13L 1s

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← 12L 1s 13L 1s 14L 1s →
↙ 12L 2s ↓ 13L 2s 14L 2s ↘ 
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Scale structure
Step pattern LLLLLLLLLLLLLs
sLLLLLLLLLLLLL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 1\14 to 1\13 (85.7 ¢ to 92.3 ¢)
Dark 12\13 to 13\14 (1107.7 ¢ to 1114.3 ¢)
TAMNAMS information
Descends from 1L 9s (antisinatonic)
Ancestor's step ratio range 4:1 to 5:1
Related MOS scales
Parent 1L 12s
Sister 1L 13s
Daughters 14L 13s, 13L 14s
Neutralized 12L 2s
2-Flought 27L 1s, 13L 15s
Equal tunings
Equalized (L:s = 1:1) 1\14 (85.7 ¢)
Supersoft (L:s = 4:3) 4\55 (87.3 ¢)
Soft (L:s = 3:2) 3\41 (87.8 ¢)
Semisoft (L:s = 5:3) 5\68 (88.2 ¢)
Basic (L:s = 2:1) 2\27 (88.9 ¢)
Semihard (L:s = 5:2) 5\67 (89.6 ¢)
Hard (L:s = 3:1) 3\40 (90.0 ¢)
Superhard (L:s = 4:1) 4\53 (90.6 ¢)
Collapsed (L:s = 1:0) 1\13 (92.3 ¢)

13L 1s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 13 large steps and 1 small step, repeating every octave. 13L 1s is related to 1L 9s, expanding it by 4 tones. Generators that produce this scale range from 85.7 ¢ to 92.3 ¢, or from 1107.7 ¢ to 1114.3 ¢. Scales of this form are always proper because there is only one small step. This scale is notable for corresponding to octacot[14].

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 diatonic interval categories.

Intervals

The intervals of 13L 1s are named after the number of mossteps (L and s) they subtend. Each interval, apart from the root and octave (perfect 0-mosstep and perfect 14-mosstep), 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 13L 1s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-mosstep Perfect 0-mosstep P0ms 0 0.0 ¢
1-mosstep Diminished 1-mosstep d1ms s 0.0 ¢ to 85.7 ¢
Perfect 1-mosstep P1ms L 85.7 ¢ to 92.3 ¢
2-mosstep Minor 2-mosstep m2ms L + s 92.3 ¢ to 171.4 ¢
Major 2-mosstep M2ms 2L 171.4 ¢ to 184.6 ¢
3-mosstep Minor 3-mosstep m3ms 2L + s 184.6 ¢ to 257.1 ¢
Major 3-mosstep M3ms 3L 257.1 ¢ to 276.9 ¢
4-mosstep Minor 4-mosstep m4ms 3L + s 276.9 ¢ to 342.9 ¢
Major 4-mosstep M4ms 4L 342.9 ¢ to 369.2 ¢
5-mosstep Minor 5-mosstep m5ms 4L + s 369.2 ¢ to 428.6 ¢
Major 5-mosstep M5ms 5L 428.6 ¢ to 461.5 ¢
6-mosstep Minor 6-mosstep m6ms 5L + s 461.5 ¢ to 514.3 ¢
Major 6-mosstep M6ms 6L 514.3 ¢ to 553.8 ¢
7-mosstep Minor 7-mosstep m7ms 6L + s 553.8 ¢ to 600.0 ¢
Major 7-mosstep M7ms 7L 600.0 ¢ to 646.2 ¢
8-mosstep Minor 8-mosstep m8ms 7L + s 646.2 ¢ to 685.7 ¢
Major 8-mosstep M8ms 8L 685.7 ¢ to 738.5 ¢
9-mosstep Minor 9-mosstep m9ms 8L + s 738.5 ¢ to 771.4 ¢
Major 9-mosstep M9ms 9L 771.4 ¢ to 830.8 ¢
10-mosstep Minor 10-mosstep m10ms 9L + s 830.8 ¢ to 857.1 ¢
Major 10-mosstep M10ms 10L 857.1 ¢ to 923.1 ¢
11-mosstep Minor 11-mosstep m11ms 10L + s 923.1 ¢ to 942.9 ¢
Major 11-mosstep M11ms 11L 942.9 ¢ to 1015.4 ¢
12-mosstep Minor 12-mosstep m12ms 11L + s 1015.4 ¢ to 1028.6 ¢
Major 12-mosstep M12ms 12L 1028.6 ¢ to 1107.7 ¢
13-mosstep Perfect 13-mosstep P13ms 12L + s 1107.7 ¢ to 1114.3 ¢
Augmented 13-mosstep A13ms 13L 1114.3 ¢ to 1200.0 ¢
14-mosstep Perfect 14-mosstep P14ms 13L + s 1200.0 ¢

Generator chain

A chain of bright generators, each a perfect 1-mosstep, produces the following scale degrees. A chain of 14 bright generators contains the scale degrees of one of the modes of 13L 1s. Expanding the chain to 27 scale degrees produces the modes of either 14L 13s (for soft-of-basic tunings) or 13L 14s (for hard-of-basic tunings).

