Xenharmonic Wiki

2L 5s: Difference between revisions

← Older edit
VisualWikitext
Ganaram inukshuk (talk | contribs)
autopatrolled, emailconfirmed
4,810 edits
m →Theory: Minor rewording
No edit summary
 
(30 intermediate revisions by 8 users not shown)
Line 1: Line 1:
{{Infobox MOS}}
{{Infobox MOS}}
{{MOS intro}}
{{MOS intro}}
==Name==
 
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.
 
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.
 
== 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.
==Notation==
:''This article assumes [[TAMNAMS]] for naming step ratios, intervals, and scale degrees, and [[Diamond-mos notation|diamond-MOS notation]] for note names.''<!-- May be worth adding other notation schemes, such as that where standard notation is read is antidiatonic. -->
===Intervals and degrees===
Names for this scale's intervals (mossteps) and scale degrees (mosdegrees) are based on the number of large and small steps from the root, starting at 0 (0-mosstep and 0-mosdegree) for the unison, per TAMNAMS. Ordinal names, such as mos-1st for the unison, are discouraged for non-diatonic MOS scales.


Being a moment-of-symmetry scale, every [[interval class]] of 2L 5s, except for the unison and octave, has two [[Interval variety|varieties]] – large and small – whose [[Interval quality|relative qualities]] are denoted as major or minor, or augmented, perfect, and diminished for the generators.
The scale is also often called peletonic or '''peltonic''', based on its prefix.
 
== Intervals ==
{{TAMNAMS use}}
{{MOS intervals}}
{{MOS intervals}}
===Note names ===
For this article, note names are based on diamond-MOS notation, where the naturals JKLMNOP are applied to the step pattern sLsssLs and the accidentals & (pronounced "am" or "amp") and @ (pronounced "at") are used to represent sharps and flats respectively. Thus, the basic gamut for 2L 5s is the following:


{{MOS gamut}}
== Notation ==
==Theory==
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.  
Antidiatonic is similar to diatonic (5L 2s) 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" (or 4-mosstep) gets, the less the scale resembles diatonic. Additionally, there are temperaments associated with this MOS, such as [[score]], that do not have intervals that resemble a diatonic 5th, flattened or otherwise.
 
{{Mavila|Tuning=2L 5s}}
 
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}}.
 
== 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&nbsp;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}}.


===Low harmonic entropy scales===
== Tuning ranges ==
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¢).
=== Simple tunings ===
The simplest tunings are those with step ratios 2:1, 3:1, and 3:2, producing [[9edo]], [[11edo]], and [[16edo]].
{{MOS tunings}}


===Temperament interpretations===
=== Soft-of-basic tunings ===
2L 5s has several rank-2 temperament interpretations, such as:
{{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}}


*[[Chromatic pairs#Score|Score]], with generators around 540.1¢.
=== Hypohard tunings ===
*[[Liese]], with generators around 632.4¢.
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.
*[[Mavila]], with generators around 679.8¢.
{{MOS tunings|Step Ratios=Hypohard}}


==Modes==
=== Ultrahard tunings ===
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.
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}}


{{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}}
== Modes ==
{{MOS mode degrees}}


==Scale tree==
=== Proposed names ===
Generator ranges:  
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.
* Chroma-positive generator: 514.2857 cents (3\7) to 600 cents (1\2)
{{MOS modes
*Chroma-negative generator: 600 cents (1\2) to 685.7143 cents (4\7)
| 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
}}


{| class="wikitable center-all"
== Scale tree ==
! colspan="6" |Generator
{{MOS tuning spectrum
!Cents
| 6/5 = [[Gravity]]&nbsp;↑
!L
| 3/2 = [[Mavila]]
!s
| 13/8 = Golden mavila (527.1497{{c}})
!L/s
| 9/5 = [[Mabila]]/[[amavil]]
!Comments
| 2/1 = [[Pelog]]
|-
| 5/2 = Score
|3\7|| || || || || || 514.286||1||1||1.000||
| 13/5 = Unnamed golden tuning (541.3837{{c}})
|-
| 8/3 = [[Casablanca]]
| || || || || ||16\37||518.919||6||5||1.200||[[Gravity]]↑
| 11/3 = [[Freivald]]/[[emka]]
|-
| 7/15 = [[Thuja]]
| || || || || 13\30|| ||520.000||5 || 4||1.250||
| 6/1 = [[Liese]]&nbsp;↓, [[triton]]&nbsp;↓
|-
}}
| || || || || ||23\53 ||520.755||9||7||1.286||
|-
| || || ||10\23|| || ||521.739||4||3||1.333 ||
|-
| || || || || ||27\62 ||522.581||11||8||1.375||
|-
| || || ||  ||17\39|| ||523.077 ||7 ||5||1.400 ||
|-
| || || || || ||24\55 || 523.636||10 || 7||1.428||
|-
|  ||  ||7\16 ||  ||  ||  || 525.000|| 3|| 2||1.500||[[Mavila]] is in this region
|-
| || || || || ||25\57|| 526.316 ||11||7||1.571||
|-
| || || || ||18\41|| ||526.829 ||8|| 5|| 1.600||
|-
|  ||  || || ||  || 29\66||527.273||13||8 || 1.625 ||Golden mavila (527.1497¢)
|-
|  ||  ||  || 11\25|| || ||528.000||5 || 3|| 1.667 ||
|-
| || || ||  ||  || 26\59||528.814||12||7||1.714 ||
|-
| || || || ||15\34 ||  || 529.412 ||7|| 4||1.750||
|-
| || ||  ||  || ||19\43||530.233||9||5 || 1.800 ||[[Mabila]] / [[Amavil]]
|-
| ||4\9|| || || || ||533.333||2|| 1||2.000 || Basic antidiatonic <br>(Generators smaller than this are proper)
|-
| || || || ||  || 17\38||536.842||9||4||2.250||
|-
| || || || ||13\29|| ||537.931 ||7||3||2.333||
|-
| || || || || ||22\49||538.776||12 || 5||2.400||
|-
| ||  ||  ||9\20|| || ||540.000 || 5|| 2|| 2.500||Score
|-
| || || || || ||23\51||541.176||13||5||2.600 ||Unnamed golden tuning (541.3837¢)
|-
|  || ||  ||  || 14\31|| ||541.935||8||3||2.667 ||[[Casablanca]] is around here
|-
| ||  || || || ||19\42 || 542.857||11|| 4|| 2.750 ||
|-
| || ||5\11|| || || ||545.455||3||1||3.000||
|-
|  || || || || || 16\35||548.571 ||10||3||3.333||
|-
| || || || ||11\24|| ||550.000||7||2||3.500 ||
|-
| ||  ||  || || ||17\37||551.351||11||3||3.667 ||[[Freivald]] / [[emka]]
|-
|  || || ||6\13|| || ||553.846||4||1||4.000||
|-
|  ||  || ||  ||  ||13\28|| 557.143||9||2||4.500 ||
|-
| || || || ||7\15|| ||560.000||5|| 1||5.000 ||[[Thuja]] is around here
|-
| || || || || ||8\17||564.706|| 6|| 1||6.000||[[Liese]]↓, [[triton]]↓
|-
|1\2|| || || || || ||600.000 ||1||0||→ inf||
|}


[[Category:7-tone scales]]
[[Category:Antidiatonic| ]] <!-- main article -->
[[Category:Antidiatonic| ]] <!-- main article -->
Retrieved from "https://en.xen.wiki/w/2L_5s"