1L 9s: Difference between revisions

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{{MOS intro}}
{{MOS intro}}
This MOS is also called the "Happy" decatonic scale in [[Graham Breed's MOS naming scheme|Graham Breed's naming system]]. It is the simplest MOS which may be used as a complete version of [[Miracle]] temperament, which is also its harmonic entropy minimum.
This scale is the simplest MOS which may be used as a complete version{{Clarify}} of [[Miracle]] temperament, which is also its harmonic entropy minimum.
 
This scale is known as the "Happy" decatonic scale in [[Graham Breed's MOS naming scheme|Graham Breed's naming system]].


== Modes ==
== Modes ==
Line 24: Line 26:
* 0|9 sssssssssL
* 0|9 sssssssssL


== Scale tree ==
== Scale tree==
Generator ranges:
{{Scale tree|Comments=9/7: [[Miracle]];
* Chroma-positive generator: 1080 cents (9\10) to 1200 cents (1\1)
8/5: [[Misneb]];
* Chroma-negative generator: 0 cents (0\1) to 120 cents (1\10)
3/1: [[Ripple]];
 
13/5: Golden ripple (103.2877¢);
{| class="wikitable center-all"
10/3: [[Passion]] (generators close to 98.670¢);
! colspan="6" | Small step <br><span style="font-size:0.85em">(chroma-negative generator)</span>
6/1: [[Valentine]] (generators close to 78.039¢);}}
! Cents
! L
! s
! L/s
! Comments
|-
| 1\10 || || || || || || 120.000 || 1 || 1 || 1.000 ||
|-
| || || || || || 5\51 || 117.647 || 6 || 5 || 1.200 ||
|-
| || || || || 4\41 || || 117.073 || 5 || 4 || 1.250 ||
|-
| || || || || || 7\72 || 116.667 || 9 || 7 || 1.286 || [[Miracle]]
|-
| || || || 3\31 || || || 116.129 || 4 || 3 || 1.333 ||
|-
| || || || || || 8\83 || 115.663 || 11 || 8 || 1.375 ||
|-
| || || || || 5\52 || || 115.385 || 7 || 5 || 1.400 ||
|-
| || || || || || 7\73 || 115.068 || 10 || 7 || 1.429 ||
|-
| || || 2\21 || || || || 114.286 || 3 || 2 || 1.500 ||
|-
| || || || || || 7\74 || 113.514 || 11 || 7 || 1.571 ||
|-
| || || || || 5\53 || || 113.208 || 8 || 5 || 1.600 ||
|-
| || || || || || 8\85 || 112.941 || 13 || 8 || 1.625 || Golden [[misneb]] (113.0153¢)
|-
| || || || 3\32 || || || 112.500 || 5 || 3 || 1.667 ||
|-
| || || || || || 7\75 || 112.000 || 12 || 7 || 1.714 ||
|-
| || || || || 4\43 || || 111.628 || 7 || 4 || 1.750 ||
|-
| || || || || || 5\54 || 111.111 || 9 || 5 || 1.800 ||
|-
| || 1\11 || || || || || 109.091 || 2 || 1 || 2.000 || Basic 1L 9s <br>(small steps larger than this are proper)
|-
| || || || || || 4\45 || 106.667 || 9 || 4 || 2.250 ||
|-
| || || || || 3\34 || || 105.882 || 7 || 3 || 2.333 ||
|-
| || || || || || 5\57 || 105.263 || 12 || 5 || 2.400 ||
|-
| || || || 2\23 || || || 104.348 || 5 || 2 || 2.500 ||
|-
| || || || || || 5\58 || 103.448 || 13 || 5 || 2.600 || Golden [[ripple]] (103.2877¢)
|-
| || || || || 3\35 || || 102.857 || 8 || 3 || 2.667 ||
|-
| || || || || || 4\47 || 102.128 || 11 || 4 || 2.750 ||
|-
| || || 1\12 || || || || 100.000 || 3 || 1 || 3.000 || Ripple
|-
| || || || || || 3\37 || 97.297 || 10 || 3 || 3.333 || [[Passion]]
|-
| || || || || 2\25 || || 96.000 || 7 || 2 || 3.500 ||
|-
| || || || || || 3\38 || 94.737 || 11 || 3 || 3.667 ||
|-
| || || || 1\13 || || || 92.308 || 4 || 1 || 4.000 ||
|-
| || || || || || 2\27 || 88.889 || 9 || 2 || 4.500 ||
|-
| || || || || 1\14 || || 85.714 || 5 || 1 || 5.000 ||
|-
| || || || || || 1\15 || 80.000 || 6 || 1 || 6.000 || [[Valentine]]
|-
| 0\1 || || || || || || 0.000 || 1 || 0 || → inf ||
|}


