4L 6s
Jump to navigation
Jump to search
Step pattern
LsLssLsLss
ssLsLssLsL
Equave
2/1 (1200.0 ¢)
Period
1\2 (600.0 ¢)
Bright
2\10 to 1\4 (240.0 ¢ to 300.0 ¢)
Dark
1\4 to 3\10 (300.0 ¢ to 360.0 ¢)
Name
lime
Prefix
lime-
Abbrev.
lm
Parent
4L 2s
Sister
6L 4s
Daughters
10L 4s, 4L 10s
Neutralized
8L 2s
2-Flought
14L 6s, 4L 16s
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 ¢)
| ↖ 3L 5s | ↑ 4L 5s | 5L 5s ↗ |
| ← 3L 6s | 4L 6s | 5L 6s → |
| ↙ 3L 7s | ↓ 4L 7s | 5L 7s ↘ |
┌╥┬╥┬┬╥┬╥┬┬┐ │║│║││║│║│││ ││││││││││││ └┴┴┴┴┴┴┴┴┴┴┘
Scale structure
ssLsLssLsL
Generator size
TAMNAMS information
Related MOS scales
Equal tunings
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
The intervals of 4L 6s are named after the number of mossteps (L and s) they subtend. Each interval, apart from the period intervals (perfect 0-limestep, perfect 5-limestep, and perfect 10-limestep), has two varieties, or sizes, each. Interval varieties are named major and minor for the large and small sizes, respectively, and augmented, perfect, and diminished for the scale's generators.
| 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
A chain of bright generators, each a perfect 2-limestep, produces the following scale degrees. A chain of 5 bright generators from each period contains the scale degrees of one of the modes of 4L 6s. Expanding each chain to 7 scale degrees produces the modes of either 10L 4s (for soft-of-basic tunings) or 4L 10s (for hard-of-basic tunings).
| 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
| 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.
| 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
| 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
- The Hymn of Pergele, a short piece in Hemipyth[10] 4|4(2) (Pacific mode of 4L 6s)