2L 5s: Difference between revisions

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[[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, intervals, and scale degrees~~, and [[Diamond-mos notation|diamond-MOS notation]] for note names~~.''~~~~

:''This article assumes [[TAMNAMS]] for naming step ratios, with TAMNAMS-prefixed ordinal notation used for intervals and scale degrees.''

===Intervals and degrees===

~~Names~~ for this scale's intervals ~~(mossteps) and scale degrees (mosdegrees)~~ are ~~based on~~ the ~~number of large and small steps from the root, starting at 0 (0-mosstep and 0-mosdegree) for the unison, per TAMNAMS. Ordinal names, such~~ as ~~mos-1st for the unison~~, ~~are discouraged for non~~-diatonic ~~MOS scales~~.

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.

===Note names ===

~~For~~ this ~~article,~~ note names ~~are based on diamond-MOS notation, where the naturals JKLMNOP are applied to the step pattern sLsssLs~~ and ~~the~~ accidentals & (~~pronounced "am" or "amp")~~ and ~~@ (pronounced "at"~~) are ~~used to represent sharps and flats respectively. Thus~~, ~~the basic gamut for 2L 5s is the following~~:

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:

* 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.

* Melodic notation, where the meaning of sharps and flats are preserved (sharps sharpen and flats flatten).

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:

==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~~" (or 4-mosstep)~~ 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.

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===

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=== Simple tunings ===

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}}

=== Soft-of-basic tunings ===

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}}

==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.

@@ Line 5: / Line 5: @@
 [[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, intervals, and scale degrees, and [[Diamond-mos notation|diamond-MOS notation]] for note names.''<!-- May be worth adding other notation schemes, such as that where standard notation is read is antidiatonic. -->
+:''This article assumes [[TAMNAMS]] for naming step ratios, with TAMNAMS-prefixed ordinal notation used for intervals and scale degrees.''
 ===Intervals and degrees===
-Names for this scale's intervals (mossteps) and scale degrees (mosdegrees) are based on the number of large and small steps from the root, starting at 0 (0-mosstep and 0-mosdegree) for the unison, per TAMNAMS. Ordinal names, such as mos-1st for the unison, are discouraged for non-diatonic MOS scales.
+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.
-{{MOS intervals}}
+{{MOS intervals|Interval Notation=ordinals|MOS Prefix=pel}}
 ===Note names ===
-For this article, note names are based on diamond-MOS notation, where the naturals JKLMNOP are applied to the step pattern sLsssLs and the accidentals & (pronounced "am" or "amp") and @ (pronounced "at") are used to represent sharps and flats respectively. Thus, the basic gamut for 2L 5s is the following:
+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:
-{{MOS gamut}}
+* 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.
+* Melodic notation, where the meaning of sharps and flats are preserved (sharps sharpen and flats flatten).
+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:
+{{MOS gamut|Notation=DEFGABC; b; #}}
 ==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" (or 4-mosstep) 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.
+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===
@@ Line 32: / Line 37: @@
 === Simple tunings ===
 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}}
+{{MOS degrees|Step Ratio=2/1; 3/1; 3/2|Genchain Extend=7|Notation=DEFGABC; b; #|MOS Prefix=pel|Degree Notation=ordinal}}
 === Soft-of-basic tunings ===
 {{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]].
-{{MOS degrees|Step Ratio=3/2; 4/3|Genchain Extend=3}}
+{{MOS degrees|Step Ratio=3/2; 4/3|Genchain Extend=3|Notation=DEFGABC; b; #|MOS Prefix=pel|Degree Notation=ordinal}}
 ==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.