1L 14s

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1L 14s 2L 14s →
↓ 1L 15s 2L 15s ↘ 
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Scale structure
Step pattern Lssssssssssssss
ssssssssssssssL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 14\15 to 1\1 (1120.0 ¢ to 1200.0 ¢)
Dark 0\1 to 1\15 (0.0 ¢ to 80.0 ¢)
TAMNAMS information
Descends from 1L 9s (antisinatonic)
Ancestor's step ratio range 6:1 to 1:0
Related MOS scales
Parent 1L 13s
Sister 14L 1s
Daughters 15L 1s, 1L 15s
Neutralized 2L 13s
2-Flought 16L 14s, 1L 29s
Equal tunings
Equalized (L:s = 1:1) 14\15 (1120.0 ¢)
Supersoft (L:s = 4:3) 43\46 (1121.7 ¢)
Soft (L:s = 3:2) 29\31 (1122.6 ¢)
Semisoft (L:s = 5:3) 44\47 (1123.4 ¢)
Basic (L:s = 2:1) 15\16 (1125.0 ¢)
Semihard (L:s = 5:2) 31\33 (1127.3 ¢)
Hard (L:s = 3:1) 16\17 (1129.4 ¢)
Superhard (L:s = 4:1) 17\18 (1133.3 ¢)
Collapsed (L:s = 1:0) 1\1 (1200.0 ¢)

1L 14s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 1 large step and 14 small steps, repeating every octave. 1L 14s is related to 1L 9s, expanding it by 5 tones. Generators that produce this scale range from 1120 ¢ to 1200 ¢, or from 0 ¢ to 80 ¢.

Valentine temperament, with generators around 77.8¢, maps the interval of 3/2 to +9 dark generators.

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 1L 14s 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 15-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 1L 14s
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 80.0 ¢
Augmented 1-mosstep A1ms L 80.0 ¢ to 1200.0 ¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0 ¢ to 160.0 ¢
Major 2-mosstep M2ms L + s 160.0 ¢ to 1200.0 ¢
3-mosstep Minor 3-mosstep m3ms 3s 0.0 ¢ to 240.0 ¢
Major 3-mosstep M3ms L + 2s 240.0 ¢ to 1200.0 ¢
4-mosstep Minor 4-mosstep m4ms 4s 0.0 ¢ to 320.0 ¢
Major 4-mosstep M4ms L + 3s 320.0 ¢ to 1200.0 ¢
5-mosstep Minor 5-mosstep m5ms 5s 0.0 ¢ to 400.0 ¢
Major 5-mosstep M5ms L + 4s 400.0 ¢ to 1200.0 ¢
6-mosstep Minor 6-mosstep m6ms 6s 0.0 ¢ to 480.0 ¢
Major 6-mosstep M6ms L + 5s 480.0 ¢ to 1200.0 ¢
7-mosstep Minor 7-mosstep m7ms 7s 0.0 ¢ to 560.0 ¢
Major 7-mosstep M7ms L + 6s 560.0 ¢ to 1200.0 ¢
8-mosstep Minor 8-mosstep m8ms 8s 0.0 ¢ to 640.0 ¢
Major 8-mosstep M8ms L + 7s 640.0 ¢ to 1200.0 ¢
9-mosstep Minor 9-mosstep m9ms 9s 0.0 ¢ to 720.0 ¢
Major 9-mosstep M9ms L + 8s 720.0 ¢ to 1200.0 ¢
10-mosstep Minor 10-mosstep m10ms 10s 0.0 ¢ to 800.0 ¢
Major 10-mosstep M10ms L + 9s 800.0 ¢ to 1200.0 ¢
11-mosstep Minor 11-mosstep m11ms 11s 0.0 ¢ to 880.0 ¢
Major 11-mosstep M11ms L + 10s 880.0 ¢ to 1200.0 ¢
12-mosstep Minor 12-mosstep m12ms 12s 0.0 ¢ to 960.0 ¢
Major 12-mosstep M12ms L + 11s 960.0 ¢ to 1200.0 ¢
13-mosstep Minor 13-mosstep m13ms 13s 0.0 ¢ to 1040.0 ¢
Major 13-mosstep M13ms L + 12s 1040.0 ¢ to 1200.0 ¢
14-mosstep Diminished 14-mosstep d14ms 14s 0.0 ¢ to 1120.0 ¢
Perfect 14-mosstep P14ms L + 13s 1120.0 ¢ to 1200.0 ¢
15-mosstep Perfect 15-mosstep P15ms L + 14s 1200.0 ¢

Generator chain

A chain of bright generators, each a perfect 14-mosstep, produces the following scale degrees. A chain of 15 bright generators contains the scale degrees of one of the modes of 1L 14s. Expanding the chain to 16 scale degrees produces the modes of either 15L 1s (for soft-of-basic tunings) or 1L 15s (for hard-of-basic tunings).

