13L 2s

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↖ 12L 1s ↑ 13L 1s 14L 1s ↗
← 12L 2s 13L 2s 14L 2s →
↙ 12L 3s ↓ 13L 3s 14L 3s ↘ 
┌╥╥╥╥╥╥╥┬╥╥╥╥╥╥┬┐
│║║║║║║║│║║║║║║││
│││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLLLLLLsLLLLLLs
sLLLLLLsLLLLLLL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 8\15 to 7\13 (640.0 ¢ to 646.2 ¢)
Dark 6\13 to 7\15 (553.8 ¢ to 560.0 ¢)
TAMNAMS information
Related to 2L 7s (balzano)
With tunings 3:1 to 4:1 (parahard)
Related MOS scales
Parent 2L 11s
Sister 2L 13s
Daughters 15L 13s, 13L 15s
Neutralized 11L 4s
2-Flought 28L 2s, 13L 17s
Equal tunings
Equalized (L:s = 1:1) 8\15 (640.0 ¢)
Supersoft (L:s = 4:3) 31\58 (641.4 ¢)
Soft (L:s = 3:2) 23\43 (641.9 ¢)
Semisoft (L:s = 5:3) 38\71 (642.3 ¢)
Basic (L:s = 2:1) 15\28 (642.9 ¢)
Semihard (L:s = 5:2) 37\69 (643.5 ¢)
Hard (L:s = 3:1) 22\41 (643.9 ¢)
Superhard (L:s = 4:1) 29\54 (644.4 ¢)
Collapsed (L:s = 1:0) 7\13 (646.2 ¢)

13L 2s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 13 large steps and 2 small steps, repeating every octave. 13L 2s is a great-grandchild scale of 2L 7s, expanding it by 6 tones. Generators that produce this scale range from 640 ¢ to 646.2 ¢, or from 553.8 ¢ to 560 ¢.

The dark generator for this scale corresponds to a superfourth (interval sharper than 4/3). This generator has almost no sensible interpretation except to be taken as 11/8, meaning the MOS is an 11+-limit scale.

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 of 13L 2s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-mosstep Perfect 0-mosstep P0ms 0 0.0 ¢
1-mosstep Minor 1-mosstep m1ms s 0.0 ¢ to 80.0 ¢
Major 1-mosstep M1ms L 80.0 ¢ to 92.3 ¢
2-mosstep Minor 2-mosstep m2ms L + s 92.3 ¢ to 160.0 ¢
Major 2-mosstep M2ms 2L 160.0 ¢ to 184.6 ¢
3-mosstep Minor 3-mosstep m3ms 2L + s 184.6 ¢ to 240.0 ¢
Major 3-mosstep M3ms 3L 240.0 ¢ to 276.9 ¢
4-mosstep Minor 4-mosstep m4ms 3L + s 276.9 ¢ to 320.0 ¢
Major 4-mosstep M4ms 4L 320.0 ¢ to 369.2 ¢
5-mosstep Minor 5-mosstep m5ms 4L + s 369.2 ¢ to 400.0 ¢
Major 5-mosstep M5ms 5L 400.0 ¢ to 461.5 ¢
6-mosstep Minor 6-mosstep m6ms 5L + s 461.5 ¢ to 480.0 ¢
Major 6-mosstep M6ms 6L 480.0 ¢ to 553.8 ¢
7-mosstep Perfect 7-mosstep P7ms 6L + s 553.8 ¢ to 560.0 ¢
Augmented 7-mosstep A7ms 7L 560.0 ¢ to 646.2 ¢
8-mosstep Diminished 8-mosstep d8ms 6L + 2s 553.8 ¢ to 640.0 ¢
Perfect 8-mosstep P8ms 7L + s 640.0 ¢ to 646.2 ¢
9-mosstep Minor 9-mosstep m9ms 7L + 2s 646.2 ¢ to 720.0 ¢
Major 9-mosstep M9ms 8L + s 720.0 ¢ to 738.5 ¢
10-mosstep Minor 10-mosstep m10ms 8L + 2s 738.5 ¢ to 800.0 ¢
Major 10-mosstep M10ms 9L + s 800.0 ¢ to 830.8 ¢
11-mosstep Minor 11-mosstep m11ms 9L + 2s 830.8 ¢ to 880.0 ¢
Major 11-mosstep M11ms 10L + s 880.0 ¢ to 923.1 ¢
12-mosstep Minor 12-mosstep m12ms 10L + 2s 923.1 ¢ to 960.0 ¢
Major 12-mosstep M12ms 11L + s 960.0 ¢ to 1015.4 ¢
13-mosstep Minor 13-mosstep m13ms 11L + 2s 1015.4 ¢ to 1040.0 ¢
Major 13-mosstep M13ms 12L + s 1040.0 ¢ to 1107.7 ¢
14-mosstep Minor 14-mosstep m14ms 12L + 2s 1107.7 ¢ to 1120.0 ¢
Major 14-mosstep M14ms 13L + s 1120.0 ¢ to 1200.0 ¢
15-mosstep Perfect 15-mosstep P15ms 13L + 2s 1200.0 ¢