Generator chain of 13L 1s
Bright gens Scale degree Abbrev.
26 Augmented 12-mosdegree A12md
25 Augmented 11-mosdegree A11md
24 Augmented 10-mosdegree A10md
23 Augmented 9-mosdegree A9md
22 Augmented 8-mosdegree A8md
21 Augmented 7-mosdegree A7md
20 Augmented 6-mosdegree A6md
19 Augmented 5-mosdegree A5md
18 Augmented 4-mosdegree A4md
17 Augmented 3-mosdegree A3md
16 Augmented 2-mosdegree A2md
15 Augmented 1-mosdegree A1md
14 Augmented 0-mosdegree A0md
13 Augmented 13-mosdegree A13md
12 Major 12-mosdegree M12md
11 Major 11-mosdegree M11md
10 Major 10-mosdegree M10md
9 Major 9-mosdegree M9md
8 Major 8-mosdegree M8md
7 Major 7-mosdegree M7md
6 Major 6-mosdegree M6md
5 Major 5-mosdegree M5md
4 Major 4-mosdegree M4md
3 Major 3-mosdegree M3md
2 Major 2-mosdegree M2md
1 Perfect 1-mosdegree P1md
0 Perfect 0-mosdegree
Perfect 14-mosdegree		 P0md
P14md
−1 Perfect 13-mosdegree P13md
−2 Minor 12-mosdegree m12md
−3 Minor 11-mosdegree m11md
−4 Minor 10-mosdegree m10md
−5 Minor 9-mosdegree m9md
−6 Minor 8-mosdegree m8md
−7 Minor 7-mosdegree m7md
−8 Minor 6-mosdegree m6md
−9 Minor 5-mosdegree m5md
−10 Minor 4-mosdegree m4md
−11 Minor 3-mosdegree m3md
−12 Minor 2-mosdegree m2md
−13 Diminished 1-mosdegree d1md
−14 Diminished 14-mosdegree d14md
−15 Diminished 13-mosdegree d13md
−16 Diminished 12-mosdegree d12md
−17 Diminished 11-mosdegree d11md
−18 Diminished 10-mosdegree d10md
−19 Diminished 9-mosdegree d9md
−20 Diminished 8-mosdegree d8md
−21 Diminished 7-mosdegree d7md
−22 Diminished 6-mosdegree d6md
−23 Diminished 5-mosdegree d5md
−24 Diminished 4-mosdegree d4md
−25 Diminished 3-mosdegree d3md
−26 Diminished 2-mosdegree d2md

Modes

Scale degrees of the modes of 13L 1s 
UDP Cyclic
order		 Step
pattern		 Scale degree (mosdegree)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
13|0 1 LLLLLLLLLLLLLs Perf. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Aug. Perf.
12|1 2 LLLLLLLLLLLLsL Perf. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf.
11|2 3 LLLLLLLLLLLsLL Perf. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Min. Perf. Perf.
10|3 4 LLLLLLLLLLsLLL Perf. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Min. Min. Perf. Perf.
9|4 5 LLLLLLLLLsLLLL Perf. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Min. Min. Min. Perf. Perf.
8|5 6 LLLLLLLLsLLLLL Perf. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Min. Min. Min. Min. Perf. Perf.
7|6 7 LLLLLLLsLLLLLL Perf. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Min. Min. Min. Min. Min. Perf. Perf.
6|7 8 LLLLLLsLLLLLLL Perf. Perf. Maj. Maj. Maj. Maj. Maj. Min. Min. Min. Min. Min. Min. Perf. Perf.
5|8 9 LLLLLsLLLLLLLL Perf. Perf. Maj. Maj. Maj. Maj. Min. Min. Min. Min. Min. Min. Min. Perf. Perf.
4|9 10 LLLLsLLLLLLLLL Perf. Perf. Maj. Maj. Maj. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Perf.
3|10 11 LLLsLLLLLLLLLL Perf. Perf. Maj. Maj. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Perf.
2|11 12 LLsLLLLLLLLLLL Perf. Perf. Maj. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Perf.
1|12 13 LsLLLLLLLLLLLL Perf. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Perf.
0|13 14 sLLLLLLLLLLLLL Perf. Dim. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Perf.

Scale tree

Scale tree and tuning spectrum of 13L 1s
Generator(edo) Cents Step ratio Comments(always proper)
Bright Dark L:s Hardness
1\14 85.714 1114.286 1:1 1.000 Equalized 13L 1s
6\83 86.747 1113.253 6:5 1.200
5\69 86.957 1113.043 5:4 1.250
9\124 87.097 1112.903 9:7 1.286
4\55 87.273 1112.727 4:3 1.333 Supersoft 13L 1s
11\151 87.417 1112.583 11:8 1.375
7\96 87.500 1112.500 7:5 1.400
10\137 87.591 1112.409 10:7 1.429
3\41 87.805 1112.195 3:2 1.500 Soft 13L 1s
11\150 88.000 1112.000 11:7 1.571 ↕ Octacot
8\109 88.073 1111.927 8:5 1.600
13\177 88.136 1111.864 13:8 1.625
5\68 88.235 1111.765 5:3 1.667 Semisoft 13L 1s
12\163 88.344 1111.656 12:7 1.714
7\95 88.421 1111.579 7:4 1.750
9\122 88.525 1111.475 9:5 1.800
2\27 88.889 1111.111 2:1 2.000 Basic 13L 1s
9\121 89.256 1110.744 9:4 2.250
7\94 89.362 1110.638 7:3 2.333
12\161 89.441 1110.559 12:5 2.400
5\67 89.552 1110.448 5:2 2.500 Semihard 13L 1s
13\174 89.655 1110.345 13:5 2.600
8\107 89.720 1110.280 8:3 2.667
11\147 89.796 1110.204 11:4 2.750
3\40 90.000 1110.000 3:1 3.000 Hard 13L 1s
10\133 90.226 1109.774 10:3 3.333
7\93 90.323 1109.677 7:2 3.500
11\146 90.411 1109.589 11:3 3.667
4\53 90.566 1109.434 4:1 4.000 Superhard 13L 1s
9\119 90.756 1109.244 9:2 4.500
5\66 90.909 1109.091 5:1 5.000
6\79 91.139 1108.861 6:1 6.000
1\13 92.308 1107.692 1:0 → ∞ Collapsed 13L 1s
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