Generator chain of 1L 14s
Bright gens Scale degree Abbrev.
15 Augmented 0-mosdegree A0md
14 Augmented 1-mosdegree A1md
13 Major 2-mosdegree M2md
12 Major 3-mosdegree M3md
11 Major 4-mosdegree M4md
10 Major 5-mosdegree M5md
9 Major 6-mosdegree M6md
8 Major 7-mosdegree M7md
7 Major 8-mosdegree M8md
6 Major 9-mosdegree M9md
5 Major 10-mosdegree M10md
4 Major 11-mosdegree M11md
3 Major 12-mosdegree M12md
2 Major 13-mosdegree M13md
1 Perfect 14-mosdegree P14md
0 Perfect 0-mosdegree
Perfect 15-mosdegree		 P0md
P15md
−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 Minor 13-mosdegree m13md
−14 Diminished 14-mosdegree d14md
−15 Diminished 15-mosdegree d15md

Modes

Scale degrees of the modes of 1L 14s 
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 Lssssssssssssss Perf. Aug. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf.
13|1 15 sLsssssssssssss Perf. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf.
12|2 14 ssLssssssssssss Perf. Perf. Min. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf.
11|3 13 sssLsssssssssss Perf. Perf. Min. Min. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf.
10|4 12 ssssLssssssssss Perf. Perf. Min. Min. Min. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf.
9|5 11 sssssLsssssssss Perf. Perf. Min. Min. Min. Min. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf.
8|6 10 ssssssLssssssss Perf. Perf. Min. Min. Min. Min. Min. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf.
7|7 9 sssssssLsssssss Perf. Perf. Min. Min. Min. Min. Min. Min. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf.
6|8 8 ssssssssLssssss Perf. Perf. Min. Min. Min. Min. Min. Min. Min. Maj. Maj. Maj. Maj. Maj. Perf. Perf.
5|9 7 sssssssssLsssss Perf. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Maj. Maj. Maj. Maj. Perf. Perf.
4|10 6 ssssssssssLssss Perf. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Maj. Maj. Maj. Perf. Perf.
3|11 5 sssssssssssLsss Perf. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Maj. Maj. Perf. Perf.
2|12 4 ssssssssssssLss Perf. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Maj. Perf. Perf.
1|13 3 sssssssssssssLs Perf. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Perf.
0|14 2 ssssssssssssssL Perf. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Dim. Perf.

Scale tree

Scale tree and tuning spectrum of 1L 14s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
14\15 1120.000 80.000 1:1 1.000 Equalized 1L 14s
71\76 1121.053 78.947 6:5 1.200
57\61 1121.311 78.689 5:4 1.250
100\107 1121.495 78.505 9:7 1.286
43\46 1121.739 78.261 4:3 1.333 Supersoft 1L 14s
115\123 1121.951 78.049 11:8 1.375
72\77 1122.078 77.922 7:5 1.400 ↕ Valentine
101\108 1122.222 77.778 10:7 1.429
29\31 1122.581 77.419 3:2 1.500 Soft 1L 14s
102\109 1122.936 77.064 11:7 1.571
73\78 1123.077 76.923 8:5 1.600
117\125 1123.200 76.800 13:8 1.625 Unnamed golden tuning
44\47 1123.404 76.596 5:3 1.667 Semisoft 1L 14s
103\110 1123.636 76.364 12:7 1.714
59\63 1123.810 76.190 7:4 1.750
74\79 1124.051 75.949 9:5 1.800
15\16 1125.000 75.000 2:1 2.000 Basic 1L 14s
Scales with tunings softer than this are proper
61\65 1126.154 73.846 9:4 2.250
46\49 1126.531 73.469 7:3 2.333
77\82 1126.829 73.171 12:5 2.400
31\33 1127.273 72.727 5:2 2.500 Semihard 1L 14s
Slurpee
78\83 1127.711 72.289 13:5 2.600 Unnamed golden tuning
47\50 1128.000 72.000 8:3 2.667
63\67 1128.358 71.642 11:4 2.750
16\17 1129.412 70.588 3:1 3.000 Hard 1L 14s
49\52 1130.769 69.231 10:3 3.333
33\35 1131.429 68.571 7:2 3.500
50\53 1132.075 67.925 11:3 3.667
17\18 1133.333 66.667 4:1 4.000 Superhard 1L 14s
35\37 1135.135 64.865 9:2 4.500 Sycamore, betic
18\19 1136.842 63.158 5:1 5.000 Unicorn, rhinoceros
19\20 1140.000 60.000 6:1 6.000 ↓Hemimiracle
1\1 1200.000 0.000 1:0 → ∞ Collapsed 1L 14s
Icon-Todo.png Todo: expand
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