5L 14s: Difference between revisions

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{{Infobox MOS}}
{{Infobox MOS}}
{| class="wikitable"
{{MOS intro}}
! colspan="9" | generator
== Scale properties ==
!
{{TAMNAMS use}}
! | L
! | s
! | L/s
! | gen (cents)
! | comment
|-
| | 1\5
| |
| |
| |
| |
| |
| |
|
|
|
| | 1
| | 0
| |
| | 240.000
| |
|-
| |
| |
| |
| |
| |
| |
| |
|
|
|13\64
| | 10
| | 1
| | 10.000
| | 243.750
| |
|-
| |
| |
| |
| |
| |
| |
| |
|
|12\59
|
| | 9
| | 1
| | 9.000
| | 244.068
| |
|-
| |
| |
| |
| |
| |
| |
| |
|
|
|23\113
| | 17
| | 2
| | 8.500
| | 244.248
| |
|-
| |
| |
| |
| |
| |
| |
| |
|11\54
|
|
| | 8
| | 1
| | 8.000
| | 244.444
| |
|-
| |
| |
| |
| |
| |
| |
| |
|
|21\103
|
| | 15
| | 2
| | 7.500
| | 244.660
| |
|-
| |
| |
| |
| |
| |
| |
| |10\49
|
|
|
| | 7
| | 1
| | 7.000
| | 244.898
| |
|-
| |
| |
| |
| |
| |
| |
| |
|19\93
|
|
| | 13
| | 2
| | 6.500
| | 245.161
| |
|-
| |
| |
| |
| |
| |
| | 9\44
| |
|
|
|
| | 6
| | 1
| | 6.000
| | 245.455
| |
|-
| |
| |
| |
| |
| |
| |
| |17\83
|
|
|
| | 11
| | 2
| | 5.500
| | 245.783
| |
|-
| |
| |
| |
| |
| | 8\39
| |
| |
|
|
|
| | 5
| | 1
| | 5.000
| | 246.154
| |
|-
| |
| |
| |
| |
| |
| |
| |23\112
|
|
|
| | 14
| | 3
| | 4.667
| | 246.429
| |
|-
| |
| |
| |
| |
| |
| | 15\73
| |
|
|
|
| | 9
| | 2
| | 4.500
| | 246.575
| |
|-
| |
| |
| |
| |
| |
| |
| |22\107
|
|
|
| | 13
| | 3
| | 4.333
| | 246.729
| |
|-
| |
| |
| |
| | 7\34
| |
| |
| |
|
|
|
| | 4
| | 1
| | 4.000
| | 247.059
| |
|-
| |
| |
| |
| |
| |
| | 20\97
| |
|
|
|
| | 11
| | 3
| | 3.667
| | 247.423
| |
|-
| |
| |
| |
| |
| | 13\63
| |
| |
|
|
|
| | 7
| | 2
| | 3.500
| | 247.619
| |
|-
| |
| |
| |
| |
| |
| | 19\92
| |
|
|
|
| | 10
| | 3
| | 3.333
| | 247.826
| |
|-
| |
| |
| | 6\29
| |
| |
| |
| |
|
|
|
| | 3
| | 1
| | 3.000
| | 248.276
| |
|-
| |
| |
| |
| |
| |
| | 23\111
| |
|
|
|
| | 11
| | 4
| | 2.750
| | 248.649
| |
|-
| |
| |
| |
| |
| | 17\82
| |
| |
|
|
|
| | 8
| | 3
| | 2.667
| | 248.780
| |
|-
| |
| |
| |
| | 11\53
| |
| |
| |
|
|
|
| | 5
| | 2
| | 2.500
| | 249.057
| |
|-
| |
| |
| |
| |
| | 16\77
| |
| |
|
|
|
| | 7
| | 3
| | 2.333
| | 249.351
| |
|-
| |
| |
| |
| |
| |
| | 21\101
| |
|
|
|
| | 9
| | 4
| | 2.250
| | 249.505
| |
|-
| |
| | 5\24
| |
| |
| |
| |
| |
|
|
|
| | 2
| | 1
| | 2.000
| | 250.000
| |
|-
| |
| |
| |
| |
| |
| | 24\115
| |
|
|
|
| | 9
| | 5
| | 1.800
| | 250.435
| |
|-
| |
| |
| |
| |
| | 19\91
| |
| |
|
|
|
| | 7
| | 4
| | 1.750
| | 250.549
| |
|-
| |
| |
| |
| | 14\67
| |
| |
| |
|
|
|
| | 5
| | 3
| | 1.667
| | 250.746
| |
|-
| |
| |
| |
| |
| | 23\110
| |
| |
|
|
|
| | 8
| | 5
| | 1.600
| | 250.909
| |
|-
| |
| |
| | 9\43
| |
| |
| |
| |
|
|
|
| | 3
| | 2
| | 1.500
| | 251.163
| |
|-
| |
| |
| |
| |
| | 22\105
| |
| |
|
|
|
| | 7
| | 5
| | 1.400
| | 251.429
| |
|-
| |
| |
| |
| | 13\62
| |
| |
| |
|
|
|
| | 4
| | 3
| | 1.333
| | 251.613
| |
|-
| |
| |
| |
| |
| | 17\81
| |
| |
|
|
|
| | 5
| | 4
| | 1.250
| | 251.852
| |
|-
| |
| |
| |
| |
| |
| | 21\100
| |
|
|
|
| | 6
| | 5
| | 1.200
| | 252.000
| |
|-
| |
| |
| |
| |
| |
| |
| |25\119
|
|
|
| | 7
| | 6
| | 1.167
| | 252.101
| |
|-
|
|
|
|
|
|
|
|29\138
|
|
|8
|7
|1.143
|252.174
|
|-
|
|
|
|
|
|
|
|
|33\157
|
|9
|8
|1.125
|252.229
|
|-
|
|
|
|
|
|
|
|
|
|37\176
|10
|9
|1.111
|252.273
|
|-
| | 4\19
| |
| |
| |
| |
| |
| |
|
|
|
| | 1
| | 1
| | 1.000
| | 252.632
| |
|}


