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Introduction


Mavila is the regular temperament eliminating 135/128. As a consequence, this means that it will have a generator significantly flat of 3/2 so that 4 of them add up to a minor third. For any decent tuning of mavila, another consequence of this tempering is that we end up with an "antidiatonic" 7-note MOS, such that the LLsLLLs melodic pattern becomes inverted into the ssLsssL pattern. (see 2L 5s) Additionally, while mavila supports 5-note and 7-note MOS's like meantone, it has an additional 9-note "superdiatonic" MOS scale as well, in which the LLsLLLs melodic pattern becomes extended into the LLLsLLLLs pattern. (see 7L 2s) These correspondences can be harnessed to create an intuitive naming system for the modes of mavila[7] and mavila[9] which reference the names of the existing familiar modes of meantone[7].

How to read these charts

  • The 6|0, 5|1, 4|2 markings are an instance of Modal UDP Notation.
  • Unless otherwise specified, all transversals occur in the 2.3.5.7.11 extension of Mavila which tempers out 135/128, 36/35, 45/44, 33/32, called 11-limit Armodue temperament.
  • Additionally, "diatonic" names make use of the following abbreviations:
    • SM - Supermajor
    • M - Major
    • N - Neutral
    • m - Minor
    • sm - Subminor


2L3s Pentatonic MOS: Pelogic

4|0 - LsLss - Patet deng
3|1 - LssLs - Patet dang
2|2 - sLsLs - Patet dong
3|1 - sLssL - Patet dung
0|4 - ssLsL - Patet ding

In cyclic permutational order: Patet ding | Patet dong | Patet deng | Patet dung | Patet dang

Transversal

UDP
Imprint
(Patet) Name
1
2
3
4
5
4|0
LsLss
deng
1/1
5/4
4/3
5/3
11/6
3|1
LssLs
dang
1/1
5/4
4/3
3/2
11/6
2|2
sLsLs
dong
1/1
12/11
4/3
3/2
11/6
1|3
sLssL
dung
1/1
12/11
4/3
3/2
8/5
0|4
ssLsL
ding
1/1
12/11
6/5
3/2
8/5

"Diatonic" Names

UDP
Imprint
(Patet) Name
1
2
3
4
5
4|0
LsLss
deng
P1
M3
P4
M6
N7
3|1
LssLs
dang
P1
M3
P4
P5
N7
2|2
sLsLs
dong
P1
N2
P4
P5
N7
1|3
sLssL
dung
P1
N2
P4
P5
m6
0|4
ssLsL
ding
P1
N2
m3
P5
m6


2L5s Heptatonic MOS: Antidiatonic

6|0 - LssLsss - (Anti)Locrian

5|1 - LsssLss - (Anti)Phrygian

4|2 - sLssLss - (Anti)Aeolian ("major")

3|3 - sLsssLs - (Anti)Dorian

2|4 - ssLssLs - (Anti)Mixolydian ("harmonic minor")

1|5 - ssLsssL - (Anti)Ionian ("minor")

0|6 - sssLssL - (Anti)Lydian

In cyclic permutational order: Ionian | Dorian | Phrygian | Lydian | Mixolydian | Aeolian | Locrian

Transversal

UDP
Imprint
(Anti)Name
1
2
3
4
5
6
7
6|0
LssLsss
Locrian
1/1
8/7
5/4
4/3
14/9
5/3
11/6
5|1
LsssLss
Phrygian
1/1
8/7
5/4
4/3
3/2
5/3
11/6
4|2
sLssLss
Aeolian
1/1
12/11
5/4
4/3
3/2
5/3
11/6
3|3
sLsssLs
Dorian
1/1
12/11
5/4
4/3
3/2
8/5
11/6
2|4
ssLssLs
Mixolydian
1/1
12/11
6/5
4/3
3/2
8/5
11/6
1|5
ssLsssL
Ionian
1/1
12/11
6/5
4/3
3/2
8/5
7/4
0|6
sssLssL
Lydian
1/1
12/11
6/5
9/7
3/2
8/5
7/4

"Diatonic" Names

UDP
Imprint
(Anti)Name
1
2
3
4
5
6
7
6|0
LssLsss
Locrian
P1
SM2
M3
P4
sm6
M6
N7
5|1
LsssLss
Phrygian
P1
SM2
M3
P4
P5
M6
N7
4|2
sLssLss
Aeolian
P1
N2
M3
P4
P5
M6
N7
3|3
sLsssLs
Dorian
P1
N2
M3
P4
P5
m6
N7
2|4
ssLssLs
Mixolydian
P1
N2
m3
P4
P5
m6
N7
1|5
ssLsssL
Ionian
P1
N2
m3
P4
P5
m6
sm7
0|6
sssLssL
Lydian
P1
N2
m3
SM3
P5
m6
sm7


