1L 13s

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↑ 1L 12s 2L 12s ↗
1L 13s 2L 13s →
↓ 1L 14s 2L 14s ↘ 
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││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern Lsssssssssssss
sssssssssssssL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 13\14 to 1\1 (1114.3 ¢ to 1200.0 ¢)
Dark 0\1 to 1\14 (0.0 ¢ to 85.7 ¢)
TAMNAMS information
Related to 1L 9s (antisinatonic)
With tunings 5:1 to 1:0
Related MOS scales
Parent 1L 12s
Sister 13L 1s
Daughters 14L 1s, 1L 14s
Neutralized 2L 12s
2-Flought 15L 13s, 1L 27s
Equal tunings
Equalized (L:s = 1:1) 13\14 (1114.3 ¢)
Supersoft (L:s = 4:3) 40\43 (1116.3 ¢)
Soft (L:s = 3:2) 27\29 (1117.2 ¢)
Semisoft (L:s = 5:3) 41\44 (1118.2 ¢)
Basic (L:s = 2:1) 14\15 (1120.0 ¢)
Semihard (L:s = 5:2) 29\31 (1122.6 ¢)
Hard (L:s = 3:1) 15\16 (1125.0 ¢)
Superhard (L:s = 4:1) 16\17 (1129.4 ¢)
Collapsed (L:s = 1:0) 1\1 (1200.0 ¢)

1L 13s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 1 large step and 13 small steps, repeating every octave. 1L 13s is related to 1L 9s, expanding it by 4 tones. Generators that produce this scale range from 1114.3 ¢ to 1200 ¢, or from 0 ¢ to 85.7 ¢.

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 1L 13s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-mosstep Perfect 0-mosstep P0ms 0 0.0 ¢
1-mosstep Perfect 1-mosstep P1ms s 0.0 ¢ to 85.7 ¢
Augmented 1-mosstep A1ms L 85.7 ¢ to 1200.0 ¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0 ¢ to 171.4 ¢
Major 2-mosstep M2ms L + s 171.4 ¢ to 1200.0 ¢
3-mosstep Minor 3-mosstep m3ms 3s 0.0 ¢ to 257.1 ¢
Major 3-mosstep M3ms L + 2s 257.1 ¢ to 1200.0 ¢
4-mosstep Minor 4-mosstep m4ms 4s 0.0 ¢ to 342.9 ¢
Major 4-mosstep M4ms L + 3s 342.9 ¢ to 1200.0 ¢
5-mosstep Minor 5-mosstep m5ms 5s 0.0 ¢ to 428.6 ¢
Major 5-mosstep M5ms L + 4s 428.6 ¢ to 1200.0 ¢
6-mosstep Minor 6-mosstep m6ms 6s 0.0 ¢ to 514.3 ¢
Major 6-mosstep M6ms L + 5s 514.3 ¢ to 1200.0 ¢
7-mosstep Minor 7-mosstep m7ms 7s 0.0 ¢ to 600.0 ¢
Major 7-mosstep M7ms L + 6s 600.0 ¢ to 1200.0 ¢
8-mosstep Minor 8-mosstep m8ms 8s 0.0 ¢ to 685.7 ¢
Major 8-mosstep M8ms L + 7s 685.7 ¢ to 1200.0 ¢
9-mosstep Minor 9-mosstep m9ms 9s 0.0 ¢ to 771.4 ¢
Major 9-mosstep M9ms L + 8s 771.4 ¢ to 1200.0 ¢
10-mosstep Minor 10-mosstep m10ms 10s 0.0 ¢ to 857.1 ¢
Major 10-mosstep M10ms L + 9s 857.1 ¢ to 1200.0 ¢
11-mosstep Minor 11-mosstep m11ms 11s 0.0 ¢ to 942.9 ¢
Major 11-mosstep M11ms L + 10s 942.9 ¢ to 1200.0 ¢
12-mosstep Minor 12-mosstep m12ms 12s 0.0 ¢ to 1028.6 ¢
Major 12-mosstep M12ms L + 11s 1028.6 ¢ to 1200.0 ¢
13-mosstep Diminished 13-mosstep d13ms 13s 0.0 ¢ to 1114.3 ¢
Perfect 13-mosstep P13ms L + 12s 1114.3 ¢ to 1200.0 ¢
14-mosstep Perfect 14-mosstep P14ms L + 13s 1200.0 ¢