[[category:todo:intro]]
=== Intervals ===
[[category:todo:expand]]
{{MOS intervals}}
 
=== Generator chain ===
{{MOS genchain}}
 
=== Modes ===
{{MOS mode degrees}}
 
== Scale tree ==
{{MOS tuning spectrum}}
 
{{Stub}}

Latest revision as of 14:12, 5 May 2025

↖ 4L 13s ↑ 5L 13s 6L 13s ↗
← 4L 14s 5L 14s 6L 14s →
↙ 4L 15s ↓ 5L 15s 6L 15s ↘
Scale structure
Step pattern LssLsssLsssLsssLsss
sssLsssLsssLsssLssL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 15\19 to 4\5 (947.4 ¢ to 960.0 ¢)
Dark 1\5 to 4\19 (240.0 ¢ to 252.6 ¢)
TAMNAMS information
Related to 5L 4s (semiquartal)
With tunings 3:1 to 1:0 (hard)
Related MOS scales
Parent 5L 9s
Sister 14L 5s
Daughters 19L 5s, 5L 19s
Neutralized 10L 9s
2-Flought 24L 14s, 5L 33s
Equal tunings
Equalized (L:s = 1:1) 15\19 (947.4 ¢)
Supersoft (L:s = 4:3) 49\62 (948.4 ¢)
Soft (L:s = 3:2) 34\43 (948.8 ¢)
Semisoft (L:s = 5:3) 53\67 (949.3 ¢)
Basic (L:s = 2:1) 19\24 (950.0 ¢)
Semihard (L:s = 5:2) 42\53 (950.9 ¢)
Hard (L:s = 3:1) 23\29 (951.7 ¢)
Superhard (L:s = 4:1) 27\34 (952.9 ¢)
Collapsed (L:s = 1:0) 4\5 (960.0 ¢)
View • Talk • Edit

5L 14s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 5 large steps and 14 small steps, repeating every octave. 5L 14s is a grandchild scale of 5L 4s, expanding it by 10 tones. Generators that produce this scale range from 947.4 ¢ to 960 ¢, or from 240 ¢ to 252.6 ¢.

