4L 6s

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↖ 3L 5s ↑ 4L 5s 5L 5s ↗
← 3L 6s 4L 6s 5L 6s →
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Scale structure
Step pattern LsLssLsLss
ssLsLssLsL
Equave 2/1 (1200.0 ¢)
Period 1\2 (600.0 ¢)
Generator size
Bright 2\10 to 1\4 (240.0 ¢ to 300.0 ¢)
Dark 1\4 to 3\10 (300.0 ¢ to 360.0 ¢)
TAMNAMS information
Name lime
Prefix lime-
Abbrev. lm
Related MOS scales
Parent 4L 2s
Sister 6L 4s
Daughters 10L 4s, 4L 10s
Neutralized 8L 2s
2-Flought 14L 6s, 4L 16s
Equal tunings
Equalized (L:s = 1:1) 2\10 (240.0 ¢)
Supersoft (L:s = 4:3) 7\34 (247.1 ¢)
Soft (L:s = 3:2) 5\24 (250.0 ¢)
Semisoft (L:s = 5:3) 8\38 (252.6 ¢)
Basic (L:s = 2:1) 3\14 (257.1 ¢)
Semihard (L:s = 5:2) 7\32 (262.5 ¢)
Hard (L:s = 3:1) 4\18 (266.7 ¢)
Superhard (L:s = 4:1) 5\22 (272.7 ¢)
Collapsed (L:s = 1:0) 1\4 (300.0 ¢)

4L 6s, named lime in TAMNAMS, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 4 large steps and 6 small steps, with a period of 2 large steps and 3 small steps that repeats every 600.0 ¢, or twice every octave. Generators that produce this scale range from 240 ¢ to 300 ¢, or from 300 ¢ to 360 ¢.

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 diatonic interval categories.

Intervals

Intervals of 4L 6s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-limestep Perfect 0-limestep P0lms 0 0.0 ¢
1-limestep Minor 1-limestep m1lms s 0.0 ¢ to 120.0 ¢
Major 1-limestep M1lms L 120.0 ¢ to 300.0 ¢
2-limestep Diminished 2-limestep d2lms 2s 0.0 ¢ to 240.0 ¢
Perfect 2-limestep P2lms L + s 240.0 ¢ to 300.0 ¢
3-limestep Perfect 3-limestep P3lms L + 2s 300.0 ¢ to 360.0 ¢
Augmented 3-limestep A3lms 2L + s 360.0 ¢ to 600.0 ¢
4-limestep Minor 4-limestep m4lms L + 3s 300.0 ¢ to 480.0 ¢
Major 4-limestep M4lms 2L + 2s 480.0 ¢ to 600.0 ¢
5-limestep Perfect 5-limestep P5lms 2L + 3s 600.0 ¢
6-limestep Minor 6-limestep m6lms 2L + 4s 600.0 ¢ to 720.0 ¢
Major 6-limestep M6lms 3L + 3s 720.0 ¢ to 900.0 ¢
7-limestep Diminished 7-limestep d7lms 2L + 5s 600.0 ¢ to 840.0 ¢
Perfect 7-limestep P7lms 3L + 4s 840.0 ¢ to 900.0 ¢
8-limestep Perfect 8-limestep P8lms 3L + 5s 900.0 ¢ to 960.0 ¢
Augmented 8-limestep A8lms 4L + 4s 960.0 ¢ to 1200.0 ¢
9-limestep Minor 9-limestep m9lms 3L + 6s 900.0 ¢ to 1080.0 ¢
Major 9-limestep M9lms 4L + 5s 1080.0 ¢ to 1200.0 ¢
10-limestep Perfect 10-limestep P10lms 4L + 6s 1200.0 ¢

Generator chain

Generator chain of 4L 6s
Bright gens Scale degree Abbrev. Scale degree Abbrev.
6 Augmented 2-limedegree A2lmd Augmented 7-limedegree A7lmd
5 Augmented 0-limedegree A0lmd Augmented 5-limedegree A5lmd
4 Augmented 3-limedegree A3lmd Augmented 8-limedegree A8lmd
3 Major 1-limedegree M1lmd Major 6-limedegree M6lmd
2 Major 4-limedegree M4lmd Major 9-limedegree M9lmd
1 Perfect 2-limedegree P2lmd Perfect 7-limedegree P7lmd
0 Perfect 0-limedegree
Perfect 5-limedegree		 P0lmd
P5lmd		 Perfect 5-limedegree
Perfect 10-limedegree		 P5lmd
P10lmd
−1 Perfect 3-limedegree P3lmd Perfect 8-limedegree P8lmd
−2 Minor 1-limedegree m1lmd Minor 6-limedegree m6lmd
−3 Minor 4-limedegree m4lmd Minor 9-limedegree m9lmd
−4 Diminished 2-limedegree d2lmd Diminished 7-limedegree d7lmd
−5 Diminished 5-limedegree d5lmd Diminished 10-limedegree d10lmd
−6 Diminished 3-limedegree d3lmd Diminished 8-limedegree d8lmd