Generator chain

Generator chain of 13L 2s
Bright gens Scale degree Abbrev.
27 Augmented 6-mosdegree A6md
26 Augmented 13-mosdegree A13md
25 Augmented 5-mosdegree A5md
24 Augmented 12-mosdegree A12md
23 Augmented 4-mosdegree A4md
22 Augmented 11-mosdegree A11md
21 Augmented 3-mosdegree A3md
20 Augmented 10-mosdegree A10md
19 Augmented 2-mosdegree A2md
18 Augmented 9-mosdegree A9md
17 Augmented 1-mosdegree A1md
16 Augmented 8-mosdegree A8md
15 Augmented 0-mosdegree A0md
14 Augmented 7-mosdegree A7md
13 Major 14-mosdegree M14md
12 Major 6-mosdegree M6md
11 Major 13-mosdegree M13md
10 Major 5-mosdegree M5md
9 Major 12-mosdegree M12md
8 Major 4-mosdegree M4md
7 Major 11-mosdegree M11md
6 Major 3-mosdegree M3md
5 Major 10-mosdegree M10md
4 Major 2-mosdegree M2md
3 Major 9-mosdegree M9md
2 Major 1-mosdegree M1md
1 Perfect 8-mosdegree P8md
0 Perfect 0-mosdegree
Perfect 15-mosdegree		 P0md
P15md
−1 Perfect 7-mosdegree P7md
−2 Minor 14-mosdegree m14md
−3 Minor 6-mosdegree m6md
−4 Minor 13-mosdegree m13md
−5 Minor 5-mosdegree m5md
−6 Minor 12-mosdegree m12md
−7 Minor 4-mosdegree m4md
−8 Minor 11-mosdegree m11md
−9 Minor 3-mosdegree m3md
−10 Minor 10-mosdegree m10md
−11 Minor 2-mosdegree m2md
−12 Minor 9-mosdegree m9md
−13 Minor 1-mosdegree m1md
−14 Diminished 8-mosdegree d8md
−15 Diminished 15-mosdegree d15md
−16 Diminished 7-mosdegree d7md
−17 Diminished 14-mosdegree d14md
−18 Diminished 6-mosdegree d6md
−19 Diminished 13-mosdegree d13md
−20 Diminished 5-mosdegree d5md
−21 Diminished 12-mosdegree d12md
−22 Diminished 4-mosdegree d4md
−23 Diminished 11-mosdegree d11md
−24 Diminished 3-mosdegree d3md
−25 Diminished 10-mosdegree d10md
−26 Diminished 2-mosdegree d2md
−27 Diminished 9-mosdegree d9md

