8 cents, placing it in between the [[9/8\|diatonic major second]] and the [[6/5\|diatonic minor third]], usually representing a subminor third of some type (like [[7/6]]). The bright (chroma-positive) generator is, however, its fifth complement (468 to 421.2 cents).		The generator range is 234 to 280.8 cents, placing it in between the [[9/8\|diatonic major second]] and the [[6/5\|diatonic minor third]], usually representing a subminor third of some type (like [[7/6]]). The bright (chroma-positive) generator is, however, its fifth complement (468 to 421.2 cents).

Inthar at 14:42, 1 April 2023

2023-04-01T14:42:06Z

← Older revision		Revision as of 14:42, 1 April 2023
Line 7:		Line 7:
	\| Pattern = LLsLs		\| Pattern = LLsLs
	}}		}}
	'''3L 2s<3/2>''' (sometimes called '''uranian'''), is a fifth-repeating MOS scale. The notation "<3/2>" means the period of the MOS is 3/2, disambiguating it from octave-repeating [[3L 2s]]. The name of the period interval is called the '''sesquitave''' (by analogy to the [[tritave]]). It is a [[Warped diatonic\|warped diatonic scale]] because it has one extra small step compared to diatonic ([[3L 1s (~~fifth~~-equivalent)]]): for example, the Ionian diatonic fifth LLsL can be distorted to the Oberonan mode LsLLs.		'''3L 2s<3/2>''' (sometimes called '''uranian'''), is a fifth-repeating MOS scale. The notation "<3/2>" means the period of the MOS is 3/2, disambiguating it from octave-repeating [[3L 2s]]. The name of the period interval is called the '''sesquitave''' (by analogy to the [[tritave]]). It is a [[Warped diatonic\|warped diatonic scale]] because it has one extra small step compared to the 3/2-equivalent version diatonic ([[3L 1s (3/2-equivalent)\|3L 1s<3/2>]]): for example, the Ionian diatonic fifth LLsL can be distorted to the Oberonan mode LsLLs.

	The generator range is 234 to 280.8 cents, placing it in between the [[9/8\|diatonic major second]] and the [[6/5\|diatonic minor third]], usually representing a subminor third of some type (like [[7/6]]). The bright (chroma-positive) generator is, however, its fifth complement (468 to 421.2 cents).		The generator range is 234 to 280.8 cents, placing it in between the [[9/8\|diatonic major second]] and the [[6/5\|diatonic minor third]], usually representing a subminor third of some type (like [[7/6]]). The bright (chroma-positive) generator is, however, its fifth complement (468 to 421.2 cents).

Inthar: Inthar moved page 3L 2s (fifth-equivalent) to 3L 2s (3/2-equivalent): "Fifth" has a slight ambiguity and it's now easy to update the mos infobox module accordingly

2023-04-01T14:14:24Z

Inthar moved page 3L 2s (fifth-equivalent) to 3L 2s (3/2-equivalent): "Fifth" has a slight ambiguity and it's now easy to update the mos infobox module accordingly

← Older revision	Revision as of 14:14, 1 April 2023
(No difference)

Fredg999 category edits: Copying from Category:Abstract MOS patterns to Category:5-tone scales using Cat-a-lot

2023-01-06T16:10:06Z

Copying from Category:Abstract MOS patterns to Category:5-tone scales using Cat-a-lot

← Older revision		Revision as of 16:10, 6 January 2023
Line 1,174:		Line 1,174:
	\|}		\|}
	[[Category:Nonoctave]]		[[Category:Nonoctave]]
			[[Category:5-tone scales]]

