7L 2s: Difference between revisions

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{{MOS intro}}
{{MOS intro}}
Scales of this form are strongly associated with [[Armodue theory]], as applied to septimal mavila and Hornbostel temperaments.
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 ==
== Name ==
The [[TAMNAMS]] name for this pattern is '''armotonic''', in reference to Armodue theory. '''Superdiatonic''' is also in use.
The [[TAMNAMS]] name for this pattern is '''armotonic''', in reference to Armodue theory. '''Superdiatonic''' is also in use.
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== Scale properties ==
== Scale properties ==
{{TAMNAMS use}}
{{TAMNAMS use}}
{{MOS data}}
 
=== Intervals ===
{{MOS intervals}}
 
=== Generator chain ===
{{MOS genchain}}
 
=== Modes ===
{{MOS mode degrees}}


=== Proposed mode names ===
=== Proposed mode names ===
Line 42: Line 50:
== Theory ==
== Theory ==
=== Temperament interpretations ===
=== Temperament interpretations ===
[[Pelogic family#Mavila|Mavila]] is an important harmonic entropy minimum here, insofar as 678{{c}} can be considered a fifth. Other temperaments include septimal mavila and Hornbostel.
[[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.


== Scale tree ==
== Scale tree ==
{{MOS tuning spectrum
{{MOS tuning spectrum
| 1/1 = Near exact-7/6 [[Pelogic_family#Armodue|Armodue]]
| 1/1 = Near exact-7/6 [[Pelogic_family#Armodue|Armodue]]
| 5/4 = Near exact-16/15 [[Amavil]]
| 4/3 = Near exact-20/17 [[Pentagoth]]
| 4/3 = Near exact-20/17 [[Pentagoth]]
| 7/5 = Near exact-5/4 [[Mavila]]
| 7/5 = Near exact-5/4 [[Mavila]]

Latest revision as of 04:11, 27 May 2026

↖ 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 ¢)
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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 Near exact-16/15 Amavil
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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