[[Category:10-tone scales]]
[[Category:10-tone scales]]

Revision as of 02:16, 2 March 2024

↑ 1L 8s 2L 8s ↗
1L 9s 2L 9s →
↓ 1L 10s 2L 10s ↘
Scale structure
Step pattern Lsssssssss
sssssssssL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 9\10 to 1\1 (1080.0 ¢ to 1200.0 ¢)
Dark 0\1 to 1\10 (0.0 ¢ to 120.0 ¢)
TAMNAMS information
Name antisinatonic
Prefix asina-
Abbrev. asi
Related MOS scales
Parent 1L 8s
Sister 9L 1s
Daughters 10L 1s, 1L 10s
Neutralized 2L 8s
2-Flought 11L 9s, 1L 19s
Equal tunings
Equalized (L:s = 1:1) 9\10 (1080.0 ¢)
Supersoft (L:s = 4:3) 28\31 (1083.9 ¢)
Soft (L:s = 3:2) 19\21 (1085.7 ¢)
Semisoft (L:s = 5:3) 29\32 (1087.5 ¢)
Basic (L:s = 2:1) 10\11 (1090.9 ¢)
Semihard (L:s = 5:2) 21\23 (1095.7 ¢)
Hard (L:s = 3:1) 11\12 (1100.0 ¢)
Superhard (L:s = 4:1) 12\13 (1107.7 ¢)
Collapsed (L:s = 1:0) 1\1 (1200.0 ¢)
View • Talk • Edit

1L 9s, named antisinatonic in TAMNAMS, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 1 large step and 9 small steps, repeating every octave. Generators that produce this scale range from 1080 ¢ to 1200 ¢, or from 0 ¢ to 120 ¢. This scale is the simplest MOS which may be used as a complete version[clarification needed] of Miracle temperament, which is also its harmonic entropy minimum.

This scale is known as the "Happy" decatonic scale in Graham Breed's naming system.

Modes

  • 9|0 Lsssssssss
  • 8|1 sLssssssss
  • 7|2 ssLsssssss
  • 6|3 sssLssssss
  • 5|4 ssssLsssss
  • 4|5 sssssLssss
  • 3|6 ssssssLsss
  • 2|7 sssssssLss
  • 1|8 ssssssssLs
  • 0|9 sssssssssL

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 1L 9s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
9\10 1080.000 120.000 1:1 1.000 Equalized 1L 9s
46\51 1082.353 117.647 6:5 1.200
37\41 1082.927 117.073 5:4 1.250
65\72 1083.333 116.667 9:7 1.286
28\31 1083.871 116.129 4:3 1.333 Supersoft 1L 9s
75\83 1084.337 115.663 11:8 1.375
47\52 1084.615 115.385 7:5 1.400
66\73 1084.932 115.068 10:7 1.429
19\21 1085.714 114.286 3:2 1.500 Soft 1L 9s
67\74 1086.486 113.514 11:7 1.571
48\53 1086.792 113.208 8:5 1.600
77\85 1087.059 112.941 13:8 1.625
29\32 1087.500 112.500 5:3 1.667 Semisoft 1L 9s
68\75 1088.000 112.000 12:7 1.714
39\43 1088.372 111.628 7:4 1.750
49\54 1088.889 111.111 9:5 1.800
10\11 1090.909 109.091 2:1 2.000 Basic 1L 9s
Scales with tunings softer than this are proper
41\45 1093.333 106.667 9:4 2.250
31\34 1094.118 105.882 7:3 2.333
52\57 1094.737 105.263 12:5 2.400
21\23 1095.652 104.348 5:2 2.500 Semihard 1L 9s
53\58 1096.552 103.448 13:5 2.600
32\35 1097.143 102.857 8:3 2.667
43\47 1097.872 102.128 11:4 2.750
11\12 1100.000 100.000 3:1 3.000 Hard 1L 9s
34\37 1102.703 97.297 10:3 3.333
23\25 1104.000 96.000 7:2 3.500
35\38 1105.263 94.737 11:3 3.667
12\13 1107.692 92.308 4:1 4.000 Superhard 1L 9s
25\27 1111.111 88.889 9:2 4.500
13\14 1114.286 85.714 5:1 5.000
14\15 1120.000 80.000 6:1 6.000
1\1 1200.000 0.000 1:0 → ∞ Collapsed 1L 9s
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