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 5L 14s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-mosstep Perfect 0-mosstep P0ms 0 0.0 ¢
1-mosstep Minor 1-mosstep m1ms s 0.0 ¢ to 63.2 ¢
Major 1-mosstep M1ms L 63.2 ¢ to 240.0 ¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0 ¢ to 126.3 ¢
Major 2-mosstep M2ms L + s 126.3 ¢ to 240.0 ¢
3-mosstep Minor 3-mosstep m3ms 3s 0.0 ¢ to 189.5 ¢
Major 3-mosstep M3ms L + 2s 189.5 ¢ to 240.0 ¢
4-mosstep Perfect 4-mosstep P4ms L + 3s 240.0 ¢ to 252.6 ¢
Augmented 4-mosstep A4ms 2L + 2s 252.6 ¢ to 480.0 ¢
5-mosstep Minor 5-mosstep m5ms L + 4s 240.0 ¢ to 315.8 ¢
Major 5-mosstep M5ms 2L + 3s 315.8 ¢ to 480.0 ¢
6-mosstep Minor 6-mosstep m6ms L + 5s 240.0 ¢ to 378.9 ¢
Major 6-mosstep M6ms 2L + 4s 378.9 ¢ to 480.0 ¢
7-mosstep Minor 7-mosstep m7ms L + 6s 240.0 ¢ to 442.1 ¢
Major 7-mosstep M7ms 2L + 5s 442.1 ¢ to 480.0 ¢
8-mosstep Minor 8-mosstep m8ms 2L + 6s 480.0 ¢ to 505.3 ¢
Major 8-mosstep M8ms 3L + 5s 505.3 ¢ to 720.0 ¢
9-mosstep Minor 9-mosstep m9ms 2L + 7s 480.0 ¢ to 568.4 ¢
Major 9-mosstep M9ms 3L + 6s 568.4 ¢ to 720.0 ¢
10-mosstep Minor 10-mosstep m10ms 2L + 8s 480.0 ¢ to 631.6 ¢
Major 10-mosstep M10ms 3L + 7s 631.6 ¢ to 720.0 ¢
11-mosstep Minor 11-mosstep m11ms 2L + 9s 480.0 ¢ to 694.7 ¢
Major 11-mosstep M11ms 3L + 8s 694.7 ¢ to 720.0 ¢
12-mosstep Minor 12-mosstep m12ms 3L + 9s 720.0 ¢ to 757.9 ¢
Major 12-mosstep M12ms 4L + 8s 757.9 ¢ to 960.0 ¢
13-mosstep Minor 13-mosstep m13ms 3L + 10s 720.0 ¢ to 821.1 ¢
Major 13-mosstep M13ms 4L + 9s 821.1 ¢ to 960.0 ¢
14-mosstep Minor 14-mosstep m14ms 3L + 11s 720.0 ¢ to 884.2 ¢
Major 14-mosstep M14ms 4L + 10s 884.2 ¢ to 960.0 ¢
15-mosstep Diminished 15-mosstep d15ms 3L + 12s 720.0 ¢ to 947.4 ¢
Perfect 15-mosstep P15ms 4L + 11s 947.4 ¢ to 960.0 ¢
16-mosstep Minor 16-mosstep m16ms 4L + 12s 960.0 ¢ to 1010.5 ¢
Major 16-mosstep M16ms 5L + 11s 1010.5 ¢ to 1200.0 ¢
17-mosstep Minor 17-mosstep m17ms 4L + 13s 960.0 ¢ to 1073.7 ¢
Major 17-mosstep M17ms 5L + 12s 1073.7 ¢ to 1200.0 ¢
18-mosstep Minor 18-mosstep m18ms 4L + 14s 960.0 ¢ to 1136.8 ¢
Major 18-mosstep M18ms 5L + 13s 1136.8 ¢ to 1200.0 ¢
19-mosstep Perfect 19-mosstep P19ms 5L + 14s 1200.0 ¢

