1L 9s: Difference between revisions

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| nSmallSteps = 9
| nSmallSteps = 9
| Equalized = 9
| Equalized = 9
| Paucitonic = 1
| Collapsed = 1
| Pattern = Lsssssssss
| Pattern = Lsssssssss
}}
}}


This MOS, generated by any interval up to a diatonic semitone of 1/10edo (120 cents), is called the "Happy" decatonic scale in Graham Breed's system, or, potentially, antisinatonic in [[TAMNAMS]] by analogy to its sister MOS. It is the simplest MOS which may be used as a complete version of [[Miracle]] temperament, which is also its harmonic entropy minimum.
{{MOS intro}}


== Modes ==
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.
* 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 ==
This scale is known as the '''Happy decatonic scale''' in [[Graham Breed's MOS naming scheme|Graham Breed's naming system]].
Generator ranges:
* Chroma-positive generator: 1080 cents (9\10) to 1200 cents (1\1)
* Chroma-negative generator: 0 cents (0\1) to 120 cents (1\10)


{| class="wikitable center-all"
== Scale properties ==
! colspan="6" | Small step <br><span style="font-size:0.85em">(chroma-negative generator)</span>
{{TAMNAMS use}}
! Cents
 
! L
=== Intervals ===
! s
{{MOS intervals}}
! L/s
 
! Comments
=== Generator chain ===
|-
{{MOS genchain}}
| 1\10 || || || || || || 120.000 || 1 || 1 || 1.000 ||
 
|-
=== Modes ===
| || || || || || 5\51 || 117.647 || 6 || 5 || 1.200 ||
{{MOS mode degrees}}
|-
 
| || || || || 4\41 || || 117.073 || 5 || 4 || 1.250 ||
== Scale tree==
|-
{{MOS tuning spectrum
| || || || || || 7\72 || 116.667 || 9 || 7 || 1.286 || [[Miracle]]
| 9/7 = [[Miracle]]
|-
| 8/5 = [[Misneb]]
| || || || 3\31 || || || 116.129 || 4 || 3 || 1.333 ||
| 3/1 = [[Ripple]]
|-
| 13/5 = Golden ripple (103.288¢)
| || || || || || 8\83 || 115.663 || 11 || 8 || 1.375 ||
| 10/3 = [[Passion]]
|-
| 6/1 = [[Nautilus]], [[nuke]], ↓[[valentine]]
| || || || || 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 || Unnamed golden tuning (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:Abstract MOS patterns]]
[[Category:10-tone scales]]
[[Category:10-tone scales]]

Latest revision as of 18:50, 3 March 2025

↑ 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.

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 interval regions.

Intervals

Intervals of 1L 9s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-asinastep Perfect 0-asinastep P0asis 0 0.0 ¢
1-asinastep Perfect 1-asinastep P1asis s 0.0 ¢ to 120.0 ¢
Augmented 1-asinastep A1asis L 120.0 ¢ to 1200.0 ¢
2-asinastep Minor 2-asinastep m2asis 2s 0.0 ¢ to 240.0 ¢
Major 2-asinastep M2asis L + s 240.0 ¢ to 1200.0 ¢
3-asinastep Minor 3-asinastep m3asis 3s 0.0 ¢ to 360.0 ¢
Major 3-asinastep M3asis L + 2s 360.0 ¢ to 1200.0 ¢
4-asinastep Minor 4-asinastep m4asis 4s 0.0 ¢ to 480.0 ¢
Major 4-asinastep M4asis L + 3s 480.0 ¢ to 1200.0 ¢
5-asinastep Minor 5-asinastep m5asis 5s 0.0 ¢ to 600.0 ¢
Major 5-asinastep M5asis L + 4s 600.0 ¢ to 1200.0 ¢
6-asinastep Minor 6-asinastep m6asis 6s 0.0 ¢ to 720.0 ¢
Major 6-asinastep M6asis L + 5s 720.0 ¢ to 1200.0 ¢
7-asinastep Minor 7-asinastep m7asis 7s 0.0 ¢ to 840.0 ¢
Major 7-asinastep M7asis L + 6s 840.0 ¢ to 1200.0 ¢
8-asinastep Minor 8-asinastep m8asis 8s 0.0 ¢ to 960.0 ¢
Major 8-asinastep M8asis L + 7s 960.0 ¢ to 1200.0 ¢
9-asinastep Diminished 9-asinastep d9asis 9s 0.0 ¢ to 1080.0 ¢
Perfect 9-asinastep P9asis L + 8s 1080.0 ¢ to 1200.0 ¢
10-asinastep Perfect 10-asinastep P10asis L + 9s 1200.0 ¢

Generator chain

Generator chain of 1L 9s
Bright gens Scale degree Abbrev.
10 Augmented 0-asinadegree A0asid
9 Augmented 1-asinadegree A1asid
8 Major 2-asinadegree M2asid
7 Major 3-asinadegree M3asid
6 Major 4-asinadegree M4asid
5 Major 5-asinadegree M5asid
4 Major 6-asinadegree M6asid
3 Major 7-asinadegree M7asid
2 Major 8-asinadegree M8asid
1 Perfect 9-asinadegree P9asid
0 Perfect 0-asinadegree
Perfect 10-asinadegree		 P0asid
P10asid
−1 Perfect 1-asinadegree P1asid
−2 Minor 2-asinadegree m2asid
−3 Minor 3-asinadegree m3asid
−4 Minor 4-asinadegree m4asid
−5 Minor 5-asinadegree m5asid
−6 Minor 6-asinadegree m6asid
−7 Minor 7-asinadegree m7asid
−8 Minor 8-asinadegree m8asid
−9 Diminished 9-asinadegree d9asid
−10 Diminished 10-asinadegree d10asid

Modes

Scale degrees of the modes of 1L 9s
UDP Cyclic
order 		Step
pattern 		Scale degree (asinadegree)
0 1 2 3 4 5 6 7 8 9 10
9|0 1 Lsssssssss Perf. Aug. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf.
8|1 10 sLssssssss Perf. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf.
7|2 9 ssLsssssss Perf. Perf. Min. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf.
6|3 8 sssLssssss Perf. Perf. Min. Min. Maj. Maj. Maj. Maj. Maj. Perf. Perf.
5|4 7 ssssLsssss Perf. Perf. Min. Min. Min. Maj. Maj. Maj. Maj. Perf. Perf.
4|5 6 sssssLssss Perf. Perf. Min. Min. Min. Min. Maj. Maj. Maj. Perf. Perf.
3|6 5 ssssssLsss Perf. Perf. Min. Min. Min. Min. Min. Maj. Maj. Perf. Perf.
2|7 4 sssssssLss Perf. Perf. Min. Min. Min. Min. Min. Min. Maj. Perf. Perf.
1|8 3 ssssssssLs Perf. Perf. Min. Min. Min. Min. Min. Min. Min. Perf. Perf.
0|9 2 sssssssssL Perf. Perf. Min. Min. Min. Min. Min. Min. Min. Dim. Perf.

Scale tree

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 Miracle
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 Misneb
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 Golden ripple (103.288¢)
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
Ripple
34\37 1102.703 97.297 10:3 3.333 Passion
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 Nautilus, nuke, ↓valentine
1\1 1200.000 0.000 1:0 → ∞ Collapsed 1L 9s
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