15L 1s: Difference between revisions

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== Scale tree ==
== Scale tree ==
{| class="wikitable"
{{Scale tree|Comments=8/3: [[Valentine]];
! colspan="9" | generator
9/5: [[Tertia]] / [[Tertiaseptal]];}}
! L
! s
! L/s
! gen (cents)
! comment
|-
| 1\15
|
|
|
|
|
|
|
|
| 1
| 0
|
| 80.000
|
|-
|
|
|
|
|
|
|
|
| 9\136
| 9
| 1
| 9.000
| 79.412
|
|-
|
|
|
|
|
|
|
| 8\121
|
| 8
| 1
| 8.000
| 79.339
|
|-
|
|
|
|
|
|
| 7\106
|
|
| 7
| 1
| 7.000
| 79.245
|
|-
|
|
|
|
|
| 6\91
|
|
|
| 6
| 1
| 6.000
| 79.121
|
|-
|
|
|
|
| 5\76
|
|
|
|
| 5
| 1
| 5.000
| 78.947
|
|-
|
|
|
| 4\61
|
|
|
|
|
| 4
| 1
| 4.000
| 78.689
|
|-
|
|
|
|
| 7\107
|
|
|
|
| 7
| 2
| 3.500
| 78.505
|
|-
|
|
| 3\46
|
|
|
|
|
|
| 3
| 1
| 3.000
| 78.261
|
|-
|
|
|
|
| 8\123
|
|
|
|
| 8
| 3
| 2.667
| 78.049
|
|-
|
|
|
| 5\77
|
|
|
|
|
| 5
| 2
| 2.500
| 77.922
|
|-
|
|
|
|
| 7\108
|
|
|
|
| 7
| 3
| 2.333
| 77.778
| Valentine is around here
|-
|
| 2\31
|
|
|
|
|
|
|
| 2
| 1
| 2.000
| 77.419
|
|-
|
|
|
|
| 7\109
|
|
|
|
| 7
| 4
| 1.750
| 77.064
| Tertia / Tertiaseptal are around here
|-
|
|
|
| 5\78
|
|
|
|
|
| 5
| 3
| 1.667
| 76.923
|
|-
|
|
|
|
| 8\125
|
|
|
|
| 8
| 5
| 1.600
| 76.800
|
|-
|
|
| 3\47
|
|
|
|
|
|
| 3
| 2
| 1.500
| 76.596
|
|-
|
|
|
|
| 7\110
|
|
|
|
| 7
| 5
| 1.400
| 76.364
|
|-
|
|
|
| 4\63
|
|
|
|
|
| 4
| 3
| 1.333
| 76.190
|
|-
|
|
|
|
| 5\79
|
|
|
|
| 5
| 4
| 1.250
| 75.949
|
|-
|
|
|
|
|
| 6\95
|
|
|
| 6
| 5
| 1.200
| 75.789
|
|-
|
|
|
|
|
|
| 7\111
|
|
| 7
| 6
| 1.167
| 75.676
|
|-
|
|
|
|
|
|
|
| 8\127
|
| 8
| 7
| 1.143
| 75.591
|
|-
|
|
|
|
|
|
|
|
| 9\143
| 9
| 8
| 1.125
| 75.5245
|
|-
| 1\16
|
|
|
|
|
|
|
|
| 1
| 1
| 1.000
| 75.000
|
|}

Revision as of 07:37, 1 March 2024

← 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 ¢)
View • Talk • Edit

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. It is notable for corresponding to valentine[16].

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
Retrieved from "https://en.xen.wiki/index.php?title=15L_1s&oldid=137709"