Generator chain

Generator chain of 5L 14s
Bright gens Scale degree Abbrev.
23 Augmented 3-mosdegree A3md
22 Augmented 7-mosdegree A7md
21 Augmented 11-mosdegree A11md
20 Augmented 15-mosdegree A15md
19 Augmented 0-mosdegree A0md
18 Augmented 4-mosdegree A4md
17 Major 8-mosdegree M8md
16 Major 12-mosdegree M12md
15 Major 16-mosdegree M16md
14 Major 1-mosdegree M1md
13 Major 5-mosdegree M5md
12 Major 9-mosdegree M9md
11 Major 13-mosdegree M13md
10 Major 17-mosdegree M17md
9 Major 2-mosdegree M2md
8 Major 6-mosdegree M6md
7 Major 10-mosdegree M10md
6 Major 14-mosdegree M14md
5 Major 18-mosdegree M18md
4 Major 3-mosdegree M3md
3 Major 7-mosdegree M7md
2 Major 11-mosdegree M11md
1 Perfect 15-mosdegree P15md
0 Perfect 0-mosdegree
Perfect 19-mosdegree		 P0md
P19md
−1 Perfect 4-mosdegree P4md
−2 Minor 8-mosdegree m8md
−3 Minor 12-mosdegree m12md
−4 Minor 16-mosdegree m16md
−5 Minor 1-mosdegree m1md
−6 Minor 5-mosdegree m5md
−7 Minor 9-mosdegree m9md
−8 Minor 13-mosdegree m13md
−9 Minor 17-mosdegree m17md
−10 Minor 2-mosdegree m2md
−11 Minor 6-mosdegree m6md
−12 Minor 10-mosdegree m10md
−13 Minor 14-mosdegree m14md
−14 Minor 18-mosdegree m18md
−15 Minor 3-mosdegree m3md
−16 Minor 7-mosdegree m7md
−17 Minor 11-mosdegree m11md
−18 Diminished 15-mosdegree d15md
−19 Diminished 19-mosdegree d19md
−20 Diminished 4-mosdegree d4md
−21 Diminished 8-mosdegree d8md
−22 Diminished 12-mosdegree d12md
−23 Diminished 16-mosdegree d16md