7L2s Nonatonic MOS: Superdiatonic

8|0 - LLLLsLLLs - (Super)Lydian

7|1 - LLLsLLLLs - (Super)Ionian

6|2 - LLLsLLLsL - (Super)Mixolydian

5|3 - LLsLLLLsL - (Super)Corinthian

4|4 - LLsLLLsLL - (Super)Olympian

3|5 - LsLLLLsLL - (Super)Dorian

2|6 - LsLLLsLLL - (Super)Aeolian

1|7 - sLLLLsLLL - (Super)Phrygian

0|8 - sLLLsLLLL - (Super)Locrian


In cyclic permutational order: Ionian | Corinthian | Dorian | Phrygian | Lydian | Mixolydian | Olympian | Aeolian | Locrian

Transversal

UDP
Imprint
(Super)Name
1
2
3
4
5
6
7
8
9
8|0
LLLLsLLLs
Lydian
1/1
12/11
6/5
9/7
7/5
3/2
8/5
7/4
21/11
7|1
LLLsLLLLs
Ionian
1/1
12/11
6/5
9/7
4/3
3/2
8/5
7/4
21/11
6|2
LLLsLLLsL
Mixolydian
1/1
12/11
6/5
9/7
4/3
3/2
8/5
7/4
11/6
5|3
LLsLLLLsL
Corinthian
1/1
12/11
6/5
5/4
4/3
3/2
8/5
7/4
11/6
4|4
LLsLLLsLL
Olympian
1/1
12/11
6/5
5/4
4/3
3/2
8/5
5/3
11/6
3|5
LsLLLLsLL
Dorian
1/1
12/11
8/7
5/4
4/3
3/2
8/5
5/3
11/6
2|6
LsLLLsLLL
Aeolian
1/1
12/11
8/7
5/4
4/3
3/2
14/9
5/3
11/6
1|7
sLLLLsLLL
Phrygian
1/1
22/21
8/7
5/4
4/3
3/2
14/9
5/3
11/6
0|8
sLLLsLLLL
Locrian
1/1
22/21
8/7
5/4
4/3
10/7
14/9
5/3
11/6

"Diatonic" Names

UDP
Imprint
(Super)Name
1
2
3
4
5
6
7
8
9
8|0
LLLLsLLLs
Lydian
P1
N2
m3
SM3
A4
P5
m6
sm7
SM7
7|1
LLLsLLLLs
Ionian
P1
N2
m3
SM3
P4
P5
m6
sm7
SM7
6|2
LLLsLLLsL
Mixolydian
P1
N2
m3
SM3
P4
P5
m6
sm7
N7
5|3
LLsLLLLsL
Corinthian
P1
N2
m3
M3
P4
P5
m6
sm7
N7
4|4
LLsLLLsLL
Olympian
P1
N2
m3
M3
P4
P5
m6
M6
N7
3|5
LsLLLLsLL
Dorian
P1
N2
SM2
M3
P4
P5
m6
M6
N7
2|6
LsLLLsLLL
Aeolian
P1
N2
SM2
M3
P4
P5
sm6
M6
N7
1|7
sLLLLsLLL
Phrygian
P1
sm2
SM2
M3
P4
P5
sm6
M6
N7
0|8
sLLLsLLLL
Locrian
P1
sm2
SM2
M3
P4
d5
sm6
M6
N7

Notes on Naming


The modes of the antidiatonic scale are simply named after the existing diatonic scale modes, but with the "Anti-" prefix (e.g. Anti-ionian, Anti-aeolian, etc). The modes of the superdiatonic scale are also named after the existing modes, but contain the "Super" prefix (e.g. Superionian, Superaeolian, etc.). The "anti" and "super" prefixes can be left in to explicitly distinguish which MOS's modes you're talking about, or can be omitted for convention.

Each superdiatonic mode contains its corresponding mode in the antidiatonic scale. Additionally, the superdiatonic modes also resemble the "shape" of their meantone diatonic counterparts. This leads to a pattern: LLLsLLLLs both resembles the meantone LLsLLLs Ionian mode, and contains the mavila ssLsssL anti-Ionian mode as well. Additionally, sLLLsLLLL resembles the diatonic sLLsLLL Locrian mode, and also contains the mavila LssLsss anti-Ionian mode. Furthermore, every mavila mode contains a tonic triad of the -opposite- quality as the corresponding diatonic mode, so that Superionian and Anti-ionian contain a minor triad, and Superphrygian and Antiphrygian contain a major triad.

Since there are only seven diatonic modes, two of the superdiatonic modes need additional names and cannot reference any mode of the diatonic scale. These two modes present themselves as "mixed" modes, which begin with the LLs tetrachord, and so contain both the ~300 cent minor third and the ~375 cent major third (and hence both minor and major triads). These are the only two modes to exhibit this behavior. They're interspersed on the rotational continuum between Ionian and Dorian, and Mixolydian and Aeolian.

As were the original modes named after regions of ancient Greece, so are these new superdiatonic extensions. The one between Ionian and Dorian is called Corinthian, after the Greek island of Corinth, set up so that the Ionian -> Corinthian -> Dorian cyclic sequence will resemble the columns of ancient Greek architecture. The mode cyclically placed between Mixolydian and Aeolian, which is the symmetrical LLsLLLsLL scale, has a number of noteworthy theoretical properties, in that it contains every modal rotation of mavila[5], and hence the entire mavila-tempered 5-limit tonality diamond; it was given the name of Olympian to match its unique status in this regard.