Modes

Scale degrees of the modes of 13L 2s
UDP Cyclic
order 		Step
pattern 		Scale degree (mosdegree)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
14|0 1 LLLLLLLsLLLLLLs Perf. Maj. Maj. Maj. Maj. Maj. Maj. Aug. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
13|1 9 LLLLLLsLLLLLLLs Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
12|2 2 LLLLLLsLLLLLLsL Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf. Maj. Maj. Maj. Maj. Maj. Min. Perf.
11|3 10 LLLLLsLLLLLLLsL Perf. Maj. Maj. Maj. Maj. Maj. Min. Perf. Perf. Maj. Maj. Maj. Maj. Maj. Min. Perf.
10|4 3 LLLLLsLLLLLLsLL Perf. Maj. Maj. Maj. Maj. Maj. Min. Perf. Perf. Maj. Maj. Maj. Maj. Min. Min. Perf.
9|5 11 LLLLsLLLLLLLsLL Perf. Maj. Maj. Maj. Maj. Min. Min. Perf. Perf. Maj. Maj. Maj. Maj. Min. Min. Perf.
8|6 4 LLLLsLLLLLLsLLL Perf. Maj. Maj. Maj. Maj. Min. Min. Perf. Perf. Maj. Maj. Maj. Min. Min. Min. Perf.
7|7 12 LLLsLLLLLLLsLLL Perf. Maj. Maj. Maj. Min. Min. Min. Perf. Perf. Maj. Maj. Maj. Min. Min. Min. Perf.
6|8 5 LLLsLLLLLLsLLLL Perf. Maj. Maj. Maj. Min. Min. Min. Perf. Perf. Maj. Maj. Min. Min. Min. Min. Perf.
5|9 13 LLsLLLLLLLsLLLL Perf. Maj. Maj. Min. Min. Min. Min. Perf. Perf. Maj. Maj. Min. Min. Min. Min. Perf.
4|10 6 LLsLLLLLLsLLLLL Perf. Maj. Maj. Min. Min. Min. Min. Perf. Perf. Maj. Min. Min. Min. Min. Min. Perf.
3|11 14 LsLLLLLLLsLLLLL Perf. Maj. Min. Min. Min. Min. Min. Perf. Perf. Maj. Min. Min. Min. Min. Min. Perf.
2|12 7 LsLLLLLLsLLLLLL Perf. Maj. Min. Min. Min. Min. Min. Perf. Perf. Min. Min. Min. Min. Min. Min. Perf.
1|13 15 sLLLLLLLsLLLLLL Perf. Min. Min. Min. Min. Min. Min. Perf. Perf. Min. Min. Min. Min. Min. Min. Perf.
0|14 8 sLLLLLLsLLLLLLL Perf. Min. Min. Min. Min. Min. Min. Perf. Dim. Min. Min. Min. Min. Min. Min. Perf.

Scale tree

Scale tree and tuning spectrum of 13L 2s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
8\15 640.000 560.000 1:1 1.000 Equalized 13L 2s
47\88 640.909 559.091 6:5 1.200
39\73 641.096 558.904 5:4 1.250
70\131 641.221 558.779 9:7 1.286
31\58 641.379 558.621 4:3 1.333 Supersoft 13L 2s
85\159 641.509 558.491 11:8 1.375
54\101 641.584 558.416 7:5 1.400
77\144 641.667 558.333 10:7 1.429
23\43 641.860 558.140 3:2 1.500 Soft 13L 2s
84\157 642.038 557.962 11:7 1.571
61\114 642.105 557.895 8:5 1.600
99\185 642.162 557.838 13:8 1.625
38\71 642.254 557.746 5:3 1.667 Semisoft 13L 2s
91\170 642.353 557.647 12:7 1.714
53\99 642.424 557.576 7:4 1.750
68\127 642.520 557.480 9:5 1.800
15\28 642.857 557.143 2:1 2.000 Basic 13L 2s
Scales with tunings softer than this are proper
67\125 643.200 556.800 9:4 2.250
52\97 643.299 556.701 7:3 2.333
89\166 643.373 556.627 12:5 2.400
37\69 643.478 556.522 5:2 2.500 Semihard 13L 2s
96\179 643.575 556.425 13:5 2.600
59\110 643.636 556.364 8:3 2.667
81\151 643.709 556.291 11:4 2.750
22\41 643.902 556.098 3:1 3.000 Hard 13L 2s
73\136 644.118 555.882 10:3 3.333
51\95 644.211 555.789 7:2 3.500
80\149 644.295 555.705 11:3 3.667
29\54 644.444 555.556 4:1 4.000 Superhard 13L 2s
65\121 644.628 555.372 9:2 4.500
36\67 644.776 555.224 5:1 5.000
43\80 645.000 555.000 6:1 6.000
7\13 646.154 553.846 1:0 → ∞ Collapsed 13L 2s
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