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2L 5s: Difference between revisions

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Include both harmonic and melodic notations rather than only harmonic since the distinction only matters in the "Notation' section–I might be biased here because I prefer melodic notation, but I think most will agree a neutral approach is best.
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{{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.


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.
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.
==Name==
 
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 ==
[[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==
:''This article assumes [[TAMNAMS]] for naming step ratios, mossteps, and mosdegrees.''
Names for this scale's intervals are the same as that as diatonic intervals (prefixed with pel- to distinguish them from diatonic intervals), but with the harmonic qualities of diatonic switched: major and minor are switched, as are augmented and diminished.{{MOS intervals|Interval Notation=ordinals|MOS Prefix=pel}}
==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:


*Harmonic antidiatonic notation, where the sharps and flats of diatonic switch roles: sharps flatten and flats sharpen.
The scale is also often called peletonic or '''peltonic''', based on its prefix.
*Melodic antidiatonic notation, where the meaning of sharps and flats is preserved: sharps sharpen and flats flatten.
 
Under harmonnic antidiatonic notation, the basic gamut (for D anti-dorian) is the following: {{MOS gamut|Notation=DEFGABC; b; #|Step Ratio=2/1}}
== Intervals ==
Under melodic antidiatonic notation, the basic gamut (for D anti-dorian) is the following: {{MOS gamut|Notation=DEFGABC; #; b|Step Ratio=2/1}}
{{TAMNAMS use}}
{{MOS intervals}}
 
== 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.
 
{{Mavila|Tuning=2L 5s}}


==Theory==
Under harmonic antidiatonic notation, the basic gamut (for D anti-dorian) is the following: {{MOS gamut|Notation=DEFGABC; b; #|Step Ratio=2/1}}.
===Low harmonic entropy scales===
There is one notable harmonic entropy minimum: [[Liese]]/triton, in which the generator is [[7/5]] (582.5¢) and three of them make a [[3/1]] (1902¢).


===Temperament interpretations===
Under melodic antidiatonic notation, the basic gamut is the following: {{MOS gamut|Notation=DEFGABC; #; b|Step Ratio=2/1}}.
2L 5s has several rank-2 temperament interpretations, such as:


*[[Mavila]], with generators around 679.8¢.
== Theory ==
*[[Casablanca]], with generators around 657.8¢.
=== Low harmonic entropy scales ===
*[[Liese]], with generators around 632.4¢.
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}}).


==Tuning ranges ==
=== Temperament interpretations ===
2L 5s has several rank-2 temperament interpretations, such as:
* [[Mavila]], with generators around 679.8{{c}}.
* [[Casablanca]], with generators around 657.8{{c}}.
* [[Liese]], with generators around 632.4{{c}}.


===Simple tunings===
== Tuning ranges ==
=== 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 degrees|Step Ratio=2/1; 3/1; 3/2|Genchain Extend=7|Notation=NONE|MOS Prefix=pel|Degree Notation=ordinal}}
{{MOS tunings}}
===Soft-of-basic tunings===
 
{{Main|Mavila}}
=== Soft-of-basic tunings ===
{{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 degrees|Step Ratio=3/2; 4/3|Genchain Extend=3|Notation=NONE|MOS Prefix=pel|Degree Notation=ordinal}}
{{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 degrees|Step Ratio=5/2; 8/3|Genchain Extend=3|Notation=NONE|MOS Prefix=pel|Degree Notation=ordinal}}
{{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 degrees|Step Ratio=6/1; 7/1; 20/3|Genchain Extend=3|Notation=NONE|MOS Prefix=pel|Degree Notation=ordinal}}
{{MOS tunings|Step Ratios=4/1; 5/1; 6/1; 7/1}}
==Modes==
 
== Modes ==
{{MOS mode degrees}}
 
=== 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
==Scale tree==
| Mode Names=
{{Scale tree|Comments=6/5: [[Gravity]]↑;
Anti-locrian $
3/2: [[Mavila]];
Anti-phrygian $
13/8: Golden mavila (527.1497¢);
Anti-aeolian $
9/5: [[Mabila]]/[[Amavil]];
Anti-dorian $
5/2: Score;
Anti-mixolydian $
13/5: Unnamed golden tuning (541.3837¢);
Anti-ionian $
8/3: [[Casablanca]];
Anti-lydian
11/3: [[Freivald]]/[[emka]];
| Table Headers=CompactStar's names
7/15: [[Thuja]];
| Table Entries=
6/1: [[Liese]]↓, [[triton]]↓}}
Corsican $
[[Category:7-tone scales]]
Breton $
Burgundian $
Picardian $
Norman $
Provencal $
Alsatian
}}
 
== Scale tree ==
{{MOS tuning spectrum
| 6/5 = [[Gravity]] ↑
| 3/2 = [[Mavila]]
| 13/8 = Golden mavila (527.1497{{c}})
| 9/5 = [[Mabila]]/[[amavil]]
| 2/1 = [[Pelog]]
| 5/2 = Score
| 13/5 = Unnamed golden tuning (541.3837{{c}})
| 8/3 = [[Casablanca]]
| 11/3 = [[Freivald]]/[[emka]]
| 7/15 = [[Thuja]]
| 6/1 = [[Liese]] ↓, [[triton]] ↓
}}
 
[[Category:Antidiatonic| ]] <!-- main article -->
[[Category:Antidiatonic| ]] <!-- main article -->
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