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{{Infobox MOS
{{Infobox MOS}}
| Name = mavila, superdiatonic
| Periods = 1
| nLargeSteps = 7
| nSmallSteps = 2
| Equalized = 5
| Paucitonic = 4
| Pattern = LLLsLLLLs
}}


'''7L 2s''', '''mavila superdiatonic''' or '''superdiatonic''' refers to the structure of octave-equivalent [[MOS]] scales with generators ranging from 4\7 (four degrees of [[7edo]] = 685.71¢) to 5\9 (five degrees of [[9edo]] = 666.67¢). In the case of 9edo, L and s are the same size; in the case of 7edo, s becomes so small it disappears (and all that remains are the seven equal L's).
{{MOS intro}}
Scales of this form are strongly associated with [[Armodue theory]], as applied to septimal mavila and Hornbostel temperaments. [[Trismegistus]] is also a usable temperament.
== Name ==
The [[TAMNAMS]] name for this pattern is '''armotonic''', in reference to Armodue theory. '''Superdiatonic''' is also in use.


From a regular temperament perspective (i.e. approximating [[low JI]] intervals with stacks of a single generator), this MOS pattern is essentially synonymous to [[mavila]]. If you're looking for scales that are highly accurate to low JI, there are much better scale patterns to look at. However, if 678 cents is an acceptable fifth to you, then [[Pelogic_family|mavila]] is an important [[harmonic entropy]] minimum here.
== Scale properties ==
{{TAMNAMS use}}


These scales are strongly associated with [[mavila]] temperament, which can be divided into two tuning ranges:
=== Intervals ===
* the [[Armodue|Armodue]] project/system and its associated [[armodue]] temperament, with fifths sharper than 5\9 (666.7¢) and flatter than 9\16 (675¢). The minor mavilaseventh approximates 7/4 in these tunings.
{{MOS intervals}}
* Hornbostel temperament, with fifths sharper than 9\16 (675¢) and flatter than 4\7 (685.71¢).


Some high JI approximations of the generator: 31/21, 34/23, 65/44, 71/48, 99/67, 105/71, 108/73, 133/90, 145/98, 176/119, 250/169. These could be used to guide the construction of neji versions of superdiatonic scales or edos.
=== Generator chain ===
== Notation ==
{{MOS genchain}}
== Scale tree ==
{| class="wikitable"
|-
! colspan="5" | Generator
! | Generator size (cents)
! | L/s
! | Comments
|-
| | 4\[[7edo|7]]
| |
| |
| |
| |
| | 685.714
| | 1/0
| |
|-
| |
| |
| |
| |
| | 21\37
| | 681.08
| | 5/1
| |
|-
| |
| |
| |
| | 17\30
| |
| | 680
| | 4/1
| |
|-
| |
| |
| | 13\23
| |
| |
| | 678.261
| | 3/1
| |
|-
| |
| |
| |
| | 22\39
| |
| | 676.923
| | 5/2
|-
| |
| | 9\16
| |
| |
| |
| | 675
| | 2/1
| | Boundary of propriety; smaller generators are strictly proper
|-
| |
| |
| | 23\41
| |
| |
| | 673.171
| | 5/3
| |
|-
| |
| |
| |
| |
| |
| | 672.85
| | φ/1
| | Golden mavila
|-
| |
| |
| | 14\25
| |
| |
| | 672
| | 3/2
| |
|-
| |
| |
| |
| | 19\34
| |
| | 670.588
| | 4/3
| |
|-
| |
| |
| |
| |
| | 24\43
| | 669.767
| | 5/4
| |
|-
| | 5\[[9edo|9]]
| |
| |
| |
| |
| | 666.667
| | 1/1
| |
|}
== Tunings ==
Much like meantone temperament, mavila is supported by several low-numbered EDOs, which will basically be the same size as the MOS's listed above.


