2L 5s - Revision history

Furcht968 at 18:34, 3 April 2026

2026-04-03T18:34:12Z

← Older revision		Revision as of 18:34, 3 April 2026
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			{{Interwiki
			\|en=2L 5s
			\|es=
			\|de=
			\|ja=2L 5s
			}}
	{{Infobox MOS}}		{{Infobox MOS}}
	{{MOS intro}}		{{MOS intro}}

VectorGraphics at 07:44, 30 July 2025

2025-07-30T07:44:43Z

← Older revision		Revision as of 07:44, 30 July 2025
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	== Notation ==		== Notation ==
	The most common way of notating this scale, particularly when working with mavila, is to use the same note names and accidentals as that of diatonic (CDEFGAB, #, and b), but read as antidiatonic instead. ~~There are, however, two ways of notating accidentals:~~		The most common way of notating this scale, particularly when working with mavila, is to use the same note names and accidentals as that of diatonic (CDEFGAB, #, and b), but read as antidiatonic instead.
	* Harmonic antidiatonic notation, where the sharps and flats of diatonic switch roles: sharps flatten and flats sharpen.
	* Melodic antidiatonic notation, where the meaning of sharps and flats is preserved: sharps sharpen and flats flatten.		{{Mavila\|Tuning=2L 5s}}

	Under harmonic antidiatonic notation, the basic gamut (for D anti-dorian) is the following: {{MOS gamut\|Notation=DEFGABC; b; #\|Step Ratio=2/1}}.		Under harmonic antidiatonic notation, the basic gamut (for D anti-dorian) is the following: {{MOS gamut\|Notation=DEFGABC; b; #\|Step Ratio=2/1}}.

VectorGraphics at 05:49, 21 March 2025

2025-03-21T05:49:39Z

← Older revision		Revision as of 05:49, 21 March 2025
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	== Name ==		== Name ==
	[[TAMNAMS]] suggests the temperament-agnostic name '''antidiatonic''' for this scale, adopted from the common use of the term to refer to diatonic ([[5L 2s]]) but with the large and small steps switched.		[[TAMNAMS]] suggests the temperament-agnostic name '''antidiatonic''' for this scale, adopted from the common use of the term to refer to diatonic ([[5L 2s]]) but with the large and small steps switched.

			The scale is also often called peletonic or '''peltonic''', based on its prefix.

	== Intervals ==		== Intervals ==

ArrowHead294: /* Scale tree */

2025-03-06T16:50:55Z

Scale tree

← Older revision		Revision as of 16:50, 6 March 2025
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	\| 13/8 = Golden mavila (527.1497{{c}})		\| 13/8 = Golden mavila (527.1497{{c}})
	\| 9/5 = [[Mabila]]/[[amavil]]		\| 9/5 = [[Mabila]]/[[amavil]]
			\| 2/1 = [[Pelog]]
	\| 5/2 = Score		\| 5/2 = Score
	\| 13/5 = Unnamed golden tuning (541.3837{{c}})		\| 13/5 = Unnamed golden tuning (541.3837{{c}})

ArrowHead294 at 17:28, 28 February 2025

2025-02-28T17:28:02Z

← Older revision		Revision as of 17:28, 28 February 2025
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	=== Simple tunings ===		=== Simple tunings ===
	The simplest tunings are those with step ratios 2:1, 3:1, and 3:2, producing [[9edo]], [[11edo]], and [[16edo]].		The simplest tunings are those with step ratios 2:1, 3:1, and 3:2, producing [[9edo]], [[11edo]], and [[16edo]].

	{{MOS tunings}}		{{MOS tunings}}

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	{{See also\| Mavila }}		{{See also\| Mavila }}
	Much of the range for soft-of-basic antidiatonic tunings (1:1 to 2:1) corresponds to mavila temperament. Edos include 9edo (not shown), [[16edo]], and [[23edo]].		Much of the range for soft-of-basic antidiatonic tunings (1:1 to 2:1) corresponds to mavila temperament. Edos include 9edo (not shown), [[16edo]], and [[23edo]].