Inthar: /* Intervals */ changed ordinal interval names to k-mosstep names

2022-09-15T18:53:55Z

Intervals: changed ordinal interval names to k-mosstep names

← Older revision		Revision as of 18:53, 15 September 2022
Line 524:		Line 524:
	\|1		\|1
	\|C		\|C
	\|perfect ~~mosthird~~ (min third)		\|perfect 2-mosstep (min third)
	\| -1		\| -1
	\|D		\|D
	\|perfect ~~mosfourth~~ (maj third)		\|perfect 3-mosstep (maj third)
	\|-		\|-
	\|2		\|2
	\|Eb		\|Eb
	\|minor ~~mosfifth~~		\|minor 4-mosstep
	\| -2		\| -2
	\|B		\|B
	\|major ~~mossecond~~		\|major 1-mosstep
	\|-		\|-
	\|3		\|3
	\|Bb		\|Bb
	\|minor ~~mossecond~~		\|minor 1-mosstep
	\| -3		\| -3
	\|E		\|E
	\|major ~~mosfifth~~		\|major 4-mosstep
	\|-		\|-
	\|4		\|4
	\|Db		\|Db
	\|diminished ~~mosfourth~~		\|diminished 3-mosstep
	\| -4		\| -4
	\|C#		\|C#
	\|augmented ~~mosthird~~		\|augmented 2-mosstep
	\|-		\|-
	\| colspan="6" \|The chromatic 8-note MOS also has the following intervals (from some root):		\| colspan="6" \|The chromatic 8-note MOS also has the following intervals (from some root):
Line 557:		Line 557:
	\| -5		\| -5
	\|A#		\|A#
	\|augmented ~~unison~~ (chroma)		\|augmented 0-mosstep (chroma)
	\|-		\|-
	\|6		\|6
	\|Cb		\|Cb
	\|diminished ~~mosthird~~		\|diminished 2-mosstep
	\| -6		\| -6
	\|D#		\|D#
	\|augmented ~~mosfourth~~		\|augmented 3-mosstep
	\|-		\|-
	\|7		\|7
	\|Ebb		\|Ebb
	\|diminished ~~mosfifth~~		\|diminished 4-mosstep
	\| -7		\| -7
	\|B#		\|B#
	\|augmented ~~mossecond~~		\|augmented 1-mosstep
	\|}		\|}

Inthar: /* Temperaments */

2022-09-15T18:52:04Z

Temperaments

← Older revision		Revision as of 18:52, 15 September 2022
Line 672:		Line 672:

	== Temperaments ==		== Temperaments ==
	The most basic rank-2 temperament interpretation of uranian is '''semiwolf''', which has 4:7:10 chords spelled <code>root-(p+1g)-(3p-2g)</code> (p = 3/2, g = the approximate 7/6). The name "semiwolf" comes from two [[7/6]] generators approximating a [[27/20]] wolf fourth. This is further extended to the 11-limit in two interpretations: '''semilupine''' where 2 major ~~mos2nds~~ (LL) equal 11/9, and '''hemilycan''' where 1 major and 2 minor ~~mos2nds~~ (sLs) equal 11/9. Basic 8edf fits both extensions.		The most basic rank-2 temperament interpretation of uranian is '''semiwolf''', which has 4:7:10 chords spelled <code>root-(p+1g)-(3p-2g)</code> (p = 3/2, g = the approximate 7/6). The name "semiwolf" comes from two [[7/6]] generators approximating a [[27/20]] wolf fourth. This is further extended to the 11-limit in two interpretations: '''semilupine''' where 2 major 2-mossteps (LL) equal 11/9, and '''hemilycan''' where 1 major and 2 minor 2-mossteps (sLs) equal 11/9. Basic 8edf fits both extensions.
	===Semiwolf===		===Semiwolf===
	[[Subgroup]]: 3/2.7/4.5/2		[[Subgroup]]: 3/2.7/4.5/2

Inthar at 18:14, 17 August 2022

2022-08-17T18:14:43Z

← Older revision		Revision as of 18:14, 17 August 2022
Line 1,171:		Line 1,171:
	\|0		\|0
	\|→ inf		\|→ inf
	\|~~Paucitonic~~		\|Collapsed
	\|}		\|}
	[[Category:Nonoctave]]		[[Category:Nonoctave]]

← Older revision		Revision as of 01:34, 2 April 2023
Line 1:		Line 1:
	{{Infobox MOS		{{Infobox MOS}}
	~~\| Equave = 3/2~~
	~~\| nLargeSteps = 3~~
	~~\| nSmallSteps = 2~~
	~~\| Equalized = 2~~
	~~\| Collapsed = 1~~
	~~\| Pattern = LLsLs~~
	}}
	'''3L 2s<3/2>''' (sometimes called '''uranian'''), is a fifth-repeating MOS scale. The notation "<3/2>" means the period of the MOS is 3/2, disambiguating it from octave-repeating [[3L 2s]]. The name of the period interval is called the '''sesquitave''' (by analogy to the [[tritave]]). It is a [[Warped diatonic\|warped diatonic scale]] because it has one extra small step compared to the 3/2-equivalent version of diatonic ([[3L 1s (3/2-equivalent)\|3L 1s<3/2>]]): for example, the Ionian diatonic fifth LLsL can be distorted to the Oberonan mode LsLLs.		'''3L 2s<3/2>''' (sometimes called '''uranian'''), is a fifth-repeating MOS scale. The notation "<3/2>" means the period of the MOS is 3/2, disambiguating it from octave-repeating [[3L 2s]]. The name of the period interval is called the '''sesquitave''' (by analogy to the [[tritave]]). It is a [[Warped diatonic\|warped diatonic scale]] because it has one extra small step compared to the 3/2-equivalent version of diatonic ([[3L 1s (3/2-equivalent)\|3L 1s<3/2>]]): for example, the Ionian diatonic fifth LLsL can be distorted to the Oberonan mode LsLLs.