The basic superdiatonic EDO is 16-EDO, which is probably the most common tuning for mavila temperament. This can be thought of as the first EDO offering the potential for chromatic mavila harmony, similar to 12-EDO for meantone. This is also the usual setting for the aforementioned Armodue theory, although the Armodue theory can easily be extended to larger mavila scales such as mavila[23]. The fifth is 675 cents.
=== Modes ===
{{MOS mode degrees}}


The next EDO supporting mavila is 23-EDO, which is the second-most common tuning for mavila temperament, used frequently by Igliashon Jones in his Cryptic Ruse albums. The fifth is 678 cents, and as a result the harmonic properties are slightly better than 16-EDO, although still fairly inharmonic compared to meantone. The anti-diatonic scale is more "quasi-equal" in this tuning than in 16-EDO.
=== Proposed mode names ===
The Ad- mode names proposed by [[groundfault]] have the feature of matching up the middle 7 modes with the antidiatonic mode names in the generator arc.
{{MOS modes
| Table Headers=
Super- Mode Names $
Ad- Mode Names (ground) $
| Table Entries=
Superlydian $
TBD $
Superionian $
Adlocrian $
Supermixolydian $
Adphrygian $
Supercorinthian $
Adaeolian $
Superolympian $
Addorian $
Superdorian $
Admixolydian $
Superaeolian $
Adionian $
Superphrygian $
Adlydian $
Superlocrian $
TBD
}}


25-EDO also supports mavila, although the tuning is 672 cents and hence very flat, even flatter than 16-EDO.
== Note names==
== Intervals ==
7L 2s, when viewed under Armodue theory, can be notated using Armodue notation.


== Modes ==
== Theory ==
From brightest to darkest, the superdiatonic modes are:
=== Temperament interpretations ===
{| class="wikitable"
[[Pelogic family#Mavila|Mavila]] is an important harmonic entropy minimum here, insofar as 670-680{{c}} can be considered a fifth. Other temperaments include septimal mavila, hornbostel, and trismegistus.
|-
| | LLLLsLLLs - (Super)Lydian
| |
|-
| | LLLsLLLLs - (Super)Ionian
| |
|-
| | LLLsLLLsL - (Super)Mixolydian
| |
|-
| | LLsLLLLsL - (Super)Corinthian
| |
|-
| | LLsLLLsLL - (Super)Olympian
| | [[File:MavilaOlympian16edo.mp3]]
|-
| | LsLLLLsLL - (Super)Dorian
| |
|-
| | LsLLLsLLL - (Super)Aeolian
| |
|-
| | sLLLLsLLL - (Super)Phrygian
| |
|-
| | sLLLsLLLL - (Super)Locrian
| | [[File:MavilaSuperdiatonic16edo.mp3]]
|}


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.
== Scale tree ==
 
{{MOS tuning spectrum
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.
| 1/1 = Near exact-7/6 [[Pelogic_family#Armodue|Armodue]]
 
| 4/3 = Near exact-20/17 [[Pentagoth]]
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.
| 7/5 = Near exact-5/4 [[Mavila]]
 
| 3/2 = Near exact-13/11 Pentagoth
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.
| 7/4 = Near exact-7/4 [[Pelogic_family#Armodue|Armodue]]
=== Table of modes ===
| 10/3 = Near exact-6/5 [[Mavila]]
== Chords and extended harmony ==
| 6/1 = [[Gravity]] ↓
 
}}
== Primodal theory ==
=== Neji versions of superdiatonic modes ===
* 40:48:52:54:59:64:70:77:80 Pental Superionian
=== 16nejis ===
=== 23nejis ===
=== 25nejis ===


[[Category:Theory]]
[[Category:9-tone scales]]
[[Category:Scales]]
[[Category:MOS scales]]
[[Category:Abstract MOS patterns]]
[[Category:Mavila]]
[[Category:Mavila]]
[[Category:Superdiatonic]]

Latest revision as of 06:24, 30 July 2025

↖ 6L 1s ↑ 7L 1s 8L 1s ↗
← 6L 2s 7L 2s 8L 2s →
↙ 6L 3s ↓ 7L 3s 8L 3s ↘ 
┌╥╥╥╥┬╥╥╥┬┐
│║║║║│║║║││
│││││││││││
└┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLLLsLLLs
sLLLsLLLL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 5\9 to 4\7 (666.7 ¢ to 685.7 ¢)
Dark 3\7 to 4\9 (514.3 ¢ to 533.3 ¢)
TAMNAMS information
Name armotonic
Prefix arm-
Abbrev. arm
Related MOS scales
Parent 2L 5s
Sister 2L 7s
Daughters 9L 7s, 7L 9s
Neutralized 5L 4s
2-Flought 16L 2s, 7L 11s
Equal tunings
Equalized (L:s = 1:1) 5\9 (666.7 ¢)
Supersoft (L:s = 4:3) 19\34 (670.6 ¢)
Soft (L:s = 3:2) 14\25 (672.0 ¢)
Semisoft (L:s = 5:3) 23\41 (673.2 ¢)
Basic (L:s = 2:1) 9\16 (675.0 ¢)
Semihard (L:s = 5:2) 22\39 (676.9 ¢)
Hard (L:s = 3:1) 13\23 (678.3 ¢)
Superhard (L:s = 4:1) 17\30 (680.0 ¢)
Collapsed (L:s = 1:0) 4\7 (685.7 ¢)

7L 2s, named armotonic in TAMNAMS, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 7 large steps and 2 small steps, repeating every octave. Generators that produce this scale range from 666.7 ¢ to 685.7 ¢, or from 514.3 ¢ to 533.3 ¢. Scales of this form are strongly associated with Armodue theory, as applied to septimal mavila and Hornbostel temperaments. Trismegistus is also a usable temperament.