	{{MOS tunings\|Step Ratios=Soft-of-basic}}		{{MOS tunings\|Step Ratios=Soft-of-basic}}

	=== Hypohard tunings ===		=== Hypohard tunings ===
	The range of hard-of-basic tunings correspond to temperaments that have significantly flattened antidiatonic 5ths, such as score and casablanca. [[20edo]] and [[31edo]] represent these two temperaments quite well.		The range of hard-of-basic tunings correspond to temperaments that have significantly flattened antidiatonic 5ths, such as score and casablanca. [[20edo]] and [[31edo]] represent these two temperaments quite well.

	{{MOS tunings\|Step Ratios=Hypohard}}		{{MOS tunings\|Step Ratios=Hypohard}}

	=== Ultrahard tunings ===		=== Ultrahard tunings ===
	Ultrahard tunings, particularly with the harder end of the spectrum, correspond to [[liese]] temperament, represent by edos such as 17edo, 19edo, and larger edos such as 55edo.		Ultrahard tunings, particularly with the harder end of the spectrum, correspond to [[liese]] temperament, represent by edos such as 17edo, 19edo, and larger edos such as 55edo.

	{{MOS tunings\|Step Ratios=4/1; 5/1; 6/1; 7/1}}		{{MOS tunings\|Step Ratios=4/1; 5/1; 6/1; 7/1}}

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	=== Proposed names ===		=== Proposed names ===
	Modes of antidiatonic are usually named as "anti-" combined with the corresponding mode of the diatonic scale, where anti-locrian is the brightest mode and anti-lydian is the darkest mode. [[User:CompactStar\|CompactStar]] also gave original names based on regions of France to mirror how modes of the diatonic scale are named on regions of Greece and Turkey.		Modes of antidiatonic are usually named as "anti-" combined with the corresponding mode of the diatonic scale, where anti-locrian is the brightest mode and anti-lydian is the darkest mode. [[User:CompactStar\|CompactStar]] also gave original names based on regions of France to mirror how modes of the diatonic scale are named on regions of Greece and Turkey.
	{{MOS modes\|Mode Names=Anti-locrian; Anti-phrygian; Anti-aeolian; Anti-dorian; Anti-mixolydian; Anti-ionian; Anti-lydian\|Table Headers=CompactStar's names\|Table Entries=Corsican; Breton; Burgundian; Picardian; Norman; Provencal; Alsatian}}		{{MOS modes
			\| Mode Names=
			Anti-locrian $
			Anti-phrygian $
			Anti-aeolian $
			Anti-dorian $
			Anti-mixolydian $
			Anti-ionian $
			Anti-lydian
			\| Table Headers=CompactStar's names
			\| Table Entries=
			Corsican $
			Breton $
			Burgundian $
			Picardian $
			Norman $
			Provencal $
			Alsatian
			}}

	== Scale tree ==		== Scale tree ==
	{{~~Scale tree~~\|~~Comments=~~6/5: [[Gravity]]↑;		{{MOS tuning spectrum
	3/2: [[Mavila]];		\| 6/5 = [[Gravity]] ↑
	13/8: Golden mavila (527.~~1497¢~~);		\| 3/2 = [[Mavila]]
	9/5: [[Mabila]]/[[amavil]];		\| 13/8 = Golden mavila (527.1497{{c}})
	5/2: Score;		\| 9/5 = [[Mabila]]/[[amavil]]
	13/5: Unnamed golden tuning (541.~~3837¢~~);		\| 5/2 = Score
	8/3: [[Casablanca]];		\| 13/5 = Unnamed golden tuning (541.3837{{c}})
	11/3: [[Freivald]]/[[emka]];		\| 8/3 = [[Casablanca]]
	7/15: [[Thuja]];		\| 11/3 = [[Freivald]]/[[emka]]
	6/1: [[Liese]]↓, [[triton]]↓}}		\| 7/15 = [[Thuja]]
			\| 6/1 = [[Liese]] ↓, [[triton]] ↓
			}}

	[[Category:Antidiatonic\| ]] <!-- main article -->		[[Category:Antidiatonic\| ]] <!-- main article -->

