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{{User:IlL/Template:RTT restriction}}
{{Infobox MOS}}
{{Infobox MOS
{{MOS intro}}
| Name = antidiatonic
 
| Periods = 1
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.
| nLargeSteps = 2
 
| nSmallSteps = 5
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.
| Equalized = 3
 
| Paucitonic = 1
== Name ==
| Pattern = ssLsssL
[[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.
| Neutral = 4L 3s
 
}}
The scale is also often called peletonic or '''peltonic''', based on its prefix.


'''2L 5s''' or '''antidiatonic''' refers to the structure of octave-equivalent [[MOS]] scales with generators ranging from 3\7 (3 degrees of [[7edo|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).
== Intervals ==
{{TAMNAMS use}}
{{MOS intervals}}


While antidiatonic is closely associated with [[mavila]], 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.
== Notation ==
== Notation ==
Diamond MOS notation, &/@ = raise and lower by one chroma. We'll write this using CDEFGABC is C Antiionian (ssLsssL); C = 261.6256 Hz. 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.  


== Scale tree ==
{{Mavila|Tuning=2L 5s}}
{| class="wikitable"
 
|-
Under harmonic antidiatonic notation, the basic gamut (for D anti-dorian) is the following: {{MOS gamut|Notation=DEFGABC; b; #|Step Ratio=2/1}}.
! colspan="7" | generator in degrees of an [[EDO|edo]]
! | generator in cents
! | tetrachord
! | L in cents
! | s in cents
! | L to s ratio
! | comments
|-
| style="text-align:center;" | 3\7
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| |
| |
| style="text-align:center;" | 514.3
| style="text-align:center;" | 1 1 1
| style="text-align:center;" | 171.4
| style="text-align:center;" | 171.4
| style="text-align:center;" | 1.00
| style="text-align:center;" |
|-
|
|
|
|
|
|
|19\44
|518.2
|6 6 7
|190.9
|163.6
|1.17
|
|-
|
|
|
|
|
|16\37
|
|518.9
|5 5 6
|194.6
|162.2
|1.20
|
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 13\30
| |
| |
| style="text-align:center;" | 520.0
| style="text-align:center;" | 4 4 5
| style="text-align:center;" | 200.0
| style="text-align:center;" | 160.0
| style="text-align:center;" | 1.25
| style="text-align:center;" | Mavila extends from here...
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 10\23
| style="text-align:center;" |
| |
| |
| style="text-align:center;" | 521.7
| style="text-align:center;" | 3 3 4
| style="text-align:center;" | 208.7
| style="text-align:center;" | 156.5
| style="text-align:center;" | 1.33
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 17\39
| |
| |
| style="text-align:center;" | 523.1
| style="text-align:center;" | 5 5 7
| style="text-align:center;" | 215.4
| style="text-align:center;" | 153.8
| style="text-align:center;" | 1.40
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 7\16
| style="text-align:center;" |
| style="text-align:center;" |
| |
| |
| style="text-align:center;" | 525.0
| style="text-align:center;" | 2 2 3
| style="text-align:center;" | 225.0
| style="text-align:center;" | 150.0
| style="text-align:center;" | 1.50
| style="text-align:center;" | Mavila in Armodue


