1L 10s: Difference between revisions

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{{Todo|review|inline=1|text=Adopt scale tree template, review entries}}{{Infobox MOS}}
{{Infobox MOS}}
{{MOS intro}}
{{MOS intro}}
This MOS achieves its simplest harmonic entropy minimum where two generators equal 9/8. The temperament which occupies this harmonic entropy minimum is called Ripple, but there are several lower (and more complex) harmonic entropy minima of note including (in descending order of generator height): Passion (6/5 = +3 generators), Octacot (3/2 = +8 generators), Nautilus (3/2 = -6 generators) and Valentine (7/4 = -3 generators).
This MOS achieves its simplest harmonic entropy minimum where two generators equal 9/8. The temperament which occupies this harmonic entropy minimum is called Ripple, but there are several lower (and more complex) harmonic entropy minima of note including (in descending order of generator height): Passion (6/5 = +3 generators), Octacot (3/2 = +8 generators), Nautilus (3/2 = -6 generators) and Valentine (7/4 = -3 generators).
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* Chroma-positive generator: 1090.9091 cents (10\11) to 1200 cents (1\1)
* Chroma-positive generator: 1090.9091 cents (10\11) to 1200 cents (1\1)
* Chroma-negative generator: 0 cents (0\1) to 109.0909 cents (1\11)
* Chroma-negative generator: 0 cents (0\1) to 109.0909 cents (1\11)
 
{{Scale tree}}
{| class="wikitable center-all"
! colspan="6" | Small step <br><span style="font-size:0.85em">(chroma-negative generator)</span>
! Cents
! L
! s
! L/s
! Comments
|-
| 1\11 || || || || || || 109.091 || 1 || 1 || 1.000 ||
|-
| || || || || || 5\56 || 107.143 || 6 || 5 || 1.200 ||
|-
| || || || || 4\45 || || 106.667 || 5 || 4 || 1.250 ||
|-
| || || || || || 7\79 || 106.329 || 9 || 7 || 1.286 ||
|-
| || || || 3\34 || || || 105.882 || 4 || 3 || 1.333 ||
|-
| || || || || || 8\91 || 105.495 || 11 || 8 || 1.375 ||
|-
| || || || || 5\57 || || 105.263 || 7 || 5 || 1.400 ||
|-
| || || || || || 7\80 || 105.000 || 10 || 7 || 1.429 || [[Septendesemi]]
|-
| || || 2\23 || || || || 104.348 || 3 || 2 || 1.500 ||
|-
| || || || || || 7\81 || 103.704 || 11 || 7 || 1.571 ||
|-
| || || || || 5\58 || || 103.448 || 8 || 5 || 1.600 ||
|-
| || || || || || 8\93 || 103.226 || 13 || 8 || 1.625 || Golden [[ripple]] (103.2877¢)
|-
| || || || 3\35 || || || 102.857 || 5 || 3 || 1.667 ||
|-
| || || || || || 7\82 || 102.439 || 12 || 7 || 1.714 ||
|-
| || || || || 4\47 || || 102.128 || 7 || 4 || 1.750 ||
|-
| || || || || || 5\59 || 101.695 || 9 || 5 || 1.800 ||
|-
| || 1\12 || || || || || 100.000 || 2 || 1 || 2.000 || Basic 1L 10s <br>(small steps larger than this are proper)
|-
| || || || || || 4\49 || 97.959 || 9 || 4 || 2.250 ||
|-
| || || || || 3\37 || || 97.297 || 7 || 3 || 2.333 || [[Passion]]
|-
| || || || || || 5\62 || 96.774 || 12 || 5 || 2.400 ||
|-
| || || || 2\25 || || || 96.000 || 5 || 2 || 2.500 ||
|-
| || || || || || 5\63 || 95.238 || 13 || 5 || 2.600 || Unnamed golden tuning (95.102¢)
|-
| || || || || 3\38 || || 94.737 || 8 || 3 || 2.667 ||
|-
| || || || || || 4\51 || 94.118 || 11 || 4 || 2.750 ||
|-
| || || 1\13 || || || || 92.308 || 3 || 1 || 3.000 ||
|-
| || || || || || 3\40 || 90.000 || 10 || 3 || 3.333 ||
|-
| || || || || 2\27 || || 88.889 || 7 || 2 || 3.500 ||
|-
| || || || || || 3\41 || 87.805 || 11 || 3 || 3.667 || [[Octacot]]
|-
| || || || 1\14 || || || 85.714 || 4 || 1 || 4.000 ||
|-
| || || || || || 2\29 || 82.759 || 9 || 2 || 4.500 ||
|-
| || || || || 1\15 || || 80.000 || 5 || 1 || 5.000 || [[Valentine]]
|-
| || || || || || 1\16 || 75.000 || 6 || 1 || 6.000 ||
|-
| 0\1 || || || || || || 0.000 || 1 || 0 || → inf ||
|}