FloraC: Style and -redundant category

2025-02-18T09:54:24Z

Style and -redundant category

← Older revision		Revision as of 09:54, 18 February 2025
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	{{MOS intro}}		{{MOS intro}}

	Antidiatonic is similar to diatonic except interval classes are flipped. For example, there are natural, harmonic, and melodic major scales instead of minor scales, and its locrian scale, called "antilocrian", has an augmented fifth instead of a diminished fifth. The flatter the fifth, the less this scale resembles diatonic.		Antidiatonic is similar to [[5L 2s\|diatonic]] except interval classes are flipped. For example, there are natural, harmonic, and melodic major scales instead of minor scales, and its locrian scale, called "antilocrian", has an augmented fifth instead of a diminished fifth. The flatter the fifth, the less this scale resembles diatonic.

	The most well-known forms of this scale are produced by ~~Mavila~~, with fifths sharp enough to resemble diatonic. Other temperaments that produce this scale include score, casablanca, and triton, whose fifths are so flat that they cannot be interpreted as a diatonic 5th, flattened or otherwise.		The most well-known forms of this scale are produced by [[mavila]], with fifths sharp enough to resemble diatonic. Other temperaments that produce this scale include [[score]], [[casablanca]], and [[triton]], whose fifths are so flat that they cannot be interpreted as a diatonic 5th, flattened or otherwise.

	== Name ==		== Name ==
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	== Notation ==		== Notation ==
	The most common way of notating this scale, particularly when working with ~~Mavila~~, is to use the same note names and accidentals as that of diatonic (CDEFGAB, #, and b), but read as antidiatonic instead. There are, however, two ways of notating accidentals:		The most common way of notating this scale, particularly when working with mavila, is to use the same note names and accidentals as that of diatonic (CDEFGAB, #, and b), but read as antidiatonic instead. There are, however, two ways of notating accidentals:

	* Harmonic antidiatonic notation, where the sharps and flats of diatonic switch roles: sharps flatten and flats sharpen.		* Harmonic antidiatonic notation, where the sharps and flats of diatonic switch roles: sharps flatten and flats sharpen.
	* Melodic antidiatonic notation, where the meaning of sharps and flats is preserved: sharps sharpen and flats flatten.		* Melodic antidiatonic notation, where the meaning of sharps and flats is preserved: sharps sharpen and flats flatten.
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	=== Temperament interpretations ===		=== Temperament interpretations ===
	2L 5s has several rank-2 temperament interpretations, such as:		2L 5s has several rank-2 temperament interpretations, such as:

	* [[Mavila]], with generators around 679.8{{c}}.		* [[Mavila]], with generators around 679.8{{c}}.
	* [[Casablanca]], with generators around 657.8{{c}}.		* [[Casablanca]], with generators around 657.8{{c}}.
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	=== Soft-of-basic tunings ===		=== Soft-of-basic tunings ===
	{{~~Main~~\|Mavila}}		{{See also\| Mavila }}
	Much of the range for soft-of-basic antidiatonic tunings (1:1 to 2:1) corresponds to mavila temperament. Edos include 9edo (not shown), [[16edo]], and [[23edo]].		Much of the range for soft-of-basic antidiatonic tunings (1:1 to 2:1) corresponds to mavila temperament. Edos include 9edo (not shown), [[16edo]], and [[23edo]].

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	3/2: [[Mavila]];		3/2: [[Mavila]];
	13/8: Golden mavila (527.1497¢);		13/8: Golden mavila (527.1497¢);
	9/5: [[Mabila]]/[[~~Amavil~~]];		9/5: [[Mabila]]/[[amavil]];
	5/2: Score;		5/2: Score;
	13/5: Unnamed golden tuning (541.3837¢);		13/5: Unnamed golden tuning (541.3837¢);
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	6/1: [[Liese]]↓, [[triton]]↓}}		6/1: [[Liese]]↓, [[triton]]↓}}

	~~[[Category:7-tone scales]]~~
	[[Category:Antidiatonic\| ]] <!-- main article -->		[[Category:Antidiatonic\| ]] <!-- main article -->

ArrowHead294 at 22:38, 17 February 2025

2025-02-17T22:38:14Z

← Older revision		Revision as of 22:38, 17 February 2025
Line 1:		Line 1:
	{{Infobox MOS}}		{{Infobox MOS}}
	{{MOS intro}}		{{MOS intro}}