Generator chain

Generator chain of 1L 13s
Bright gens Scale degree Abbrev.
14 Augmented 0-mosdegree A0md
13 Augmented 1-mosdegree A1md
12 Major 2-mosdegree M2md
11 Major 3-mosdegree M3md
10 Major 4-mosdegree M4md
9 Major 5-mosdegree M5md
8 Major 6-mosdegree M6md
7 Major 7-mosdegree M7md
6 Major 8-mosdegree M8md
5 Major 9-mosdegree M9md
4 Major 10-mosdegree M10md
3 Major 11-mosdegree M11md
2 Major 12-mosdegree M12md
1 Perfect 13-mosdegree P13md
0 Perfect 0-mosdegree
Perfect 14-mosdegree		 P0md
P14md
−1 Perfect 1-mosdegree P1md
−2 Minor 2-mosdegree m2md
−3 Minor 3-mosdegree m3md
−4 Minor 4-mosdegree m4md
−5 Minor 5-mosdegree m5md
−6 Minor 6-mosdegree m6md
−7 Minor 7-mosdegree m7md
−8 Minor 8-mosdegree m8md
−9 Minor 9-mosdegree m9md
−10 Minor 10-mosdegree m10md
−11 Minor 11-mosdegree m11md
−12 Minor 12-mosdegree m12md
−13 Diminished 13-mosdegree d13md
−14 Diminished 14-mosdegree d14md

Modes

Scale degrees of the modes of 1L 13s
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 Lsssssssssssss Perf. Aug. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf.
12|1 14 sLssssssssssss Perf. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf.
11|2 13 ssLsssssssssss Perf. Perf. Min. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf.
10|3 12 sssLssssssssss Perf. Perf. Min. Min. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf.
9|4 11 ssssLsssssssss Perf. Perf. Min. Min. Min. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf.
8|5 10 sssssLssssssss Perf. Perf. Min. Min. Min. Min. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf.
7|6 9 ssssssLsssssss Perf. Perf. Min. Min. Min. Min. Min. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf.
6|7 8 sssssssLssssss Perf. Perf. Min. Min. Min. Min. Min. Min. Maj. Maj. Maj. Maj. Maj. Perf. Perf.
5|8 7 ssssssssLsssss Perf. Perf. Min. Min. Min. Min. Min. Min. Min. Maj. Maj. Maj. Maj. Perf. Perf.
4|9 6 sssssssssLssss Perf. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Maj. Maj. Maj. Perf. Perf.
3|10 5 ssssssssssLsss Perf. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Maj. Maj. Perf. Perf.
2|11 4 sssssssssssLss Perf. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Maj. Perf. Perf.
1|12 3 ssssssssssssLs Perf. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Perf.
0|13 2 sssssssssssssL Perf. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Dim. Perf.

Scale tree

Scale tree and tuning spectrum of 1L 13s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
13\14 1114.286 85.714 1:1 1.000 Equalized 1L 13s
66\71 1115.493 84.507 6:5 1.200
53\57 1115.789 84.211 5:4 1.250
93\100 1116.000 84.000 9:7 1.286
40\43 1116.279 83.721 4:3 1.333 Supersoft 1L 13s
107\115 1116.522 83.478 11:8 1.375
67\72 1116.667 83.333 7:5 1.400 Marvolo
94\101 1116.832 83.168 10:7 1.429
27\29 1117.241 82.759 3:2 1.500 Soft 1L 13s
Nautilus
95\102 1117.647 82.353 11:7 1.571
68\73 1117.808 82.192 8:5 1.600
109\117 1117.949 82.051 13:8 1.625 Unnamed golden tuning
41\44 1118.182 81.818 5:3 1.667 Semisoft 1L 13s
96\103 1118.447 81.553 12:7 1.714
55\59 1118.644 81.356 7:4 1.750
69\74 1118.919 81.081 9:5 1.800
14\15 1120.000 80.000 2:1 2.000 Basic 1L 13s
Scales with tunings softer than this are proper
57\61 1121.311 78.689 9:4 2.250
43\46 1121.739 78.261 7:3 2.333
72\77 1122.078 77.922 12:5 2.400 Valentine
29\31 1122.581 77.419 5:2 2.500 Semihard 1L 13s
73\78 1123.077 76.923 13:5 2.600 Unnamed golden tuning
44\47 1123.404 76.596 8:3 2.667
59\63 1123.810 76.190 11:4 2.750
15\16 1125.000 75.000 3:1 3.000 Hard 1L 13s
46\49 1126.531 73.469 10:3 3.333
31\33 1127.273 72.727 7:2 3.500 Slurpee
47\50 1128.000 72.000 11:3 3.667
16\17 1129.412 70.588 4:1 4.000 Superhard 1L 13s
33\35 1131.429 68.571 9:2 4.500
17\18 1133.333 66.667 5:1 5.000
18\19 1136.842 63.158 6:1 6.000 Sycamore, unicorn
1\1 1200.000 0.000 1:0 → ∞ Collapsed 1L 13s


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