5L 9s: Difference between revisions

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The associated fifth ranges from 8\14 to 3\5, thus guaranteeing a diatonic fifth. 4/3 being approximated by +2 generators, the generator is called a semi-fourth. The most salient feature of the semi-fourth interval is that it is an ambiguous 8/7~7/6, or an approximate 15/13 if the scale is viewed as involving factors of 13. This MOS can be viewed as two parallel [[5L_2s|diatonic]] scales separated by a semi-fourth, and has analogous points of low harmonic entropy where two generators would approximate a [[meantone]] or [[superpyth]] 5th, plus an additional one between 15/13 & sqrt(4/3) where it is ideal for [[The_Archipelago#Barbados|barbados]] subgroup harmonies.
The associated fifth ranges from 8\14 to 3\5, thus guaranteeing a diatonic fifth. 4/3 being approximated by +2 generators, the generator is called a semi-fourth. The most salient feature of the semi-fourth interval is that it is an ambiguous 8/7~7/6, or an approximate 15/13 if the scale is viewed as involving factors of 13. This MOS can be viewed as two parallel [[5L_2s|diatonic]] scales separated by a semi-fourth, and has analogous points of low harmonic entropy where two generators would approximate a [[meantone]] or [[superpyth]] 5th, plus an additional one between 15/13 & sqrt(4/3) where it is ideal for [[The_Archipelago#Barbados|barbados]] subgroup harmonies.


{| class="wikitable"
== Scale tree ==
|-
{{Scale tree}}
| | 1/5
| |
| |
| |
| |
| | 240
|-
| |
| |
| |
| |
| | 7/34
| | 247.059
|-
| |
| |
| |
| | 6/29
| |
| | 248.276
|-
| |
| |
| |
| |
| | 11/53
| | 249.057
|-
| |
| |
| |
| |
| |
| | 249.7135
|-
| |
| |
| | 5/24
| |
| |
| | 250
|-
| |
| |
| |
| |
| |
| | 250.6235
|-
| |
| |
| |
| |
| | 14/67
| | 250.746
|-
| |
| |
| |
| |
| |
| | 250.865
|-
| |
| |
| |
| | 9/43
| |
| | 251.163
|-
| |
| |
| |
| |
| | 13/62
| | 251.613
|-
| |
| | 4/19
| |
| |
| |
| | 252.632
|-
| |
| |
| |
| |
| | 15/71
| | 253.521
|-
| |
| |
| |
| |
| |
| | 253.59
|-
| |
| |
| |
| | 11/52
| |
| | 253.846
|-
| |
| |
| |
| |
| |
| | 254.043
|-
| |
| |
| |
| |
| | 18/85
| | 254.118
|-
| |
| |
| |
| |
| |
| | 254.24
|-
| |
| |
| | 7/33
| |
| |
| | 254.5455
|-
| |
| |
| |
| |
| | 17/80
| | 255
|-
| |
| |
| |
| | 10/47
| |
| | 255.319
|-
| |
| |
| |
| |
| | 13/61
| | 255.738
|-
| | 3/14
| |
| |
| |
| |
| | 257.143
|}


[[Category:14-tone scales]]
[[Category:14-tone scales]]

Revision as of 07:58, 26 February 2024

↖ 4L 8s ↑ 5L 8s 6L 8s ↗
← 4L 9s 5L 9s 6L 9s →
↙ 4L 10s ↓ 5L 10s 6L 10s ↘
Scale structure
Step pattern LsLssLssLssLss
ssLssLssLssLsL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 11\14 to 4\5 (942.9 ¢ to 960.0 ¢)
Dark 1\5 to 3\14 (240.0 ¢ to 257.1 ¢)
TAMNAMS information
Related to 5L 4s (semiquartal)
With tunings 2:1 to 1:0 (hard-of-basic)
Related MOS scales
Parent 5L 4s
Sister 9L 5s
Daughters 14L 5s, 5L 14s
Neutralized 10L 4s
2-Flought 19L 9s, 5L 23s
Equal tunings
Equalized (L:s = 1:1) 11\14 (942.9 ¢)
Supersoft (L:s = 4:3) 37\47 (944.7 ¢)
Soft (L:s = 3:2) 26\33 (945.5 ¢)
Semisoft (L:s = 5:3) 41\52 (946.2 ¢)
Basic (L:s = 2:1) 15\19 (947.4 ¢)
Semihard (L:s = 5:2) 34\43 (948.8 ¢)
Hard (L:s = 3:1) 19\24 (950.0 ¢)
Superhard (L:s = 4:1) 23\29 (951.7 ¢)
Collapsed (L:s = 1:0) 4\5 (960.0 ¢)
View • Talk • Edit

5L 9s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 5 large steps and 9 small steps, repeating every octave. 5L 9s is a child scale of 5L 4s, expanding it by 5 tones. Generators that produce this scale range from 942.9 ¢ to 960 ¢, or from 240 ¢ to 257.1 ¢. The associated fifth ranges from 8\14 to 3\5, thus guaranteeing a diatonic fifth. 4/3 being approximated by +2 generators, the generator is called a semi-fourth. The most salient feature of the semi-fourth interval is that it is an ambiguous 8/7~7/6, or an approximate 15/13 if the scale is viewed as involving factors of 13. This MOS can be viewed as two parallel diatonic scales separated by a semi-fourth, and has analogous points of low harmonic entropy where two generators would approximate a meantone or superpyth 5th, plus an additional one between 15/13 & sqrt(4/3) where it is ideal for barbados subgroup harmonies.

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 5L 9s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
11\14 942.857 257.143 1:1 1.000 Equalized 5L 9s
59\75 944.000 256.000 6:5 1.200
48\61 944.262 255.738 5:4 1.250
85\108 944.444 255.556 9:7 1.286
37\47 944.681 255.319 4:3 1.333 Supersoft 5L 9s
100\127 944.882 255.118 11:8 1.375
63\80 945.000 255.000 7:5 1.400
89\113 945.133 254.867 10:7 1.429
26\33 945.455 254.545 3:2 1.500 Soft 5L 9s
93\118 945.763 254.237 11:7 1.571
67\85 945.882 254.118 8:5 1.600
108\137 945.985 254.015 13:8 1.625
41\52 946.154 253.846 5:3 1.667 Semisoft 5L 9s
97\123 946.341 253.659 12:7 1.714
56\71 946.479 253.521 7:4 1.750
71\90 946.667 253.333 9:5 1.800
15\19 947.368 252.632 2:1 2.000 Basic 5L 9s
Scales with tunings softer than this are proper
64\81 948.148 251.852 9:4 2.250
49\62 948.387 251.613 7:3 2.333
83\105 948.571 251.429 12:5 2.400
34\43 948.837 251.163 5:2 2.500 Semihard 5L 9s
87\110 949.091 250.909 13:5 2.600
53\67 949.254 250.746 8:3 2.667
72\91 949.451 250.549 11:4 2.750
19\24 950.000 250.000 3:1 3.000 Hard 5L 9s
61\77 950.649 249.351 10:3 3.333
42\53 950.943 249.057 7:2 3.500
65\82 951.220 248.780 11:3 3.667
23\29 951.724 248.276 4:1 4.000 Superhard 5L 9s
50\63 952.381 247.619 9:2 4.500
27\34 952.941 247.059 5:1 5.000
31\39 953.846 246.154 6:1 6.000
4\5 960.000 240.000 1:0 → ∞ Collapsed 5L 9s
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