5L 10s

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↖ 4L 9s ↑ 5L 9s 6L 9s ↗
← 4L 10s 5L 10s 6L 10s →
↙ 4L 11s ↓ 5L 11s 6L 11s ↘ 
┌╥┬┬╥┬┬╥┬┬╥┬┬╥┬┬┐
│║││║││║││║││║│││
│││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LssLssLssLssLss
ssLssLssLssLssL
Equave 2/1 (1200.0 ¢)
Period 1\5 (240.0 ¢)
Generator size
Bright 2\15 to 1\5 (160.0 ¢ to 240.0 ¢)
Dark 0\5 to 1\15 (0.0 ¢ to 80.0 ¢)
TAMNAMS information
Related to 5L 5s (pentawood)
With tunings 2:1 to 1:0 (hard-of-basic)
Related MOS scales
Parent 5L 5s
Sister 10L 5s
Daughters 15L 5s, 5L 15s
Neutralized 10L 5s
2-Flought 20L 10s, 5L 25s
Equal tunings
Equalized (L:s = 1:1) 2\15 (160.0 ¢)
Supersoft (L:s = 4:3) 7\50 (168.0 ¢)
Soft (L:s = 3:2) 5\35 (171.4 ¢)
Semisoft (L:s = 5:3) 8\55 (174.5 ¢)
Basic (L:s = 2:1) 3\20 (180.0 ¢)
Semihard (L:s = 5:2) 7\45 (186.7 ¢)
Hard (L:s = 3:1) 4\25 (192.0 ¢)
Superhard (L:s = 4:1) 5\30 (200.0 ¢)
Collapsed (L:s = 1:0) 1\5 (240.0 ¢)

5L 10s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 5 large steps and 10 small steps, with a period of 1 large step and 2 small steps that repeats every 240.0 ¢, or 5 times every octave. 5L 10s is a child scale of 5L 5s, expanding it by 5 tones. Generators that produce this scale range from 160 ¢ to 240 ¢, or from 0 ¢ to 80 ¢.

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 10s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-mosstep Perfect 0-mosstep P0ms 0 0.0 ¢
1-mosstep Perfect 1-mosstep P1ms s 0.0 ¢ to 80.0 ¢
Augmented 1-mosstep A1ms L 80.0 ¢ to 240.0 ¢
2-mosstep Diminished 2-mosstep d2ms 2s 0.0 ¢ to 160.0 ¢
Perfect 2-mosstep P2ms L + s 160.0 ¢ to 240.0 ¢
3-mosstep Perfect 3-mosstep P3ms L + 2s 240.0 ¢
4-mosstep Perfect 4-mosstep P4ms L + 3s 240.0 ¢ to 320.0 ¢
Augmented 4-mosstep A4ms 2L + 2s 320.0 ¢ to 480.0 ¢
5-mosstep Diminished 5-mosstep d5ms L + 4s 240.0 ¢ to 400.0 ¢
Perfect 5-mosstep P5ms 2L + 3s 400.0 ¢ to 480.0 ¢
6-mosstep Perfect 6-mosstep P6ms 2L + 4s 480.0 ¢
7-mosstep Perfect 7-mosstep P7ms 2L + 5s 480.0 ¢ to 560.0 ¢
Augmented 7-mosstep A7ms 3L + 4s 560.0 ¢ to 720.0 ¢
8-mosstep Diminished 8-mosstep d8ms 2L + 6s 480.0 ¢ to 640.0 ¢
Perfect 8-mosstep P8ms 3L + 5s 640.0 ¢ to 720.0 ¢
9-mosstep Perfect 9-mosstep P9ms 3L + 6s 720.0 ¢
10-mosstep Perfect 10-mosstep P10ms 3L + 7s 720.0 ¢ to 800.0 ¢
Augmented 10-mosstep A10ms 4L + 6s 800.0 ¢ to 960.0 ¢
11-mosstep Diminished 11-mosstep d11ms 3L + 8s 720.0 ¢ to 880.0 ¢
Perfect 11-mosstep P11ms 4L + 7s 880.0 ¢ to 960.0 ¢
12-mosstep Perfect 12-mosstep P12ms 4L + 8s 960.0 ¢
13-mosstep Perfect 13-mosstep P13ms 4L + 9s 960.0 ¢ to 1040.0 ¢
Augmented 13-mosstep A13ms 5L + 8s 1040.0 ¢ to 1200.0 ¢
14-mosstep Diminished 14-mosstep d14ms 4L + 10s 960.0 ¢ to 1120.0 ¢
Perfect 14-mosstep P14ms 5L + 9s 1120.0 ¢ to 1200.0 ¢
15-mosstep Perfect 15-mosstep P15ms 5L + 10s 1200.0 ¢

