2L 6s

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↖ 1L 5s↑ 2L 5s 3L 5s ↗
← 1L 6s2L 6s3L 6s →
↙ 1L 7s↓ 2L 7s 3L 7s ↘
 
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│║│││║││││
││││││││││
└┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LsssLsss
sssLsssL
Equave 2/1 (1200.0¢)
Period 1\2 (600.0¢)
Generator size
Bright 3\8 to 1\2 (450.0¢ to 600.0¢)
Dark 0\2 to 1\8 (0.0¢ to 150.0¢)
TAMNAMS information
Name subaric
Prefix subar-
Abbrev. sb
Related MOS scales
Parent 2L 4s
Sister 6L 2s
Daughters 8L 2s, 2L 8s
Neutralized 4L 4s
2-Flought 10L 6s, 2L 14s
Equal tunings
Equalized (L:s = 1:1) 3\8 (450.0¢)
Supersoft (L:s = 4:3) 10\26 (461.5¢)
Soft (L:s = 3:2) 7\18 (466.7¢)
Semisoft (L:s = 5:3) 11\28 (471.4¢)
Basic (L:s = 2:1) 4\10 (480.0¢)
Semihard (L:s = 5:2) 9\22 (490.9¢)
Hard (L:s = 3:1) 5\12 (500.0¢)
Superhard (L:s = 4:1) 6\14 (514.3¢)
Collapsed (L:s = 1:0) 1\2 (600.0¢)

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 of 2L 6s
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).

Generator chain of 2L 6s
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

Scale degrees of the modes of 2L 6s 
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
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