	Antidiatonic is similar to diatonic except interval classes are flipped. For example, there are natural, harmonic, and melodic major scales instead of minor scales, and its locrian scale, called "antilocrian", has an augmented fifth instead of a diminished fifth. The flatter the fifth, the less this scale resembles diatonic.		Antidiatonic is similar to diatonic except interval classes are flipped. For example, there are natural, harmonic, and melodic major scales instead of minor scales, and its locrian scale, called "antilocrian", has an augmented fifth instead of a diminished fifth. The flatter the fifth, the less this scale resembles diatonic.

	The most well-known forms of this scale are produced by ~~[[mavila temperament]]~~, with fifths sharp enough to resemble diatonic. Other temperaments that produce this scale include score, casablanca, and triton, whose fifths are so flat that they cannot be interpreted as a diatonic 5th, flattened or otherwise.		The most well-known forms of this scale are produced by Mavila, with fifths sharp enough to resemble diatonic. Other temperaments that produce this scale include score, casablanca, and triton, whose fifths are so flat that they cannot be interpreted as a diatonic 5th, flattened or otherwise.

	== Name ==		== Name ==
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	== Notation ==		== Notation ==
	The most common way of notating this scale, particularly when working with ~~mavila temperament~~, is to use the same note names and accidentals as that of diatonic (CDEFGAB, #, and b), but read as antidiatonic instead. There are, however, two ways of notating accidentals:		The most common way of notating this scale, particularly when working with Mavila, is to use the same note names and accidentals as that of diatonic (CDEFGAB, #, and b), but read as antidiatonic instead. There are, however, two ways of notating accidentals:

	* Harmonic antidiatonic notation, where the sharps and flats of diatonic switch roles: sharps flatten and flats sharpen.		* Harmonic antidiatonic notation, where the sharps and flats of diatonic switch roles: sharps flatten and flats sharpen.
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	=== Temperament interpretations ===		=== Temperament interpretations ===
	2L 5s has several rank-2 temperament interpretations, such as:		2L 5s has several rank-2 temperament interpretations, such as:

	*[[Mavila]], with generators around 679.8¢.		* [[Mavila]], with generators around 679.8{{c}}.
	*[[Casablanca]], with generators around 657.8¢.		* [[Casablanca]], with generators around 657.8{{c}}.
	*[[Liese]], with generators around 632.4¢.		* [[Liese]], with generators around 632.4{{c}}.

	== Tuning ranges ==		== Tuning ranges ==
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	=== Ultrahard tunings ===		=== Ultrahard tunings ===
	Ultrahard tunings, particularly with the harder end of the spectrum, correspond to [[liese]] temperament, represent by edos such as 17edo 19edo, and larger edos such as 55edo.		Ultrahard tunings, particularly with the harder end of the spectrum, correspond to [[liese]] temperament, represent by edos such as 17edo, 19edo, and larger edos such as 55edo.

	{{MOS tunings\|Step Ratios=4/1; 5/1; 6/1; 7/1}}		{{MOS tunings\|Step Ratios=4/1; 5/1; 6/1; 7/1}}

ArrowHead294 at 14:37, 3 February 2025

2025-02-03T14:37:52Z

← Older revision		Revision as of 14:37, 3 February 2025
Line 4:		Line 4:

	The most well-known forms of this scale are produced by [[mavila temperament]], with fifths sharp enough to resemble diatonic. Other temperaments that produce this scale include score, casablanca, and triton, whose fifths are so flat that they cannot be interpreted as a diatonic 5th, flattened or otherwise.		The most well-known forms of this scale are produced by [[mavila temperament]], with fifths sharp enough to resemble diatonic. Other temperaments that produce this scale include score, casablanca, and triton, whose fifths are so flat that they cannot be interpreted as a diatonic 5th, flattened or otherwise.

