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15L 1s

Revision as of 07:36, 15 December 2024 by BudjarnLambeth (talk | contribs) (== Intervals == {{MOS intervals}})

15L 1s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 15 large steps and 1 small step, repeating every octave. 15L 1s is related to 1L 9s, expanding it by 6 tones. Generators that produce this scale range from 75 ¢ to 80 ¢, or from 1120 ¢ to 1125 ¢. Scales of this form are always proper because there is only one small step.

← 14L 1s 15L 1s 16L 1s →
↙ 14L 2s ↓ 15L 2s 16L 2s ↘
Scale structure
Step pattern LLLLLLLLLLLLLLLs
sLLLLLLLLLLLLLLL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 1\16 to 1\15 (75.0 ¢ to 80.0 ¢)
Dark 14\15 to 15\16 (1120.0 ¢ to 1125.0 ¢)
TAMNAMS information
Related to 1L 9s (antisinatonic)
With tunings 6:1 to 7:1
Related MOS scales
Parent 1L 14s
Sister 1L 15s
Daughters 16L 15s, 15L 16s
Neutralized 14L 2s
2-Flought 31L 1s, 15L 17s
Equal tunings
Equalized (L:s = 1:1) 1\16 (75.0 ¢)
Supersoft (L:s = 4:3) 4\63 (76.2 ¢)
Soft (L:s = 3:2) 3\47 (76.6 ¢)
Semisoft (L:s = 5:3) 5\78 (76.9 ¢)
Basic (L:s = 2:1) 2\31 (77.4 ¢)
Semihard (L:s = 5:2) 5\77 (77.9 ¢)
Hard (L:s = 3:1) 3\46 (78.3 ¢)
Superhard (L:s = 4:1) 4\61 (78.7 ¢)
Collapsed (L:s = 1:0) 1\15 (80.0 ¢)
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It is notable for corresponding to valentine[16].

Modes

Modes of 15L 1s
UDP Cyclic
order		 Step
pattern
15|0 1 LLLLLLLLLLLLLLLs
14|1 2 LLLLLLLLLLLLLLsL
13|2 3 LLLLLLLLLLLLLsLL
12|3 4 LLLLLLLLLLLLsLLL
11|4 5 LLLLLLLLLLLsLLLL
10|5 6 LLLLLLLLLLsLLLLL
9|6 7 LLLLLLLLLsLLLLLL
8|7 8 LLLLLLLLsLLLLLLL
7|8 9 LLLLLLLsLLLLLLLL
6|9 10 LLLLLLsLLLLLLLLL
5|10 11 LLLLLsLLLLLLLLLL
4|11 12 LLLLsLLLLLLLLLLL
3|12 13 LLLsLLLLLLLLLLLL
2|13 14 LLsLLLLLLLLLLLLL
1|14 15 LsLLLLLLLLLLLLLL
0|15 16 sLLLLLLLLLLLLLLL

