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| {{Infobox MOS | | {{Infobox MOS}} |
| | Name = antidiatonic
| | {{MOS intro}} |
| | Periods = 1
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| | nLargeSteps = 2 | | 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. |
| | nSmallSteps = 5
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| | Equalized = 3
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| | Collapsed = 1
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| | Pattern = LssLsss
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| | Neutral = 4L 3s
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| }}
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| '''2L 5s''' refers to the structure of octave-equivalent [[MOS]] scales with generators ranging from 3\7 (3 degrees of [[7edo]] = 514.29¢) to 1\2 (one degree of [[2edo]] = 600¢). In the case of 7edo, L and s are the same size; in the case of 2edo, s becomes so small it disappears (and all that remains are the two equal L's).
| | 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. |
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| While antidiatonic is closely associated with [[mavila temperament]] and [[7L 2s]], not every 2L 5s scale is an instance of "mavila", since some of them extend to [[2L 7s]] scales (like the 2L 5s generated by 11edo's 6\11 = 656.5657¢), not 7L 2s mavila superdiatonic scales. (In particular, between 13\29 and 14\31, and centered on 9\20, is the albitonic scale for the 2.7.11.13 subgroup temperament [[Chromatic pairs #Score|score]], which is not intended to be treated as having any kind of fifth, flat 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. |
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| In terms of harmonic entropy, the most significant minimum is at [[Meantone family #Liese|Liese]]/Triton, in which the generator is about 7/5 and three of them make a 3/1.
| | The scale is also often called peletonic or '''peltonic''', based on its prefix. |
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| == Names == | | == Intervals == |
| It is often called '''antidiatonic''', because it has the step pattern of diatonic ([[5L 2s]]), but with the large and small steps switched. [[TAMNAMS]] uses this name as well.
| | {{TAMNAMS use}} |
| | {{MOS intervals}} |
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| == Notation == | | == Notation == |
| We'll use the convention DEFGABCD (D Antidorian, sLsssLs); D = 293.665 Hz, &/@ = raise and lower by one chroma. The chain of mavila fifths becomes … E& B& F C G D A E B F@ C@ … Note that 7 fifths up ''flattens'' a note by a chroma, rather than sharpening it as in diatonic ([[5L 2s]]).
| | 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. |
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| | {{Mavila|Tuning=2L 5s}} |
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| | 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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| | Under melodic antidiatonic notation, the basic gamut is the following: {{MOS gamut|Notation=DEFGABC; #; b|Step Ratio=2/1}}. |
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| | == Theory == |
| | === Low harmonic entropy scales === |
| | 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}}). |
| | |
| | === Temperament interpretations === |
| | 2L 5s has several rank-2 temperament interpretations, such as: |
| | * [[Mavila]], with generators around 679.8{{c}}. |
| | * [[Casablanca]], with generators around 657.8{{c}}. |
| | * [[Liese]], with generators around 632.4{{c}}. |
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| | == 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 === |
| | {{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}} |
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| | === 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}} |
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| == Intervals == | | === Ultrahard tunings === |
| Note: In TAMNAMS, a k-step interval class in antidiatonic may be called a "k-step", "k-mosstep", or "k-pelstep". 1-indexed terms such as "mos(k+1)th" are discouraged for non-diatonic mosses.