	== Name ==		== Name ==
	[[TAMNAMS]] suggests the temperament-agnostic name '''antidiatonic''' for this scale, adopted from the common use of the term to refer to diatonic ([[5L 2s]]) but with the large and small steps switched.		[[TAMNAMS]] suggests the temperament-agnostic name '''antidiatonic''' for this scale, adopted from the common use of the term to refer to diatonic ([[5L 2s]]) but with the large and small steps switched.

ArrowHead294 at 14:32, 3 February 2025

2025-02-03T14:32:00Z

← Older revision		Revision as of 14:32, 3 February 2025
Line 4:		Line 4:

	The most well-known forms of this scale are produced by [[mavila temperament]], with fifths sharp enough to resemble diatonic. Other temperaments that produce this scale include score, casablanca, and triton, whose fifths are so flat that they cannot be interpreted as a diatonic 5th, flattened or otherwise.		The most well-known forms of this scale are produced by [[mavila temperament]], with fifths sharp enough to resemble diatonic. Other temperaments that produce this scale include score, casablanca, and triton, whose fifths are so flat that they cannot be interpreted as a diatonic 5th, flattened or otherwise.
	==Name==		== Name ==
	[[TAMNAMS]] suggests the temperament-agnostic name '''antidiatonic''' for this scale, adopted from the common use of the term to refer to diatonic ([[5L 2s]]) but with the large and small steps switched.		[[TAMNAMS]] suggests the temperament-agnostic name '''antidiatonic''' for this scale, adopted from the common use of the term to refer to diatonic ([[5L 2s]]) but with the large and small steps switched.
	==Intervals==
			== Intervals ==
	{{TAMNAMS use}}		{{TAMNAMS use}}
	{{MOS intervals}}		{{MOS intervals}}
	==Notation==
			== Notation ==
	The most common way of notating this scale, particularly when working with mavila temperament, is to use the same note names and accidentals as that of diatonic (CDEFGAB, #, and b), but read as antidiatonic instead. There are, however, two ways of notating accidentals:		The most common way of notating this scale, particularly when working with mavila temperament, is to use the same note names and accidentals as that of diatonic (CDEFGAB, #, and b), but read as antidiatonic instead. There are, however, two ways of notating accidentals:

	*Harmonic antidiatonic notation, where the sharps and flats of diatonic switch roles: sharps flatten and flats sharpen.		* Harmonic antidiatonic notation, where the sharps and flats of diatonic switch roles: sharps flatten and flats sharpen.
	*Melodic antidiatonic notation, where the meaning of sharps and flats is preserved: sharps sharpen and flats flatten.		* Melodic antidiatonic notation, where the meaning of sharps and flats is preserved: sharps sharpen and flats flatten.

	Under harmonic antidiatonic notation, the basic gamut (for D anti-dorian) is the following: {{MOS gamut\|Notation=DEFGABC; b; #\|Step Ratio=2/1}}.		Under harmonic antidiatonic notation, the basic gamut (for D anti-dorian) is the following: {{MOS gamut\|Notation=DEFGABC; b; #\|Step Ratio=2/1}}.
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	Under melodic antidiatonic notation, the basic gamut is the following: {{MOS gamut\|Notation=DEFGABC; #; b\|Step Ratio=2/1}}.		Under melodic antidiatonic notation, the basic gamut is the following: {{MOS gamut\|Notation=DEFGABC; #; b\|Step Ratio=2/1}}.

	==Theory==		== Theory ==
	===Low harmonic entropy scales===		=== Low harmonic entropy scales ===
	There is one notable harmonic entropy minimum: [[Liese]]/triton, in which the generator is [[10/7]] (632.5{{cent}}) and three of them make a [[3/1]] (1897.6{{cent}}).		There is one notable harmonic entropy minimum: [[Liese]]/triton, in which the generator is [[10/7]] (632.5{{cent}}) and three of them make a [[3/1]] (1897.6{{cent}}).

	===Temperament interpretations===		=== Temperament interpretations ===
	2L 5s has several rank-2 temperament interpretations, such as:		2L 5s has several rank-2 temperament interpretations, such as:

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	*[[Liese]], with generators around 632.4¢.		*[[Liese]], with generators around 632.4¢.