[[Category:11-tone scales]]
[[Category:11-tone scales]]

Revision as of 20:42, 22 September 2024

↑ 1L 9s 2L 9s ↗
1L 10s 2L 10s →
↓ 1L 11s 2L 11s ↘
Scale structure
Step pattern Lssssssssss
ssssssssssL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 10\11 to 1\1 (1090.9 ¢ to 1200.0 ¢)
Dark 0\1 to 1\11 (0.0 ¢ to 109.1 ¢)
TAMNAMS information
Related to 1L 9s (antisinatonic)
With tunings 2:1 to 1:0 (hard-of-basic)
Related MOS scales
Parent 1L 9s
Sister 10L 1s
Daughters 11L 1s, 1L 11s
Neutralized 2L 9s
2-Flought 12L 10s, 1L 21s
Equal tunings
Equalized (L:s = 1:1) 10\11 (1090.9 ¢)
Supersoft (L:s = 4:3) 31\34 (1094.1 ¢)
Soft (L:s = 3:2) 21\23 (1095.7 ¢)
Semisoft (L:s = 5:3) 32\35 (1097.1 ¢)
Basic (L:s = 2:1) 11\12 (1100.0 ¢)
Semihard (L:s = 5:2) 23\25 (1104.0 ¢)
Hard (L:s = 3:1) 12\13 (1107.7 ¢)
Superhard (L:s = 4:1) 13\14 (1114.3 ¢)
Collapsed (L:s = 1:0) 1\1 (1200.0 ¢)
View • Talk • Edit

1L 10s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 1 large step and 10 small steps, repeating every octave. 1L 10s is a child scale of 1L 9s, expanding it by 1 tones. Generators that produce this scale range from 1090.9 ¢ to 1200 ¢, or from 0 ¢ to 109.1 ¢. This MOS achieves its simplest harmonic entropy minimum where two generators equal 9/8. The temperament which occupies this harmonic entropy minimum is called Ripple, but there are several lower (and more complex) harmonic entropy minima of note including (in descending order of generator height): Passion (6/5 = +3 generators), Octacot (3/2 = +8 generators), Nautilus (3/2 = -6 generators) and Valentine (7/4 = -3 generators).

Modes

Modes of 1L 10s
UDP Cyclic
order		 Step
pattern
10|0 1 Lssssssssss
9|1 11 sLsssssssss
8|2 10 ssLssssssss
7|3 9 sssLsssssss
6|4 8 ssssLssssss
5|5 7 sssssLsssss
4|6 6 ssssssLssss
3|7 5 sssssssLsss
2|8 4 ssssssssLss
1|9 3 sssssssssLs
0|10 2 ssssssssssL

Scale tree

Generator ranges:

  • Chroma-positive generator: 1090.9091 cents (10\11) to 1200 cents (1\1)
  • Chroma-negative generator: 0 cents (0\1) to 109.0909 cents (1\11)
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 1L 10s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
10\11 1090.909 109.091 1:1 1.000 Equalized 1L 10s
51\56 1092.857 107.143 6:5 1.200
41\45 1093.333 106.667 5:4 1.250
72\79 1093.671 106.329 9:7 1.286
31\34 1094.118 105.882 4:3 1.333 Supersoft 1L 10s
83\91 1094.505 105.495 11:8 1.375
52\57 1094.737 105.263 7:5 1.400
73\80 1095.000 105.000 10:7 1.429
21\23 1095.652 104.348 3:2 1.500 Soft 1L 10s
74\81 1096.296 103.704 11:7 1.571
53\58 1096.552 103.448 8:5 1.600
85\93 1096.774 103.226 13:8 1.625
32\35 1097.143 102.857 5:3 1.667 Semisoft 1L 10s
75\82 1097.561 102.439 12:7 1.714
43\47 1097.872 102.128 7:4 1.750
54\59 1098.305 101.695 9:5 1.800
11\12 1100.000 100.000 2:1 2.000 Basic 1L 10s
Scales with tunings softer than this are proper
45\49 1102.041 97.959 9:4 2.250
34\37 1102.703 97.297 7:3 2.333
57\62 1103.226 96.774 12:5 2.400
23\25 1104.000 96.000 5:2 2.500 Semihard 1L 10s
58\63 1104.762 95.238 13:5 2.600
35\38 1105.263 94.737 8:3 2.667
47\51 1105.882 94.118 11:4 2.750
12\13 1107.692 92.308 3:1 3.000 Hard 1L 10s
37\40 1110.000 90.000 10:3 3.333
25\27 1111.111 88.889 7:2 3.500
38\41 1112.195 87.805 11:3 3.667
13\14 1114.286 85.714 4:1 4.000 Superhard 1L 10s
27\29 1117.241 82.759 9:2 4.500
14\15 1120.000 80.000 5:1 5.000
15\16 1125.000 75.000 6:1 6.000
1\1 1200.000 0.000 1:0 → ∞ Collapsed 1L 10s
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