| | 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}} |
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| == Modes == | | == Modes == |
| * 6|0 LssLsss (anti-locrian)
| | {{MOS mode degrees}} |
| * 5|1 LsssLss (anti-phrygian)
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| * 4|2 sLssLss (anti-aeolian)
| | === Proposed names === |
| * 3|3 sLsssLs (anti-dorian)
| | 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. |
| * 2|4 ssLssLs (anti-mixolydian)
| | {{MOS modes |
| * 1|5 ssLsssL (anti-ionian)
| | | Mode Names= |
| * 0|6 sssLssL (anti-lydian)
| | 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 |
| | }} |
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| == Scale tree == | | == Scale tree == |
| Generator ranges:
| | {{MOS tuning spectrum |
| * Chroma-positive generator: 514.2857 cents (3\7) to 600 cents (1\2)
| | | 6/5 = [[Gravity]] ↑ |
| * Chroma-negative generator: 600 cents (1\2) to 685.7143 cents (4\7)
| | | 3/2 = [[Mavila]] |
| | | | 13/8 = Golden mavila (527.1497{{c}}) |
| {| class="wikitable center-all"
| | | 9/5 = [[Mabila]]/[[amavil]] |
| ! colspan="6" | Generator
| | | 2/1 = [[Pelog]] |
| ! Cents
| | | 5/2 = Score |
| ! L
| | | 13/5 = Unnamed golden tuning (541.3837{{c}}) |
| ! s
| | | 8/3 = [[Casablanca]] |
| ! L/s
| | | 11/3 = [[Freivald]]/[[emka]] |
| ! Comments
| | | 7/15 = [[Thuja]] |
| |-
| | | 6/1 = [[Liese]] ↓, [[triton]] ↓ |
| | 3\7 || || || || || || 514.286 || 1 || 1 || 1.000 ||
| | }} |
| |-
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| | || || || || || 16\37 || 518.919 || 6 || 5 || 1.200 || [[Gravity]]↑
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| |-
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| | || || || || 13\30 || || 520.000 || 5 || 4 || 1.250 ||
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| |-
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| | || || || || || 23\53 || 520.755 || 9 || 7 || 1.286 ||
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| |-
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| | || || || 10\23 || || || 521.739 || 4 || 3 || 1.333 ||
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| |-
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| | || || || || || 27\62 || 522.581 || 11 || 8 || 1.375 ||
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| |-
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| | || || || || 17\39 || || 523.077 || 7 || 5 || 1.400 ||
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| |-
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| | || || || || || 24\55 || 523.636 || 10 || 7 || 1.428 ||
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| |-
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| | || || 7\16 || || || || 525.000 || 3 || 2 || 1.500 || [[Mavila]] is in this region
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| |-
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| | || || || || || 25\57 || 526.316 || 11 || 7 || 1.571 ||
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| |-
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| | || || || || 18\41 || || 526.829 || 8 || 5 || 1.600 ||
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| |-
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| | || || || || || 29\66 || 527.273 || 13 || 8 || 1.625 || Golden mavila (527.1497¢)
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| |-
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| | || || || 11\25 || || || 528.000 || 5 || 3 || 1.667 ||
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| |-
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| | || || || || || 26\59 || 528.814 || 12 || 7 || 1.714 ||
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| |-
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| | || || || || 15\34 || || 529.412 || 7 || 4 || 1.750 ||
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| |-
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| | || || || || || 19\43 || 530.233 || 9 || 5 || 1.800 || [[Mabila]] / [[Amavil]]
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| |-
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| | || 4\9 || || || || || 533.333 || 2 || 1 || 2.000 || Basic antidiatonic <br>(Generators smaller than this are proper)
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| |-
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| | || || || || || 17\38 || 536.842 || 9 || 4 || 2.250 ||
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| |-
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| | || || || || 13\29 || || 537.931 || 7 || 3 || 2.333 ||
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| |-
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| | || || || || || 22\49 || 538.776 || 12 || 5 || 2.400 ||
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| |-
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| | || || || 9\20 || || || 540.000 || 5 || 2 || 2.500 || Score
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| |-
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| | || || || || || 23\51 || 541.176 || 13 || 5 || 2.600 || Unnamed golden tuning (541.3837¢)
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| |-
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| | || || || || 14\31 || || 541.935 || 8 || 3 || 2.667 || [[Casablanca]] is around here
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| |-
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| | || || || || || 19\42 || 542.857 || 11 || 4 || 2.750 ||
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| |-
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| | || || 5\11 || || || || 545.455 || 3 || 1 || 3.000 ||
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| |-
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| | || || || || || 16\35 || 548.571 || 10 || 3 || 3.333 ||
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| |-
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| | || || || || 11\24 || || 550.000 || 7 || 2 || 3.500 ||
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| |-
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| | || || || || || 17\37 || 551.351 || 11 || 3 || 3.667 || [[Freivald]] / [[emka]]
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| |-
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| | || || || 6\13 || || || 553.846 || 4 || 1 || 4.000 ||
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| |-
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| | || || || || || 13\28 || 557.143 || 9 || 2 || 4.500 ||
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| |-
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| | || || || || 7\15 || || 560.000 || 5 || 1 || 5.000 || [[Thuja]] is around here
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| |-
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| | || || || || || 8\17 || 564.706 || 6 || 1 || 6.000 || [[Liese]]↓, [[triton]]↓
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| |-
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| | 1\2 || || || || || || 600.000 || 1 || 0 || → inf ||
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| |}
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| [[Category:7-tone scales]]
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| [[Category:Antidiatonic| ]] <!-- main article --> | | [[Category:Antidiatonic| ]] <!-- main article --> |