Name

The TAMNAMS name for this pattern is armotonic, in reference to Armodue theory. Superdiatonic is also in use.

Scale properties

This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for interval regions.

Intervals

Intervals of 7L 2s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-armstep Perfect 0-armstep P0arms 0 0.0 ¢
1-armstep Minor 1-armstep m1arms s 0.0 ¢ to 133.3 ¢
Major 1-armstep M1arms L 133.3 ¢ to 171.4 ¢
2-armstep Minor 2-armstep m2arms L + s 171.4 ¢ to 266.7 ¢
Major 2-armstep M2arms 2L 266.7 ¢ to 342.9 ¢
3-armstep Minor 3-armstep m3arms 2L + s 342.9 ¢ to 400.0 ¢
Major 3-armstep M3arms 3L 400.0 ¢ to 514.3 ¢
4-armstep Perfect 4-armstep P4arms 3L + s 514.3 ¢ to 533.3 ¢
Augmented 4-armstep A4arms 4L 533.3 ¢ to 685.7 ¢
5-armstep Diminished 5-armstep d5arms 3L + 2s 514.3 ¢ to 666.7 ¢
Perfect 5-armstep P5arms 4L + s 666.7 ¢ to 685.7 ¢
6-armstep Minor 6-armstep m6arms 4L + 2s 685.7 ¢ to 800.0 ¢
Major 6-armstep M6arms 5L + s 800.0 ¢ to 857.1 ¢
7-armstep Minor 7-armstep m7arms 5L + 2s 857.1 ¢ to 933.3 ¢
Major 7-armstep M7arms 6L + s 933.3 ¢ to 1028.6 ¢
8-armstep Minor 8-armstep m8arms 6L + 2s 1028.6 ¢ to 1066.7 ¢
Major 8-armstep M8arms 7L + s 1066.7 ¢ to 1200.0 ¢
9-armstep Perfect 9-armstep P9arms 7L + 2s 1200.0 ¢

Generator chain

Generator chain of 7L 2s
Bright gens Scale degree Abbrev.
15 Augmented 3-armdegree A3armd
14 Augmented 7-armdegree A7armd
13 Augmented 2-armdegree A2armd
12 Augmented 6-armdegree A6armd
11 Augmented 1-armdegree A1armd
10 Augmented 5-armdegree A5armd
9 Augmented 0-armdegree A0armd
8 Augmented 4-armdegree A4armd
7 Major 8-armdegree M8armd
6 Major 3-armdegree M3armd
5 Major 7-armdegree M7armd
4 Major 2-armdegree M2armd
3 Major 6-armdegree M6armd
2 Major 1-armdegree M1armd
1 Perfect 5-armdegree P5armd
0 Perfect 0-armdegree
Perfect 9-armdegree		 P0armd
P9armd
−1 Perfect 4-armdegree P4armd
−2 Minor 8-armdegree m8armd
−3 Minor 3-armdegree m3armd
−4 Minor 7-armdegree m7armd
−5 Minor 2-armdegree m2armd
−6 Minor 6-armdegree m6armd
−7 Minor 1-armdegree m1armd
−8 Diminished 5-armdegree d5armd
−9 Diminished 9-armdegree d9armd
−10 Diminished 4-armdegree d4armd
−11 Diminished 8-armdegree d8armd
−12 Diminished 3-armdegree d3armd
−13 Diminished 7-armdegree d7armd
−14 Diminished 2-armdegree d2armd
−15 Diminished 6-armdegree d6armd