	==Tuning ranges ==		== Tuning ranges ==
			=== Simple tunings ===
	===Simple tunings===
	The simplest tunings are those with step ratios 2:1, 3:1, and 3:2, producing [[9edo]], [[11edo]], and [[16edo]].		The simplest tunings are those with step ratios 2:1, 3:1, and 3:2, producing [[9edo]], [[11edo]], and [[16edo]].

	{{MOS tunings}}		{{MOS tunings}}

	===Soft-of-basic tunings===		=== Soft-of-basic tunings ===
	{{Main\|Mavila}}		{{Main\|Mavila}}
	Much of the range for soft-of-basic antidiatonic tunings (1:1 to 2:1) corresponds to mavila temperament. Edos include 9edo (not shown), [[16edo]], and [[23edo]].		Much of the range for soft-of-basic antidiatonic tunings (1:1 to 2:1) corresponds to mavila temperament. Edos include 9edo (not shown), [[16edo]], and [[23edo]].
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	{{MOS tunings\|Step Ratios=4/1; 5/1; 6/1; 7/1}}		{{MOS tunings\|Step Ratios=4/1; 5/1; 6/1; 7/1}}

	==Modes==		== Modes ==
	{{MOS mode degrees}}		{{MOS mode degrees}}
	===Proposed ~~Names~~===
			=== Proposed names ===
	Modes of antidiatonic are usually named as "anti-" combined with the corresponding mode of the diatonic scale, where anti-locrian is the brightest mode and anti-lydian is the darkest mode. [[User:CompactStar\|CompactStar]] also gave original names based on regions of France to mirror how modes of the diatonic scale are named on regions of Greece and Turkey.		Modes of antidiatonic are usually named as "anti-" combined with the corresponding mode of the diatonic scale, where anti-locrian is the brightest mode and anti-lydian is the darkest mode. [[User:CompactStar\|CompactStar]] also gave original names based on regions of France to mirror how modes of the diatonic scale are named on regions of Greece and Turkey.
	{{MOS modes\|Mode Names=Anti-locrian; Anti-phrygian; Anti-aeolian; Anti-dorian; Anti-mixolydian; Anti-ionian; Anti-lydian\|Table Headers=CompactStar's names\|Table Entries=Corsican; Breton; Burgundian; Picardian; Norman; Provencal; Alsatian}}		{{MOS modes\|Mode Names=Anti-locrian; Anti-phrygian; Anti-aeolian; Anti-dorian; Anti-mixolydian; Anti-ionian; Anti-lydian\|Table Headers=CompactStar's names\|Table Entries=Corsican; Breton; Burgundian; Picardian; Norman; Provencal; Alsatian}}

	==Scale tree==		== Scale tree ==
	{{Scale tree\|Comments=6/5: [[Gravity]]↑;		{{Scale tree\|Comments=6/5: [[Gravity]]↑;
	3/2: [[Mavila]];		3/2: [[Mavila]];
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	7/15: [[Thuja]];		7/15: [[Thuja]];
	6/1: [[Liese]]↓, [[triton]]↓}}		6/1: [[Liese]]↓, [[triton]]↓}}

	[[Category:7-tone scales]]		[[Category:7-tone scales]]
	[[Category:Antidiatonic\| ]] <!-- main article -->		[[Category:Antidiatonic\| ]] <!-- main article -->

Recentlymaterialized: the accuracy of the generator interpretation does not determine the HE minimum

2024-11-05T00:03:21Z

the accuracy of the generator interpretation does not determine the HE minimum

← Older revision		Revision as of 00:03, 5 November 2024
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	==Theory==		==Theory==
	===Low harmonic entropy scales===		===Low harmonic entropy scales===
	There is one notable harmonic entropy minimum: [[Liese]]/triton, in which the generator is [[10/7]] (~~617~~.5¢) and three of them make a [[3/1]]. ~~(Though it should be noted 3^(1/3~~) ~~is much closer to [[23/16]] and [[36/25]] than [[10/7]]~~.)		There is one notable harmonic entropy minimum: [[Liese]]/triton, in which the generator is [[10/7]] (632.5{{cent}}) and three of them make a [[3/1]] (1897.6{{cent}}).

	===Temperament interpretations===		===Temperament interpretations===