7L 2s

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↖ 6L 1s ↑7L 1s 8L 1s ↗
← 6L 2s7L 2s 8L 2s →
↙ 6L 3s ↓7L 3s 8L 3s ↘
 
┌╥╥╥╥┬╥╥╥┬┐
│║║║║│║║║││
│││││││││││
└┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLLLsLLLs
sLLLsLLLL
Equave 2/1 (1200.0¢)
Period 1\9 (133.3¢)
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.

Name

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

Intervals

This article assumes TAMNAMS for naming step ratios, mossteps, and mosdegrees.
Intervals of 7L 2s
Intervals Steps subtended Range in cents Average of HE
(from HE Calc) 		Min of HE
Generic[1] Specific[2] Abbrev.[3]
0-armstep Perfect 0-armstep P0ms 0 0.0¢ ~2.4654 nats ~2.4654 nats
1-armstep Minor 1-armstep m1ms s 0.0¢ to 133.3¢ ~4.7284 nats ~4.6681 nats
Major 1-armstep M1ms L 133.3¢ to 171.4¢ ~4.6229 nats ~4.6138 nats
2-armstep Minor 2-armstep m2ms L + s 171.4¢ to 266.7¢ ~4.5850 nats ~4.5841 nats
Major 2-armstep M2ms 2L 266.7¢ to 342.9¢ ~4.5613 nats ~4.5385 nats
3-armstep Minor 3-armstep m3ms 2L + s 342.9¢ to 400.0¢ ~4.5361 nats ~4.4847 nats
Major 3-armstep M3ms 3L 400.0¢ to 514.3¢ ~4.5922 nats ~4.5131 nats
4-armstep Perfect 4-armstep P4ms 3L + s 514.3¢ to 533.3¢ ~4.5785 nats ~4.5386 nats
Augmented 4-armstep A4ms 4L 533.3¢ to 685.7¢ ~4.5894 nats ~4.5597 nats
5-armstep Diminished 5-armstep d5ms 3L + 2s 514.3¢ to 666.7¢ ~4.5903 nats ~4.5596 nats
Perfect 5-armstep P5ms 4L + s 666.7¢ to 685.7¢ ~4.5639 nats ~4.4938 nats
6-armstep Minor 6-armstep m6ms 4L + 2s 685.7¢ to 800.0¢ ~4.5811 nats ~4.3710 nats
Major 6-armstep M6ms 5L + s 800.0¢ to 857.1¢ ~4.5859 nats ~4.5712 nats
7-armstep Minor 7-armstep m7ms 5L + 2s 857.1¢ to 933.3¢ ~4.5060 nats ~4.4212 nats
Major 7-armstep M7ms 6L + s 933.3¢ to 1028.6¢ ~4.5595 nats ~4.5338 nats
8-armstep Minor 8-armstep m8ms 6L + 2s 1028.6¢ to 1066.7¢ ~4.6063 nats ~4.6020 nats
Major 8-armstep M8ms 7L + s 1066.7¢ to 1200.0¢ ~4.6641 nats ~4.6139 nats
9-armstep Perfect 9-armstep P9ms 7L + 2s 1200.0¢ ~3.3273 nats ~3.3273 nats

  1. Generic intervals are denoted solely by the number of steps they subtend.
  2. Specific intervals denote whether an interval is major, minor, augmented, perfect, or diminished.
  3. Abbreviations can be further shortened to 'ms' if context allows.

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 678¢ can be considered a fifth. Other temperaments include septimal mavila and Hornbostel.

Modes

Scale degree qualities of 7L 2s modes
UDP Rotational 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 Names

Modes of 7L 2s
UDP Rotational order Step pattern Mode names
7|0 1 LLLLsLLLs Superlydian
6|1 6 LLLsLLLLs Superionian
5|2 2 LLLsLLLsL Supermixolidyan
4|3 7 LLsLLLLsL Supercorintihan
3|4 3 LLsLLLsLL Superolympian
2|5 8 LsLLLLsLL Superdorian
1|6 4 LsLLLsLLL Superaeolian
0|7 9 sLLLLsLLL Superphrygian
-1|8 5 sLLLsLLLL Superlocrian

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
4\7 685.714 514.286 1:0 → ∞ Collapsed 7L 2s
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