2L 5s: Difference between revisions

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~~{{Todo|expand|inline=1|text=Add hard-of-basic tunings, include JI ratio approximations}}~~

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*Harmonic antidiatonic notation, where the sharps and flats of diatonic switch roles: sharps flatten and flats sharpen. This article uses this interpretation of sharps and flats.

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

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

~~For this article, 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==

===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}}

{{MOS degrees|Step Ratio=2/1; 3/1; 3/2|Genchain Extend=7|Notation=NONE|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}}

=== 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 degrees|Step Ratio=5/2; 8/3|Genchain Extend=3|Notation=NONE|MOS Prefix=pel|Degree Notation=ordinal}}

=== 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.

{{MOS degrees|Step Ratio=6/1; 7/1; 20/3|Genchain Extend=3|Notation=NONE|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.

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}}

==Scale tree==

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-{{Todo|expand|inline=1|text=Add hard-of-basic tunings, include JI ratio approximations}}
 {{Infobox MOS}}
 {{MOS intro}}
@@ Line 16: / Line 15: @@
 *Harmonic antidiatonic notation, where the sharps and flats of diatonic switch roles: sharps flatten and flats sharpen. This article uses this interpretation of sharps and flats.
 *Melodic antidiatonic notation, where the meaning of sharps and flats is preserved: sharps sharpen and flats flatten.
+Under this notation, the basic gamut (for D anti-dorian) is the following: {{MOS gamut|Notation=DEFGABC; b; #|Step Ratio=2/1}}
-For this article, 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==
 ===Low harmonic entropy scales===
@@ Line 35: / Line 32: @@
 ===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}}
+{{MOS degrees|Step Ratio=2/1; 3/1; 3/2|Genchain Extend=7|Notation=NONE|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|Notation=DEFGABC; b; #|MOS Prefix=pel|Degree Notation=ordinal}}
+=== 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 degrees|Step Ratio=5/2; 8/3|Genchain Extend=3|Notation=NONE|MOS Prefix=pel|Degree Notation=ordinal}}
+=== 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.
+{{MOS degrees|Step Ratio=6/1; 7/1; 20/3|Genchain Extend=3|Notation=NONE|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.
+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}}
 ==Scale tree==