2L 5s: Difference between revisions
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{{Infobox MOS}} | {{Infobox MOS}} | ||
{{MOS intro}} | {{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. | |||
Among the most well-known 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. | |||
==Name== | ==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. | ||
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===Intervals and degrees=== | ===Intervals and degrees=== | ||
Names for this scale's intervals are the same as that as diatonic intervals (prefixed with pel- to distinguish them from diatonic intervals), but with the harmonic qualities of diatonic switched: major and minor are switched, as are augmented and diminished.{{MOS intervals|Interval Notation=ordinals|MOS Prefix=pel}} | Names for this scale's intervals are the same as that as diatonic intervals (prefixed with pel- to distinguish them from diatonic intervals), but with the harmonic qualities of diatonic switched: major and minor are switched, as are augmented and diminished.{{MOS intervals|Interval Notation=ordinals|MOS Prefix=pel}} | ||
===Note names === | ===Note names=== | ||
The most common way of notating this scale 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 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: | ||
* 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. | *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. | *Melodic antidiatonic notation, where the meaning of sharps and flats is preserved: sharps sharpen and flats flatten. | ||
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: | 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: | ||
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{{MOS gamut|Notation=DEFGABC; b; #}} | {{MOS gamut|Notation=DEFGABC; b; #}} | ||
==Theory== | ==Theory== | ||
===Low harmonic entropy scales=== | ===Low harmonic entropy scales=== | ||
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¢). | 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¢). | ||
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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¢. | *[[Mavila]], with generators around 679.8¢. | ||
* [[Casablanca]], with generators around 657.8¢. | *[[Casablanca]], with generators around 657.8¢. | ||
* [[Liese]], with generators around 632.4¢. | *[[Liese]], with generators around 632.4¢. | ||
== 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 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 === | ===Soft-of-basic tunings=== | ||
{{Main|Mavila}} | {{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]]. | 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]]. | ||