7L 2s
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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¢)
↖ 6L 1s | ↑ 7L 1s | 8L 1s ↗ |
← 6L 2s | 7L 2s | 8L 2s → |
↙ 6L 3s | ↓ 7L 3s | 8L 3s ↘ |
┌╥╥╥╥┬╥╥╥┬┐ │║║║║│║║║││ │││││││││││ └┴┴┴┴┴┴┴┴┴┘
sLLLsLLLL
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 | 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¢ |
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
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 Names
UDP | Cyclic order |
Step pattern |
Mode names |
---|---|---|---|
8|0 | 1 | LLLLsLLLs | Superlydian |
7|1 | 6 | LLLsLLLLs | Superionian |
6|2 | 2 | LLLsLLLsL | Supermixolidyan |
5|3 | 7 | LLsLLLLsL | Supercorintihan |
4|4 | 3 | LLsLLLsLL | Superolympian |
3|5 | 8 | LsLLLLsLL | Superdorian |
2|6 | 4 | LsLLLsLLL | Superaeolian |
1|7 | 9 | sLLLLsLLL | Superphrygian |
0|8 | 5 | sLLLsLLLL | Superlocrian |
Scale tree
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 |