2L 6s
↖ 1L 5s | ↑ 2L 5s | 3L 5s ↗ |
← 1L 6s | 2L 6s | 3L 6s → |
↙ 1L 7s | ↓ 2L 7s | 3L 7s ↘ |
┌╥┬┬┬╥┬┬┬┐ │║│││║││││ ││││││││││ └┴┴┴┴┴┴┴┴┘
sssLsssL
2L 6s, named subaric in TAMNAMS, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 2 large steps and 6 small steps, with a period of 1 large step and 3 small steps that repeats every 600.0¢, or twice every octave. Generators that produce this scale range from 450¢ to 600¢, or from 0¢ to 150¢. Two notable harmonic entropy minima for this MOS pattern are srutal/pajara and shrutar. They are both improper.
In addition to the true MOS form, LsssLsss, these scales also have an interesting near-MOS form, LssLssss, in which the period is the only interval with more than two interval varieties.
Name
TAMNAMS suggests the temperament-agnostic name subaric as the name of 2L 6s. The name references to how 2L 6s is the parent scale (or subset scale) of 2L 8s (jaric) and 8L 2s (taric).
Scale properties
Intervals
The intervals of 2L 6s are named after the number of mossteps (L and s) they subtend. Each interval, apart from the period intervals (perfect 0-subarstep, perfect 4-subarstep, and perfect 8-subarstep), has two varieties, or sizes, each. Interval varieties are named major and minor for the large and small sizes, respectively, and augmented, perfect, and diminished for the scale's generators.
Intervals | Steps subtended |
Range in cents | ||
---|---|---|---|---|
Generic | Specific | Abbrev. | ||
0-subarstep | Perfect 0-subarstep | P0sbs | 0 | 0.0¢ |
1-subarstep | Perfect 1-subarstep | P1sbs | s | 0.0¢ to 150.0¢ |
Augmented 1-subarstep | A1sbs | L | 150.0¢ to 600.0¢ | |
2-subarstep | Minor 2-subarstep | m2sbs | 2s | 0.0¢ to 300.0¢ |
Major 2-subarstep | M2sbs | L + s | 300.0¢ to 600.0¢ | |
3-subarstep | Diminished 3-subarstep | d3sbs | 3s | 0.0¢ to 450.0¢ |
Perfect 3-subarstep | P3sbs | L + 2s | 450.0¢ to 600.0¢ | |
4-subarstep | Perfect 4-subarstep | P4sbs | L + 3s | 600.0¢ |
5-subarstep | Perfect 5-subarstep | P5sbs | L + 4s | 600.0¢ to 750.0¢ |
Augmented 5-subarstep | A5sbs | 2L + 3s | 750.0¢ to 1200.0¢ | |
6-subarstep | Minor 6-subarstep | m6sbs | L + 5s | 600.0¢ to 900.0¢ |
Major 6-subarstep | M6sbs | 2L + 4s | 900.0¢ to 1200.0¢ | |
7-subarstep | Diminished 7-subarstep | d7sbs | L + 6s | 600.0¢ to 1050.0¢ |
Perfect 7-subarstep | P7sbs | 2L + 5s | 1050.0¢ to 1200.0¢ | |
8-subarstep | Perfect 8-subarstep | P8sbs | 2L + 6s | 1200.0¢ |
Generator chain
A chain of bright generators, each a perfect 3-subarstep, produces the following scale degrees. A chain of 4 bright generators from each period contains the scale degrees of one of the modes of 2L 6s. Expanding each chain to 5 scale degrees produces the modes of either 8L 2s (for soft-of-basic tunings) or 2L 8s (for hard-of-basic tunings).