Optimum rank range (L/s=3/2)
Under melodic antidiatonic notation, the basic gamut is the following: {{MOS gamut|Notation=DEFGABC; #; b|Step Ratio=2/1}}.
|-
| |
| |
| |
| |
| |
| |
| |
| style="text-align:center;" | 526.3
| style="text-align:center;" | <span style="display: block; text-align: center;">2 2 pi</span>
| style="text-align:center;" | 231.5
| style="text-align:center;" | 147.4
| style="text-align:center;" | <span style="display: block; text-align: center;">pi/2</span>
| |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 18\41
| |
| |
| style="text-align:center;" | 526.8
| style="text-align:center;" | 5 5 8
| style="text-align:center;" | 234.1
| style="text-align:center;" | 146.3
| style="text-align:center;" | 1.60
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| |
| style="text-align:center;" | 1200*5/(13-phi)
| style="text-align:center;" | 1 1 phi
| style="text-align:center;" | 235.7
| style="text-align:center;" | 145.7
| style="text-align:center;" | phi
| style="text-align:center;" | Golden mavila
|-
| |
| |
| |
| |
| |
| | 29\66
| |
| style="text-align:center;" | 527.3
| style="text-align:center;" | 8 8 13
| style="text-align:center;" | 236.4
| style="text-align:center;" | 145.5
| style="text-align:center;" | 1.625
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 11\25
| style="text-align:center;" |
| |
| |
| style="text-align:center;" | 528.0
| style="text-align:center;" | 3 3 5
| style="text-align:center;" | 240.0
| style="text-align:center;" | 144.0
| style="text-align:center;" | 1.67
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| |
| style="text-align:center;" | 529.1
| style="text-align:center;" | <span style="background-color: #ffffff;"><span style="line-height: 1.5;">1 1 </span>√3 </span>
| style="text-align:center;" | 245.6
| style="text-align:center;" | 141.8
| style="text-align:center;" | <span style="background-color: #ffffff; display: block; text-align: center;">√3</span>
| |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 15\34
| |
| |
| style="text-align:center;" | 529.4
| style="text-align:center;" | 4 4 7
| style="text-align:center;" | 247.1
| style="text-align:center;" | 141.2
| style="text-align:center;" | 1.75
| style="text-align:center;" | ...to somewhere around here
|-
| style="text-align:center;" |
| style="text-align:center;" | 4\9
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| |
| |
| style="text-align:center;" | 533.3
| style="text-align:center;" | 1 1 2
| style="text-align:center;" | 266.7
| style="text-align:center;" | 133.3
| style="text-align:center;" | 2.00
| style="text-align:center;" | Boundary of propriety (generators


smaller than this are proper)
== Theory ==
|-
=== Low harmonic entropy scales ===
| style="text-align:center;" |
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}}).
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 13\29
| |
| |
| style="text-align:center;" | 537.9
| style="text-align:center;" | 3 3 7
| style="text-align:center;" | 289.7
| style="text-align:center;" | 124.1
| style="text-align:center;" | 2.33
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 9\20
| style="text-align:center;" |
| |
| |
| style="text-align:center;" | 540.0
| style="text-align:center;" | 2 2 5
| style="text-align:center;" | 300.0
| style="text-align:center;" | 120.0
| style="text-align:center;" | 2.50
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| |
| style="text-align:center;" | 541.4
| style="text-align:center;" | <span style="display: block; text-align: center;">1 1 phi+1</span>
| style="text-align:center;" | 306.9
| style="text-align:center;" | 117.2
| style="text-align:center;" | <span style="display: block; text-align: center;">1 1 phi+1</span>
| |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 14\31
| |
| |
| style="text-align:center;" | 541.9
| style="text-align:center;" | 3 3 8
| style="text-align:center;" | 309.7
| style="text-align:center;" | 116.1
| style="text-align:center;" | 2.66
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |
| |
| style="text-align:center;" | 542<span style="line-height: 1.5;">.5</span>
| style="text-align:center;" | 1 1 e
| style="text-align:center;" | 321.55
| style="text-align:center;" | 115.0
| style="text-align:center;" | e
| style="text-align:center;" | L/s = e
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 5\11
| style="text-align:center;" |
| style="text-align:center;" |
| |
| |
| style="text-align:center;" | 545.5
| style="text-align:center;" | 1 1 3
| style="text-align:center;" | 327.3
| style="text-align:center;" | 109.1
| style="text-align:center;" | 3.00
| style="text-align:center;" | L/s = 3
|-
| |
| |
| |
| |
| |
| |
| |
| style="text-align:center;" | 546.8
| style="text-align:center;" | 1 1 pi
| style="text-align:center;" | 334.1
| style="text-align:center;" | 106.35
| style="text-align:center;" | pi
| style="text-align:center;" | <span style="display: block; text-align: center;">L/s = pi</span>
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 11\24
| |
| |
| style="text-align:center;" | 550.0
| style="text-align:center;" | 2 2 7
| style="text-align:center;" | 350.0
| style="text-align:center;" | 100.0
| style="text-align:center;" | 3.50
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 6\13
| style="text-align:center;" |
| |
| |
| style="text-align:center;" | 553.8
| style="text-align:center;" | 1 1 4
| style="text-align:center;" | 369.2
| style="text-align:center;" | 92.3
| style="text-align:center;" | 4.00
| style="text-align:center;" | Thuja is optimal around here


