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2L 5s: Difference between revisions

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Changed note names back to CDEFGAB and b/#, as recommended by CompactStar; since antidiatonic and diatonic intervals line up so closely, this article now uses ordinal notation instead
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{{Todo|expand|inline=1|text=Add hard-of-basic tunings, include JI ratio approximations}}
{{Infobox MOS}}
{{Infobox MOS}}
{{MOS intro}}
{{MOS intro}}
==Name==
 
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.
 
== 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.
==Notation==
:''This article assumes [[TAMNAMS]] for naming step ratios, with TAMNAMS-prefixed ordinal notation used for intervals and scale degrees.''
===Intervals and degrees===
Since diatonic and antidiatonic interval classes are so similar to one another, names for this scale's intervals are the same as that as diatonic intervals, prefixed with pel- to distinguish them from diatonic intervals.


Being a moment-of-symmetry scale, every [[interval class]] of 2L 5s, except for the unison and octave, has two [[Interval variety|varieties]] – large and small – whose [[Interval quality|relative qualities]] are denoted as major or minor, or augmented, perfect, and diminished for the generators.
The scale is also often called peletonic or '''peltonic''', based on its prefix.
{{MOS intervals|Interval Notation=ordinals|MOS Prefix=pel}}
 
===Note names ===
== Intervals ==
The most common way of notating this scale is to use the same note names (CDEFGAB) and accidentals (# and b) as that of diatonic, but read as antidiatonic instead. There are, however, two ways of notating accidentals:
{{TAMNAMS use}}
{{MOS intervals}}


* Harmonic notation, where the sharps and flats of diatonic switch roles (sharp flattens and flats sharpen). This article will use this interpretation of sharps and flats.
== Notation ==
* Melodic notation, where the meaning of sharps and flats are preserved (sharps sharpen and flats flatten).
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.  


In any case, the naturals DEFGABC are applied to the step pattern sLsssLs, the antidorian mode on D. Thus, the basic gamut for 2L 5s is the following:
{{Mavila|Tuning=2L 5s}}


{{MOS gamut|Notation=DEFGABC; b; #}}
Under harmonic antidiatonic notation, the basic gamut (for D anti-dorian) is the following: {{MOS gamut|Notation=DEFGABC; b; #|Step Ratio=2/1}}.
==Theory==
Antidiatonic is similar to diatonic (5L 2s) 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 gets, the less the scale resembles diatonic. Additionally, there are temperaments associated with this MOS, such as [[score]], that do not have intervals that resemble a diatonic 5th, flattened or otherwise.


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


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


== 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 degrees|Step Ratio=2/1; 3/1; 3/2|Genchain Extend=7|Notation=DEFGABC; b; #|MOS Prefix=pel|Degree Notation=ordinal}}
{{MOS tunings}}
 
=== 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]].
{{MOS degrees|Step Ratio=3/2; 4/3|Genchain Extend=3|Notation=DEFGABC; b; #|MOS Prefix=pel|Degree Notation=ordinal}}
{{MOS tunings|Step Ratios=Soft-of-basic}}
==Modes==
 
Modes of the antidiatonic scale are usually named as "anti-" combined with the opposite mode of the diatonic scale, e.g. 4|2 being called "antiaeolian". [[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.
=== Hypohard tunings ===
{{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}}
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.
==Scale tree==
{{MOS tunings|Step Ratios=Hypohard}}
{{Scale tree|Comments=6/5: [[Gravity]]↑;
 
3/2: [[Mavila]];
=== Ultrahard tunings ===
13/8: Golden mavila (527.1497¢);
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.
9/5: [[Mabila]]/[[Amavil]];
{{MOS tunings|Step Ratios=4/1; 5/1; 6/1; 7/1}}
2/1: Generators smaller than this are proper;
 
5/2: Score;
== Modes ==
13/5: Unnamed golden tuning (541.3837¢);
{{MOS mode degrees}}
8/3: [[Casablanca]];
 
11/3: [[Freivald]]/[[emka]];
=== Proposed names ===
7/15: [[Thuja]];
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.
6/1: [[Liese]]↓, [[triton]]↓}}
{{MOS modes
[[Category:7-tone scales]]
| 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 ==
{{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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