Intervals

Intervals of 15L 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 75.0 ¢
Perfect 1-mosstep P1ms L 75.0 ¢ to 80.0 ¢
2-mosstep Minor 2-mosstep m2ms L + s 80.0 ¢ to 150.0 ¢
Major 2-mosstep M2ms 2L 150.0 ¢ to 160.0 ¢
3-mosstep Minor 3-mosstep m3ms 2L + s 160.0 ¢ to 225.0 ¢
Major 3-mosstep M3ms 3L 225.0 ¢ to 240.0 ¢
4-mosstep Minor 4-mosstep m4ms 3L + s 240.0 ¢ to 300.0 ¢
Major 4-mosstep M4ms 4L 300.0 ¢ to 320.0 ¢
5-mosstep Minor 5-mosstep m5ms 4L + s 320.0 ¢ to 375.0 ¢
Major 5-mosstep M5ms 5L 375.0 ¢ to 400.0 ¢
6-mosstep Minor 6-mosstep m6ms 5L + s 400.0 ¢ to 450.0 ¢
Major 6-mosstep M6ms 6L 450.0 ¢ to 480.0 ¢
7-mosstep Minor 7-mosstep m7ms 6L + s 480.0 ¢ to 525.0 ¢
Major 7-mosstep M7ms 7L 525.0 ¢ to 560.0 ¢
8-mosstep Minor 8-mosstep m8ms 7L + s 560.0 ¢ to 600.0 ¢
Major 8-mosstep M8ms 8L 600.0 ¢ to 640.0 ¢
9-mosstep Minor 9-mosstep m9ms 8L + s 640.0 ¢ to 675.0 ¢
Major 9-mosstep M9ms 9L 675.0 ¢ to 720.0 ¢
10-mosstep Minor 10-mosstep m10ms 9L + s 720.0 ¢ to 750.0 ¢
Major 10-mosstep M10ms 10L 750.0 ¢ to 800.0 ¢
11-mosstep Minor 11-mosstep m11ms 10L + s 800.0 ¢ to 825.0 ¢
Major 11-mosstep M11ms 11L 825.0 ¢ to 880.0 ¢
12-mosstep Minor 12-mosstep m12ms 11L + s 880.0 ¢ to 900.0 ¢
Major 12-mosstep M12ms 12L 900.0 ¢ to 960.0 ¢
13-mosstep Minor 13-mosstep m13ms 12L + s 960.0 ¢ to 975.0 ¢
Major 13-mosstep M13ms 13L 975.0 ¢ to 1040.0 ¢
14-mosstep Minor 14-mosstep m14ms 13L + s 1040.0 ¢ to 1050.0 ¢
Major 14-mosstep M14ms 14L 1050.0 ¢ to 1120.0 ¢
15-mosstep Perfect 15-mosstep P15ms 14L + s 1120.0 ¢ to 1125.0 ¢
Augmented 15-mosstep A15ms 15L 1125.0 ¢ to 1200.0 ¢
16-mosstep Perfect 16-mosstep P16ms 15L + s 1200.0 ¢

Scale tree

  Template: Scale tree is deprecated. Please use Template: MOS tuning spectrum instead. Details:
Use of a single Comments parameter has become unmaintainable. Existing scale trees should be migrated to the new template, where comments are entered using a step ratio p/q as a parameter: 
{{MOS tuning spectrum
| 3/2 = Example comment
| 4/3 = Another example comment
}}


The parameters tuning and depth have been replaced with Scale Signature and Depth, respectively.


Scale tree and tuning spectrum of 15L 1s
Generator(edo) Cents Step ratio Comments(always proper)
Bright Dark L:s Hardness
1\16 75.000 1125.000 1:1 1.000 Equalized 15L 1s
6\95 75.789 1124.211 6:5 1.200
5\79 75.949 1124.051 5:4 1.250
9\142 76.056 1123.944 9:7 1.286
4\63 76.190 1123.810 4:3 1.333 Supersoft 15L 1s
11\173 76.301 1123.699 11:8 1.375
7\110 76.364 1123.636 7:5 1.400
10\157 76.433 1123.567 10:7 1.429
3\47 76.596 1123.404 3:2 1.500 Soft 15L 1s
11\172 76.744 1123.256 11:7 1.571
8\125 76.800 1123.200 8:5 1.600
13\203 76.847 1123.153 13:8 1.625
5\78 76.923 1123.077 5:3 1.667 Semisoft 15L 1s
12\187 77.005 1122.995 12:7 1.714
7\109 77.064 1122.936 7:4 1.750
9\140 77.143 1122.857 9:5 1.800
2\31 77.419 1122.581 2:1 2.000 Basic 15L 1s
9\139 77.698 1122.302 9:4 2.250
7\108 77.778 1122.222 7:3 2.333
12\185 77.838 1122.162 12:5 2.400
5\77 77.922 1122.078 5:2 2.500 Semihard 15L 1s
13\200 78.000 1122.000 13:5 2.600
8\123 78.049 1121.951 8:3 2.667
11\169 78.107 1121.893 11:4 2.750
3\46 78.261 1121.739 3:1 3.000 Hard 15L 1s
10\153 78.431 1121.569 10:3 3.333
7\107 78.505 1121.495 7:2 3.500
11\168 78.571 1121.429 11:3 3.667
4\61 78.689 1121.311 4:1 4.000 Superhard 15L 1s
9\137 78.832 1121.168 9:2 4.500
5\76 78.947 1121.053 5:1 5.000
6\91 79.121 1120.879 6:1 6.000
1\15 80.000 1120.000 1:0 → ∞ Collapsed 15L 1s


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