7L 2s
↖ 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. 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 | 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
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
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.
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
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 |