2L 5s: Difference between revisions

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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.

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.

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

== Intervals ==

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== 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.

* 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.

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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=== 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¢.

* [[Casablanca]], with generators around 657.8{{c}}.

*[[Casablanca]], with generators around 657.8¢.

* [[Liese]], with generators around 632.4{{c}}.

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

== Tuning ranges ==

=== Simple tunings ===

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

=== 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]].

=== 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.

=== 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.

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=== 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.

{{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~~|~~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¢~~);

| 2/1 = [[Pelog]]

8/3: [[Casablanca]];

| 5/2 = Score

11/3: [[Freivald]]/[[emka]];

| 13/5 = Unnamed golden tuning (541.3837{{c}})

7/15: [[Thuja]];

| 8/3 = [[Casablanca]]

6/1: [[Liese]]↓, [[triton]]↓}}

| 11/3 = [[Freivald]]/[[emka]]

| 7/15 = [[Thuja]]

| 6/1 = [[Liese]] ↓, [[triton]] ↓

}}

~~[[Category:7-tone scales]]~~

[[Category:Antidiatonic| ]]

@@ Line 1: / Line 1: @@
 {{Infobox MOS}}
 {{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.
+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.
+The scale is also often called peletonic or '''peltonic''', based on its prefix.
 == Intervals ==
@@ Line 13: / Line 16: @@
 == 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.
-* Harmonic antidiatonic notation, where the sharps and flats of diatonic switch roles: sharps flatten and flats sharpen.
+{{Mavila|Tuning=2L 5s}}
-* 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}}.
@@ Line 27: / Line 29: @@
 === Temperament interpretations ===
-L 5s has several rank-2 temperament interpretations, such as:
+L&nbsp;5s has several rank-2 temperament interpretations, such as:
+* [[Mavila]], with generators around 679.8{{c}}.
-*[[Mavila]], with generators around 679.8¢.
+* [[Casablanca]], with generators around 657.8{{c}}.
-*[[Casablanca]], with generators around 657.8¢.
+* [[Liese]], with generators around 632.4{{c}}.
-*[[Liese]], with generators around 632.4¢.
 == Tuning ranges ==
 === Simple tunings ===
 The simplest tunings are those with step ratios 2:1, 3:1, and 3:2, producing [[9edo]], [[11edo]], and [[16edo]].
 {{MOS 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]].
 {{MOS tunings|Step Ratios=Soft-of-basic}}
 === 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.
 {{MOS tunings|Step Ratios=Hypohard}}
 === 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}}
@@ Line 60: / Line 57: @@
 === 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.
-{{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|Comments=6/5: [[Gravity]]↑;
+{{MOS tuning spectrum
-/2: [[Mavila]];
+| 6/5 = [[Gravity]]&nbsp;↑
-/8: Golden mavila (527.1497¢);
+| 3/2 = [[Mavila]]
-/5: [[Mabila]]/[[Amavil]];
+| 13/8 = Golden mavila (527.1497{{c}})
-/2: Score;
+| 9/5 = [[Mabila]]/[[amavil]]
-/5: Unnamed golden tuning (541.3837¢);
+| 2/1 = [[Pelog]]
-/3: [[Casablanca]];
+| 5/2 = Score
-/3: [[Freivald]]/[[emka]];
+| 13/5 = Unnamed golden tuning (541.3837{{c}})
-/15: [[Thuja]];
+| 8/3 = [[Casablanca]]
-/1: [[Liese]]↓, [[triton]]↓}}
+| 11/3 = [[Freivald]]/[[emka]]
+| 7/15 = [[Thuja]]
+| 6/1 = [[Liese]]&nbsp;↓, [[triton]]&nbsp;↓
+}}
-[[Category:7-tone scales]]
 [[Category:Antidiatonic| ]] <!-- main article -->