2L 5s: Difference between revisions

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.

[[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 use}}

{{MOS intervals}}

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:

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

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 [[10/7]] (632.5{{cent}}) and three of them make a [[3/1]] (1897.6{{cent}}).

2L 5s has several rank-2 temperament interpretations, such as:

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

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

{{MOS 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 tunings|Step Ratios=4/1; 5/1; 6/1; 7/1}}

{{MOS mode degrees}}

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|Comments=6/5: [[Gravity]]↑;

3/2: [[Mavila]];

7/15: [[Thuja]];

6/1: [[Liese]]↓, [[triton]]↓}}

[[Category:7-tone scales]]

[[Category:Antidiatonic| ]] <!-- main article -->