14L 1s

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← 13L 1s 14L 1s 15L 1s →
↙ 13L 2s ↓ 14L 2s 15L 2s ↘ 
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Scale structure
Step pattern LLLLLLLLLLLLLLs
sLLLLLLLLLLLLLL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 1\15 to 1\14 (80.0 ¢ to 85.7 ¢)
Dark 13\14 to 14\15 (1114.3 ¢ to 1120.0 ¢)
TAMNAMS information
Descends from 1L 9s (antisinatonic)
Ancestor's step ratio range 5:1 to 6:1
Related MOS scales
Parent 1L 13s
Sister 1L 14s
Daughters 15L 14s, 14L 15s
Neutralized 13L 2s
2-Flought 29L 1s, 14L 16s
Equal tunings
Equalized (L:s = 1:1) 1\15 (80.0 ¢)
Supersoft (L:s = 4:3) 4\59 (81.4 ¢)
Soft (L:s = 3:2) 3\44 (81.8 ¢)
Semisoft (L:s = 5:3) 5\73 (82.2 ¢)
Basic (L:s = 2:1) 2\29 (82.8 ¢)
Semihard (L:s = 5:2) 5\72 (83.3 ¢)
Hard (L:s = 3:1) 3\43 (83.7 ¢)
Superhard (L:s = 4:1) 4\57 (84.2 ¢)
Collapsed (L:s = 1:0) 1\14 (85.7 ¢)

14L 1s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 14 large steps and 1 small step, repeating every octave. 14L 1s is related to 1L 9s, expanding it by 5 tones. Generators that produce this scale range from 80 ¢ to 85.7 ¢, or from 1114.3 ¢ to 1120 ¢. Scales of this form are always proper because there is only one small step.

This scale is notable for corresponding to 15-note scales of temperaments like nautilus and sextilififths. 6 steps of the scale cover a diatonic fourth, and they also go from the lower bound to upper bound of diatonic fourths (3\7 to 2\5) over the course of the entire step ratio spectrum, corresponding to going from 14edo perfect fourth to 15edo pefect fourth.

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

Intervals of 14L 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 80.0 ¢
Perfect 1-mosstep P1ms L 80.0 ¢ to 85.7 ¢
2-mosstep Minor 2-mosstep m2ms L + s 85.7 ¢ to 160.0 ¢
Major 2-mosstep M2ms 2L 160.0 ¢ to 171.4 ¢
3-mosstep Minor 3-mosstep m3ms 2L + s 171.4 ¢ to 240.0 ¢
Major 3-mosstep M3ms 3L 240.0 ¢ to 257.1 ¢
4-mosstep Minor 4-mosstep m4ms 3L + s 257.1 ¢ to 320.0 ¢
Major 4-mosstep M4ms 4L 320.0 ¢ to 342.9 ¢
5-mosstep Minor 5-mosstep m5ms 4L + s 342.9 ¢ to 400.0 ¢
Major 5-mosstep M5ms 5L 400.0 ¢ to 428.6 ¢
6-mosstep Minor 6-mosstep m6ms 5L + s 428.6 ¢ to 480.0 ¢
Major 6-mosstep M6ms 6L 480.0 ¢ to 514.3 ¢
7-mosstep Minor 7-mosstep m7ms 6L + s 514.3 ¢ to 560.0 ¢
Major 7-mosstep M7ms 7L 560.0 ¢ to 600.0 ¢
8-mosstep Minor 8-mosstep m8ms 7L + s 600.0 ¢ to 640.0 ¢
Major 8-mosstep M8ms 8L 640.0 ¢ to 685.7 ¢
9-mosstep Minor 9-mosstep m9ms 8L + s 685.7 ¢ to 720.0 ¢
Major 9-mosstep M9ms 9L 720.0 ¢ to 771.4 ¢
10-mosstep Minor 10-mosstep m10ms 9L + s 771.4 ¢ to 800.0 ¢
Major 10-mosstep M10ms 10L 800.0 ¢ to 857.1 ¢
11-mosstep Minor 11-mosstep m11ms 10L + s 857.1 ¢ to 880.0 ¢
Major 11-mosstep M11ms 11L 880.0 ¢ to 942.9 ¢
12-mosstep Minor 12-mosstep m12ms 11L + s 942.9 ¢ to 960.0 ¢
Major 12-mosstep M12ms 12L 960.0 ¢ to 1028.6 ¢
13-mosstep Minor 13-mosstep m13ms 12L + s 1028.6 ¢ to 1040.0 ¢
Major 13-mosstep M13ms 13L 1040.0 ¢ to 1114.3 ¢
14-mosstep Perfect 14-mosstep P14ms 13L + s 1114.3 ¢ to 1120.0 ¢
Augmented 14-mosstep A14ms 14L 1120.0 ¢ to 1200.0 ¢
15-mosstep Perfect 15-mosstep P15ms 14L + s 1200.0 ¢