Modes

Scale degrees of the modes of 4L 6s
UDP Cyclic
order 		Step
pattern 		Scale degree (limedegree)
0 1 2 3 4 5 6 7 8 9 10
8|0(2) 1 LsLssLsLss Perf. Maj. Perf. Aug. Maj. Perf. Maj. Perf. Aug. Maj. Perf.
6|2(2) 3 LssLsLssLs Perf. Maj. Perf. Perf. Maj. Perf. Maj. Perf. Perf. Maj. Perf.
4|4(2) 5 sLsLssLsLs Perf. Min. Perf. Perf. Maj. Perf. Min. Perf. Perf. Maj. Perf.
2|6(2) 2 sLssLsLssL Perf. Min. Perf. Perf. Min. Perf. Min. Perf. Perf. Min. Perf.
0|8(2) 4 ssLsLssLsL Perf. Min. Dim. Perf. Min. Perf. Min. Dim. Perf. Min. Perf.

Proposed names

Lyman Young has proposed names for the modes of 4L 6s, which are shown below. They can be found in his patent for a quartertone slide rule.

Modes of 4L 6s
UDP Cyclic
order		 Step
pattern		 Mode names
8|0(2) 1 LsLssLsLss Atlantic
6|2(2) 3 LssLsLssLs Lumian
4|4(2) 5 sLsLssLsLs Pacific
2|6(2) 2 sLssLsLssL Taliesin
0|8(2) 4 ssLsLssLsL Dresden

Scale tree

Scale tree and tuning spectrum of 4L 6s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
2\10 240.000 360.000 1:1 1.000 Equalized 4L 6s
11\54 244.444 355.556 6:5 1.200 Semiseptiquarter ↑
9\44 245.455 354.545 5:4 1.250
16\78 246.154 353.846 9:7 1.286
7\34 247.059 352.941 4:3 1.333 Supersoft 4L 6s
Hemifourths/angirus
19\92 247.826 352.174 11:8 1.375
12\58 248.276 351.724 7:5 1.400 Sruti
17\82 248.780 351.220 10:7 1.429 Semihemi, Hemipyth (249.0225 ¢)
5\24 250.000 350.000 3:2 1.500 Soft 4L 6s
Decimal is around here
18\86 251.163 348.837 11:7 1.571
13\62 251.613 348.387 8:5 1.600
21\100 252.000 348.000 13:8 1.625
8\38 252.632 347.368 5:3 1.667 Semisoft 4L 6s
19\90 253.333 346.667 12:7 1.714
11\52 253.846 346.154 7:4 1.750
14\66 254.545 345.455 9:5 1.800
3\14 257.143 342.857 2:1 2.000 Basic 4L 6s
Scales with tunings softer than this are proper
13\60 260.000 340.000 9:4 2.250
10\46 260.870 339.130 7:3 2.333 Bamity
17\78 261.538 338.462 12:5 2.400
7\32 262.500 337.500 5:2 2.500 Semihard 4L 6s
18\82 263.415 336.585 13:5 2.600
11\50 264.000 336.000 8:3 2.667
15\68 264.706 335.294 11:4 2.750
4\18 266.667 333.333 3:1 3.000 Hard 4L 6s
13\58 268.966 331.034 10:3 3.333
9\40 270.000 330.000 7:2 3.500
14\62 270.968 329.032 11:3 3.667
5\22 272.727 327.273 4:1 4.000 Superhard 4L 6s
11\48 275.000 325.000 9:2 4.500 Doublewide
6\26 276.923 323.077 5:1 5.000
7\30 280.000 320.000 6:1 6.000 Bikleismic ↓
1\4 300.000 300.000 1:0 → ∞ Collapsed 4L 6s

Music

Cole
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