Modes

Scale degrees of the modes of 7L 2s
UDP Cyclic
order 		Step
pattern 		Scale degree (armdegree)
0 1 2 3 4 5 6 7 8 9
8|0 1 LLLLsLLLs Perf. Maj. Maj. Maj. Aug. Perf. Maj. Maj. Maj. Perf.
7|1 6 LLLsLLLLs Perf. Maj. Maj. Maj. Perf. Perf. Maj. Maj. Maj. Perf.
6|2 2 LLLsLLLsL Perf. Maj. Maj. Maj. Perf. Perf. Maj. Maj. Min. Perf.
5|3 7 LLsLLLLsL Perf. Maj. Maj. Min. Perf. Perf. Maj. Maj. Min. Perf.
4|4 3 LLsLLLsLL Perf. Maj. Maj. Min. Perf. Perf. Maj. Min. Min. Perf.
3|5 8 LsLLLLsLL Perf. Maj. Min. Min. Perf. Perf. Maj. Min. Min. Perf.
2|6 4 LsLLLsLLL Perf. Maj. Min. Min. Perf. Perf. Min. Min. Min. Perf.
1|7 9 sLLLLsLLL Perf. Min. Min. Min. Perf. Perf. Min. Min. Min. Perf.
0|8 5 sLLLsLLLL Perf. Min. Min. Min. Perf. Dim. Min. Min. Min. Perf.

Proposed mode names

The Ad- mode names proposed by groundfault have the feature of matching up the middle 7 modes with the antidiatonic mode names in the generator arc.

Modes of 7L 2s
UDP Cyclic
order		 Step
pattern		 Super- Mode Names Ad- Mode Names (ground)
8|0 1 LLLLsLLLs Superlydian TBD
7|1 6 LLLsLLLLs Superionian Adlocrian
6|2 2 LLLsLLLsL Supermixolydian Adphrygian
5|3 7 LLsLLLLsL Supercorinthian Adaeolian
4|4 3 LLsLLLsLL Superolympian Addorian
3|5 8 LsLLLLsLL Superdorian Admixolydian
2|6 4 LsLLLsLLL Superaeolian Adionian
1|7 9 sLLLLsLLL Superphrygian Adlydian
0|8 5 sLLLsLLLL Superlocrian TBD

Note names

7L 2s, when viewed under Armodue theory, can be notated using Armodue notation.

Theory

Temperament interpretations

Mavila is an important harmonic entropy minimum here, insofar as 670-680 ¢ can be considered a fifth. Other temperaments include septimal mavila, hornbostel, and trismegistus.

Scale tree

Scale tree and tuning spectrum of 7L 2s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
5\9 666.667 533.333 1:1 1.000 Equalized 7L 2s
Near exact-7/6 Armodue
29\52 669.231 530.769 6:5 1.200
24\43 669.767 530.233 5:4 1.250
43\77 670.130 529.870 9:7 1.286
19\34 670.588 529.412 4:3 1.333 Supersoft 7L 2s
Near exact-20/17 Pentagoth
52\93 670.968 529.032 11:8 1.375
33\59 671.186 528.814 7:5 1.400 Near exact-5/4 Mavila
47\84 671.429 528.571 10:7 1.429
14\25 672.000 528.000 3:2 1.500 Soft 7L 2s
Near exact-13/11 Pentagoth
51\91 672.527 527.473 11:7 1.571
37\66 672.727 527.273 8:5 1.600
60\107 672.897 527.103 13:8 1.625
23\41 673.171 526.829 5:3 1.667 Semisoft 7L 2s
55\98 673.469 526.531 12:7 1.714
32\57 673.684 526.316 7:4 1.750 Near exact-7/4 Armodue
41\73 673.973 526.027 9:5 1.800
9\16 675.000 525.000 2:1 2.000 Basic 7L 2s
Scales with tunings softer than this are proper
40\71 676.056 523.944 9:4 2.250
31\55 676.364 523.636 7:3 2.333
53\94 676.596 523.404 12:5 2.400
22\39 676.923 523.077 5:2 2.500 Semihard 7L 2s
57\101 677.228 522.772 13:5 2.600
35\62 677.419 522.581 8:3 2.667
48\85 677.647 522.353 11:4 2.750
13\23 678.261 521.739 3:1 3.000 Hard 7L 2s
43\76 678.947 521.053 10:3 3.333 Near exact-6/5 Mavila
30\53 679.245 520.755 7:2 3.500
47\83 679.518 520.482 11:3 3.667
17\30 680.000 520.000 4:1 4.000 Superhard 7L 2s
38\67 680.597 519.403 9:2 4.500
21\37 681.081 518.919 5:1 5.000
25\44 681.818 518.182 6:1 6.000 Gravity ↓
4\7 685.714 514.286 1:0 → ∞ Collapsed 7L 2s
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