Generator chain

Generator chain of 5L 10s
Bright gens Scale degree Abbrev. Scale degree Abbrev. Scale degree Abbrev. Scale degree Abbrev. Scale degree Abbrev.
3 Augmented 0-mosdegree A0md Augmented 3-mosdegree A3md Augmented 6-mosdegree A6md Augmented 9-mosdegree A9md Augmented 12-mosdegree A12md
2 Augmented 1-mosdegree A1md Augmented 4-mosdegree A4md Augmented 7-mosdegree A7md Augmented 10-mosdegree A10md Augmented 13-mosdegree A13md
1 Perfect 2-mosdegree P2md Perfect 5-mosdegree P5md Perfect 8-mosdegree P8md Perfect 11-mosdegree P11md Perfect 14-mosdegree P14md
0 Perfect 0-mosdegree
Perfect 3-mosdegree		 P0md
P3md		 Perfect 3-mosdegree
Perfect 6-mosdegree		 P3md
P6md		 Perfect 6-mosdegree
Perfect 9-mosdegree		 P6md
P9md		 Perfect 9-mosdegree
Perfect 12-mosdegree		 P9md
P12md		 Perfect 12-mosdegree
Perfect 15-mosdegree		 P12md
P15md
−1 Perfect 1-mosdegree P1md Perfect 4-mosdegree P4md Perfect 7-mosdegree P7md Perfect 10-mosdegree P10md Perfect 13-mosdegree P13md
−2 Diminished 2-mosdegree d2md Diminished 5-mosdegree d5md Diminished 8-mosdegree d8md Diminished 11-mosdegree d11md Diminished 14-mosdegree d14md
−3 Diminished 3-mosdegree d3md Diminished 6-mosdegree d6md Diminished 9-mosdegree d9md Diminished 12-mosdegree d12md Diminished 15-mosdegree d15md

Modes

Scale degrees of the modes of 5L 10s
UDP Cyclic
order 		Step
pattern 		Scale degree (mosdegree)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
10|0(5) 1 LssLssLssLssLss Perf. Aug. Perf. Perf. Aug. Perf. Perf. Aug. Perf. Perf. Aug. Perf. Perf. Aug. Perf. Perf.
5|5(5) 3 sLssLssLssLssLs Perf. Perf. Perf. Perf. Perf. Perf. Perf. Perf. Perf. Perf. Perf. Perf. Perf. Perf. Perf. Perf.
0|10(5) 2 ssLssLssLssLssL Perf. Perf. Dim. Perf. Perf. Dim. Perf. Perf. Dim. Perf. Perf. Dim. Perf. Perf. Dim. Perf.

Scale tree

Scale tree and tuning spectrum of 5L 10s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
2\15 160.000 80.000 1:1 1.000 Equalized 5L 10s
11\80 165.000 75.000 6:5 1.200
9\65 166.154 73.846 5:4 1.250 Coblack, Trisedodge, and Countdown are around here
16\115 166.957 73.043 9:7 1.286
7\50 168.000 72.000 4:3 1.333 Supersoft 5L 10s
19\135 168.889 71.111 11:8 1.375
12\85 169.412 70.588 7:5 1.400
17\120 170.000 70.000 10:7 1.429
5\35 171.429 68.571 3:2 1.500 Soft 5L 10s
18\125 172.800 67.200 11:7 1.571
13\90 173.333 66.667 8:5 1.600
21\145 173.793 66.207 13:8 1.625
8\55 174.545 65.455 5:3 1.667 Semisoft 5L 10s
19\130 175.385 64.615 12:7 1.714
11\75 176.000 64.000 7:4 1.750
14\95 176.842 63.158 9:5 1.800
3\20 180.000 60.000 2:1 2.000 Basic 5L 10s
Scales with tunings softer than this are proper
13\85 183.529 56.471 9:4 2.250
10\65 184.615 55.385 7:3 2.333
17\110 185.455 54.545 12:5 2.400
7\45 186.667 53.333 5:2 2.500 Semihard 5L 10s
18\115 187.826 52.174 13:5 2.600
11\70 188.571 51.429 8:3 2.667
15\95 189.474 50.526 11:4 2.750
4\25 192.000 48.000 3:1 3.000 Hard 5L 10s
13\80 195.000 45.000 10:3 3.333
9\55 196.364 43.636 7:2 3.500
14\85 197.647 42.353 11:3 3.667
5\30 200.000 40.000 4:1 4.000 Superhard 5L 10s
11\65 203.077 36.923 9:2 4.500 Quint is around here
6\35 205.714 34.286 5:1 5.000
7\40 210.000 30.000 6:1 6.000 Pental ↓
1\5 240.000 0.000 1:0 → ∞ Collapsed 5L 10s
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