Generator chain

Generator chain of 14L 1s
Bright gens Scale degree Abbrev.
28 Augmented 13-mosdegree A13md
27 Augmented 12-mosdegree A12md
26 Augmented 11-mosdegree A11md
25 Augmented 10-mosdegree A10md
24 Augmented 9-mosdegree A9md
23 Augmented 8-mosdegree A8md
22 Augmented 7-mosdegree A7md
21 Augmented 6-mosdegree A6md
20 Augmented 5-mosdegree A5md
19 Augmented 4-mosdegree A4md
18 Augmented 3-mosdegree A3md
17 Augmented 2-mosdegree A2md
16 Augmented 1-mosdegree A1md
15 Augmented 0-mosdegree A0md
14 Augmented 14-mosdegree A14md
13 Major 13-mosdegree M13md
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 15-mosdegree		 P0md
P15md
−1 Perfect 14-mosdegree P14md
−2 Minor 13-mosdegree m13md
−3 Minor 12-mosdegree m12md
−4 Minor 11-mosdegree m11md
−5 Minor 10-mosdegree m10md
−6 Minor 9-mosdegree m9md
−7 Minor 8-mosdegree m8md
−8 Minor 7-mosdegree m7md
−9 Minor 6-mosdegree m6md
−10 Minor 5-mosdegree m5md
−11 Minor 4-mosdegree m4md
−12 Minor 3-mosdegree m3md
−13 Minor 2-mosdegree m2md
−14 Diminished 1-mosdegree d1md
−15 Diminished 15-mosdegree d15md
−16 Diminished 14-mosdegree d14md
−17 Diminished 13-mosdegree d13md
−18 Diminished 12-mosdegree d12md
−19 Diminished 11-mosdegree d11md
−20 Diminished 10-mosdegree d10md
−21 Diminished 9-mosdegree d9md
−22 Diminished 8-mosdegree d8md
−23 Diminished 7-mosdegree d7md
−24 Diminished 6-mosdegree d6md
−25 Diminished 5-mosdegree d5md
−26 Diminished 4-mosdegree d4md
−27 Diminished 3-mosdegree d3md
−28 Diminished 2-mosdegree d2md

Modes

Scale degrees of the modes of 14L 1s
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 LLLLLLLLLLLLLLs Perf. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Aug. Perf.
13|1 2 LLLLLLLLLLLLLsL Perf. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf.
12|2 3 LLLLLLLLLLLLsLL Perf. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Min. Perf. Perf.
11|3 4 LLLLLLLLLLLsLLL Perf. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Min. Min. Perf. Perf.
10|4 5 LLLLLLLLLLsLLLL Perf. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Min. Min. Min. Perf. Perf.
9|5 6 LLLLLLLLLsLLLLL Perf. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Min. Min. Min. Min. Perf. Perf.
8|6 7 LLLLLLLLsLLLLLL Perf. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Min. Min. Min. Min. Min. Perf. Perf.
7|7 8 LLLLLLLsLLLLLLL Perf. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Min. Min. Min. Min. Min. Min. Perf. Perf.
6|8 9 LLLLLLsLLLLLLLL Perf. Perf. Maj. Maj. Maj. Maj. Maj. Min. Min. Min. Min. Min. Min. Min. Perf. Perf.
5|9 10 LLLLLsLLLLLLLLL Perf. Perf. Maj. Maj. Maj. Maj. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Perf.
4|10 11 LLLLsLLLLLLLLLL Perf. Perf. Maj. Maj. Maj. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Perf.
3|11 12 LLLsLLLLLLLLLLL Perf. Perf. Maj. Maj. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Perf.
2|12 13 LLsLLLLLLLLLLLL Perf. Perf. Maj. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Perf.
1|13 14 LsLLLLLLLLLLLLL Perf. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Perf.
0|14 15 sLLLLLLLLLLLLLL Perf. Dim. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Perf.

Scale tree

Scale tree and tuning spectrum of 14L 1s
Generator(edo) Cents Step ratio Comments(always proper)
Bright Dark L:s Hardness
1\15 80.000 1120.000 1:1 1.000 Equalized 14L 1s
6\89 80.899 1119.101 6:5 1.200
5\74 81.081 1118.919 5:4 1.250
9\133 81.203 1118.797 9:7 1.286
4\59 81.356 1118.644 4:3 1.333 Supersoft 14L 1s
11\162 81.481 1118.519 11:8 1.375
7\103 81.553 1118.447 7:5 1.400
10\147 81.633 1118.367 10:7 1.429
3\44 81.818 1118.182 3:2 1.500 Soft 14L 1s
Nautilus
11\161 81.988 1118.012 11:7 1.571
8\117 82.051 1117.949 8:5 1.600
13\190 82.105 1117.895 13:8 1.625
5\73 82.192 1117.808 5:3 1.667 Semisoft 14L 1s
12\175 82.286 1117.714 12:7 1.714
7\102 82.353 1117.647 7:4 1.750
9\131 82.443 1117.557 9:5 1.800
2\29 82.759 1117.241 2:1 2.000 Basic 14L 1s
9\130 83.077 1116.923 9:4 2.250 ↕ Sextilififths
7\101 83.168 1116.832 7:3 2.333
12\173 83.237 1116.763 12:5 2.400
5\72 83.333 1116.667 5:2 2.500 Semihard 14L 1s
13\187 83.422 1116.578 13:5 2.600
8\115 83.478 1116.522 8:3 2.667
11\158 83.544 1116.456 11:4 2.750
3\43 83.721 1116.279 3:1 3.000 Hard 14L 1s
10\143 83.916 1116.084 10:3 3.333
7\100 84.000 1116.000 7:2 3.500
11\157 84.076 1115.924 11:3 3.667
4\57 84.211 1115.789 4:1 4.000 Superhard 14L 1s
9\128 84.375 1115.625 9:2 4.500
5\71 84.507 1115.493 5:1 5.000
6\85 84.706 1115.294 6:1 6.000
1\14 85.714 1114.286 1:0 → ∞ Collapsed 14L 1s
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