Bright gens | Scale Degree | Abbrev. | Scale Degree | Abbrev. |
---|---|---|---|---|
4 | Augmented 0-subardegree | A0sbd | Augmented 4-subardegree | A4sbd |
3 | Augmented 1-subardegree | A1sbd | Augmented 5-subardegree | A5sbd |
2 | Major 2-subardegree | M2sbd | Major 6-subardegree | M6sbd |
1 | Perfect 3-subardegree | P3sbd | Perfect 7-subardegree | P7sbd |
0 | Perfect 0-subardegree Perfect 4-subardegree |
P0sbd P4sbd |
Perfect 4-subardegree Perfect 8-subardegree |
P4sbd P8sbd |
-1 | Perfect 1-subardegree | P1sbd | Perfect 5-subardegree | P5sbd |
-2 | Minor 2-subardegree | m2sbd | Minor 6-subardegree | m6sbd |
-3 | Diminished 3-subardegree | d3sbd | Diminished 7-subardegree | d7sbd |
-4 | Diminished 4-subardegree | d4sbd | Diminished 8-subardegree | d8sbd |
Modes
UDP | Cyclic Order |
Step Pattern |
Scale Degree (subardegree) | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | |||
6|0(2) | 1 | LsssLsss | Perf. | Aug. | Maj. | Perf. | Perf. | Aug. | Maj. | Perf. | Perf. |
4|2(2) | 4 | sLsssLss | Perf. | Perf. | Maj. | Perf. | Perf. | Perf. | Maj. | Perf. | Perf. |
2|4(2) | 3 | ssLsssLs | Perf. | Perf. | Min. | Perf. | Perf. | Perf. | Min. | Perf. | Perf. |
0|6(2) | 2 | sssLsssL | Perf. | Perf. | Min. | Dim. | Perf. | Perf. | Min. | Dim. | Perf. |
Scale tree
Generator | Cents | L | s | L/s | Comments | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Chroma-positive | Chroma-negative | ||||||||||
3\8 | 450.000 | 150.000 | 1 | 1 | 1.000 | ||||||
16\42 | 457.143 | 142.857 | 6 | 5 | 1.200 | ||||||
13\34 | 458.824 | 141.176 | 5 | 4 | 1.250 | ||||||
23\60 | 460.000 | 140.000 | 9 | 7 | 1.286 | Fifive/crepuscular/fifives | |||||
10\26 | 461.538 | 138.462 | 4 | 3 | 1.333 | ||||||
27\70 | 462.857 | 137.143 | 11 | 8 | 1.375 | ||||||
17\44 | 463.636 | 136.364 | 7 | 5 | 1.400 | ||||||
24\62 | 464.516 | 135.484 | 10 | 7 | 1.428 | ||||||
7\18 | 466.667 | 133.333 | 3 | 2 | 1.500 | L/s = 3/2 | |||||
25\64 | 468.750 | 131.250 | 11 | 7 | 1.571 | ||||||
18\46 | 469.565 | 130.435 | 8 | 5 | 1.600 | ||||||
29\74 | 470.270 | 129.730 | 13 | 8 | 1.625 | Unnamed golden tuning | |||||
11\28 | 471.429 | 128.571 | 5 | 3 | 1.667 | Supersharp/octokaidecal is around here | |||||
26\66 | 472.727 | 127.273 | 12 | 7 | 1.714 | ||||||
15\38 | 473.864 | 126.316 | 7 | 4 | 1.750 | ||||||
19\48 | 475.000 | 125.000 | 9 | 5 | 1.800 | ||||||
4\10 | 480.000 | 120.000 | 2 | 1 | 2.000 | Basic 2L 6s (Generators smaller than this are proper) | |||||
17\42 | 485.714 | 114.286 | 9 | 4 | 2.250 | ||||||
13\32 | 487.500 | 112.500 | 7 | 3 | 2.333 | ||||||
22\54 | 488.889 | 111.111 | 12 | 5 | 2.400 | ||||||
9\22 | 490.909 | 109.091 | 5 | 2 | 2.500 | Srutal/pajara | |||||
23\56 | 492.857 | 107.143 | 13 | 5 | 2.600 | Srutal/keen | |||||
14\34 | 494.118 | 105.882 | 8 | 3 | 2.667 | Srutal | |||||
19\46 | 495.652 | 104.348 | 11 | 4 | 2.750 | Srutal/diaschismic | |||||
5\12 | 500.000 | 100.000 | 3 | 1 | 3.000 | L/s = 3/1 | |||||
16\38 | 505.263 | 94.737 | 10 | 3 | 3.333 | Bimeantone (incomplete) | |||||
11\26 | 507.692 | 92.308 | 7 | 2 | 3.500 | Injera (incomplete) | |||||
17\40 | 510.000 | 90.000 | 11 | 3 | 3.667 | ||||||
6\14 | 514.286 | 85.714 | 4 | 1 | 4.000 | ||||||
13\30 | 520.000 | 80.000 | 9 | 2 | 4.500 | ||||||
7\16 | 525.000 | 75.000 | 5 | 1 | 5.000 | ||||||
8\18 | 533.333 | 66.667 | 6 | 1 | 6.000 | Shrutar, teff/pombe (incomplete)↓ | |||||
1\2 | 600.000 | 0.000 | 1 | 0 | → inf |