L/s = 4
=== Temperament interpretations ===
|-
2L&nbsp;5s has several rank-2 temperament interpretations, such as:
| style="text-align:center;" |
* [[Mavila]], with generators around 679.8{{c}}.
| style="text-align:center;" |
* [[Casablanca]], with generators around 657.8{{c}}.
| style="text-align:center;" |
* [[Liese]], with generators around 632.4{{c}}.
| style="text-align:center;" |
| style="text-align:center;" | 7\15
| |
| |
| style="text-align:center;" | 560.0
| style="text-align:center;" | 1 1 5
| style="text-align:center;" | 400.0
| style="text-align:center;" | 80.0
| style="text-align:center;" | 5.00
| style="text-align:center;" | ie. (11/8)^5 = 5/1
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 8\17
| style="text-align:center;" |
| style="text-align:center;" | 564.7
| style="text-align:center;" | 1 1 6
| style="text-align:center;" | 423.5
| style="text-align:center;" | 70.6
| style="text-align:center;" | 6.00
| style="text-align:center;" |
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 9\19
| style="text-align:center;" | 568.4
| style="text-align:center;" | 1 1 7
| style="text-align:center;" | 442.1
| style="text-align:center;" | 63.2
| style="text-align:center;" | 7.00
| style="text-align:center;" | Liese/Triton is around here
|-
| style="text-align:center;" | 1\2
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| |
| |
| style="text-align:center;" | 600.0
| style="text-align:center;" | 0 0 1
| style="text-align:center;" | 600.0
| style="text-align:center;" | 0
| style="text-align:center;" | —
| style="text-align:center;" |
|}


== Musical Examples ==
== Tuning ranges ==
Mike Battaglia has "translated" several common practice pieces into [[mavila]] antidiatonic by using Graham Breed's Lilypond code to tune the generators flat. Musical examples are provided in 9-EDO, 16-EDO, 23-EDO, and 25-EDO, for comparison. Note that the melodic and/or intonational properties differ slightly for each tuning.
=== Simple tunings ===
The simplest tunings are those with step ratios 2:1, 3:1, and 3:2, producing [[9edo]], [[11edo]], and [[16edo]].
{{MOS tunings}}


9-EDO: <soundcloud>https://soundcloud.com/mikebattagliaexperiments/sets/the-mavila-experiments-9-edo</soundcloud>
=== 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}}


16-EDO: <soundcloud>https://soundcloud.com/mikebattagliaexperiments/sets/the-mavila-experiments-16-edo</soundcloud>
=== 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}}


23-EDO: <soundcloud>https://soundcloud.com/mikebattagliaexperiments/sets/the-mavila-experiments</soundcloud>
=== 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 tunings|Step Ratios=4/1; 5/1; 6/1; 7/1}}


25-EDO: <soundcloud>https://soundcloud.com/mikebattagliaexperiments/sets/the-mavila-experiments-25-edo</soundcloud>
== Modes ==
{{MOS mode degrees}}


=== 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
}}
== Scale tree ==
{{MOS tuning spectrum
| 6/5 = [[Gravity]]&nbsp;↑
| 3/2 = [[Mavila]]
| 13/8 = Golden mavila (527.1497{{c}})
| 9/5 = [[Mabila]]/[[amavil]]
| 2/1 = [[Pelog]]
| 5/2 = Score
| 13/5 = Unnamed golden tuning (541.3837{{c}})
| 8/3 = [[Casablanca]]
| 11/3 = [[Freivald]]/[[emka]]
| 7/15 = [[Thuja]]
| 6/1 = [[Liese]]&nbsp;↓, [[triton]]&nbsp;↓
}}


[[Category:Scales]]
[[Category:Antidiatonic| ]] <!-- main article -->
[[Category:MOS scales]]
[[Category:Abstract MOS patterns]]
Retrieved from "https://en.xen.wiki/w/2L_5s"