Modes

Scale degrees of the modes of 5L 14s
UDP Cyclic
order 		Step
pattern 		Scale degree (mosdegree)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
18|0 1 LssLsssLsssLsssLsss Perf. Maj. Maj. Maj. Aug. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Perf.
17|1 16 LsssLssLsssLsssLsss Perf. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Perf.
16|2 12 LsssLsssLssLsssLsss Perf. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Min. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Perf.
15|3 8 LsssLsssLsssLssLsss Perf. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Min. Maj. Maj. Maj. Min. Maj. Maj. Perf. Maj. Maj. Maj. Perf.
14|4 4 LsssLsssLsssLsssLss Perf. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Min. Maj. Maj. Maj. Min. Maj. Maj. Perf. Min. Maj. Maj. Perf.
13|5 19 sLssLsssLsssLsssLss Perf. Min. Maj. Maj. Perf. Maj. Maj. Maj. Min. Maj. Maj. Maj. Min. Maj. Maj. Perf. Min. Maj. Maj. Perf.
12|6 15 sLsssLssLsssLsssLss Perf. Min. Maj. Maj. Perf. Min. Maj. Maj. Min. Maj. Maj. Maj. Min. Maj. Maj. Perf. Min. Maj. Maj. Perf.
11|7 11 sLsssLsssLssLsssLss Perf. Min. Maj. Maj. Perf. Min. Maj. Maj. Min. Min. Maj. Maj. Min. Maj. Maj. Perf. Min. Maj. Maj. Perf.
10|8 7 sLsssLsssLsssLssLss Perf. Min. Maj. Maj. Perf. Min. Maj. Maj. Min. Min. Maj. Maj. Min. Min. Maj. Perf. Min. Maj. Maj. Perf.
9|9 3 sLsssLsssLsssLsssLs Perf. Min. Maj. Maj. Perf. Min. Maj. Maj. Min. Min. Maj. Maj. Min. Min. Maj. Perf. Min. Min. Maj. Perf.
8|10 18 ssLssLsssLsssLsssLs Perf. Min. Min. Maj. Perf. Min. Maj. Maj. Min. Min. Maj. Maj. Min. Min. Maj. Perf. Min. Min. Maj. Perf.
7|11 14 ssLsssLssLsssLsssLs Perf. Min. Min. Maj. Perf. Min. Min. Maj. Min. Min. Maj. Maj. Min. Min. Maj. Perf. Min. Min. Maj. Perf.
6|12 10 ssLsssLsssLssLsssLs Perf. Min. Min. Maj. Perf. Min. Min. Maj. Min. Min. Min. Maj. Min. Min. Maj. Perf. Min. Min. Maj. Perf.
5|13 6 ssLsssLsssLsssLssLs Perf. Min. Min. Maj. Perf. Min. Min. Maj. Min. Min. Min. Maj. Min. Min. Min. Perf. Min. Min. Maj. Perf.
4|14 2 ssLsssLsssLsssLsssL Perf. Min. Min. Maj. Perf. Min. Min. Maj. Min. Min. Min. Maj. Min. Min. Min. Perf. Min. Min. Min. Perf.
3|15 17 sssLssLsssLsssLsssL Perf. Min. Min. Min. Perf. Min. Min. Maj. Min. Min. Min. Maj. Min. Min. Min. Perf. Min. Min. Min. Perf.
2|16 13 sssLsssLssLsssLsssL Perf. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Maj. Min. Min. Min. Perf. Min. Min. Min. Perf.
1|17 9 sssLsssLsssLssLsssL Perf. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Perf.
0|18 5 sssLsssLsssLsssLssL Perf. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Dim. Min. Min. Min. Perf.

Scale tree

Scale tree and tuning spectrum of 5L 14s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
15\19 947.368 252.632 1:1 1.000 Equalized 5L 14s
79\100 948.000 252.000 6:5 1.200
64\81 948.148 251.852 5:4 1.250
113\143 948.252 251.748 9:7 1.286
49\62 948.387 251.613 4:3 1.333 Supersoft 5L 14s
132\167 948.503 251.497 11:8 1.375
83\105 948.571 251.429 7:5 1.400
117\148 948.649 251.351 10:7 1.429
34\43 948.837 251.163 3:2 1.500 Soft 5L 14s
121\153 949.020 250.980 11:7 1.571
87\110 949.091 250.909 8:5 1.600
140\177 949.153 250.847 13:8 1.625
53\67 949.254 250.746 5:3 1.667 Semisoft 5L 14s
125\158 949.367 250.633 12:7 1.714
72\91 949.451 250.549 7:4 1.750
91\115 949.565 250.435 9:5 1.800
19\24 950.000 250.000 2:1 2.000 Basic 5L 14s
Scales with tunings softer than this are proper
80\101 950.495 249.505 9:4 2.250
61\77 950.649 249.351 7:3 2.333
103\130 950.769 249.231 12:5 2.400
42\53 950.943 249.057 5:2 2.500 Semihard 5L 14s
107\135 951.111 248.889 13:5 2.600
65\82 951.220 248.780 8:3 2.667
88\111 951.351 248.649 11:4 2.750
23\29 951.724 248.276 3:1 3.000 Hard 5L 14s
73\92 952.174 247.826 10:3 3.333
50\63 952.381 247.619 7:2 3.500
77\97 952.577 247.423 11:3 3.667
27\34 952.941 247.059 4:1 4.000 Superhard 5L 14s
58\73 953.425 246.575 9:2 4.500
31\39 953.846 246.154 5:1 5.000
35\44 954.545 245.455 6:1 6.000
4\5 960.000 240.000 1:0 → ∞ Collapsed 5L 14s
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