7L 2s
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↖ 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 | 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 |
- Generic intervals are denoted solely by the number of steps they subtend.
- Specific intervals denote whether an interval is major, minor, augmented, perfect, or diminished.
- 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
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
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
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 |