4L 4s

From Xenharmonic Wiki
Jump to navigation Jump to search
↖3L 3s↑4L 3s 5L 3s↗
←3L 4s4L 4s5L 4s→
↙3L 5s↓4L 5s 5L 5s↘
Brightest mode LsLsLsLs
Period 1\4
Range for bright generator 1\8 (150¢) to 1\4 (300¢)
Range for dark generator 0\4 (0¢) to 1\8 (150¢)
TAMNAMS name tetrawood
TAMNAMS prefix tetrawd- (abbr. ttw)
Parent MOS none
Sister MOS 4L 4s
Daughter MOSes 8L 4s, 4L 8s
Equal tunings
Supersoft (L:s = 4:3) 4\28 (171.4¢)
Soft (L:s = 3:2) 3\20 (180¢)
Semisoft (L:s = 5:3) 5\32 (187.5¢)
Basic (L:s = 2:1) 2\12 (200¢)
Semihard (L:s = 5:2) 5\28 (214.3¢)
Hard (L:s = 3:1) 3\16 (225¢)
Superhard (L:s = 4:1) 4\20 (240¢)
Brightest-mode tunings on xenpaper
Supersoft Soft Semisoft Basic Semihard Hard Superhard

4L 4s, named tetrawood in TAMNAMS, is an octave-equivalent moment of symmetry scale containing 4 large steps and 4 small steps, with a period of 1 large step and 1 small step that repeats every 300.0¢ or 4 times every octave. Generators that produce this scale range from 150¢ to 300¢, or from 0¢ to 150¢. Scales of this form are proper if every period is the same, because there is only one small step per period.

The minimum harmonic entropy scale with this MOS pattern is diminished[8], the familiar octatonic scale of 12edo.

In addition to the true MOS form, LsLsLsLs, there are four near-MOS forms – LLsLsLss, LLsLssLs, LLssLLss, and LLssLsLs – in which the period and its multiples are the only intervals with more than two varieties. The near-MOS forms are only proper if the dark generator is larger than 1\12 (100¢).

Intervals

Intervals of 4L 4s
Intervals (with relation to root) Size Abbrev.
Generic Specific L's and s's Range in cents
0-tetrawdstep (root) Perfect 0-tetrawdstep 0 0.0¢ P0ms
1-tetrawdstep Minor 1-tetrawdstep s 0.0¢ to 150.0¢ m1ms
Major 1-tetrawdstep L 150.0¢ to 300.0¢ M1ms
2-tetrawdstep (period) Perfect 2-tetrawdstep L + s 300.0¢ P2ms
3-tetrawdstep Minor 3-tetrawdstep L + 2s 300.0¢ to 450.0¢ m3ms
Major 3-tetrawdstep 2L + s 450.0¢ to 600.0¢ M3ms
4-tetrawdstep (period) Perfect 4-tetrawdstep 2L + 2s 600.0¢ P4ms
5-tetrawdstep Minor 5-tetrawdstep 2L + 3s 600.0¢ to 750.0¢ m5ms
Major 5-tetrawdstep 3L + 2s 750.0¢ to 900.0¢ M5ms
6-tetrawdstep (period) Perfect 6-tetrawdstep 3L + 3s 900.0¢ P6ms
7-tetrawdstep Minor 7-tetrawdstep 3L + 4s 900.0¢ to 1050.0¢ m7ms
Major 7-tetrawdstep 4L + 3s 1050.0¢ to 1200.0¢ M7ms
8-tetrawdstep (octave) Perfect 8-tetrawdstep 4L + 4s 1200.0¢ P8ms

Modes

Modes of 4L 4s
UDP Rotational order Step pattern
4|0(4) 1 LsLsLsLs
0|4(4) 2 sLsLsLsL

Scale tree

Generator Cents L s L/s Comments
Chroma-positive Chroma-negative
1\8 150.000 150.000 1 1 1.000
6\44 163.636 136.364 6 5 1.200 Fourfives↑
5\36 166.667 133.333 5 4 1.250
9\64 168.750 105.000 9 7 1.286
4\28 171.429 128.571 4 3 1.333
11\76 173.684 126.316 11 8 1.375
7\48 175.000 125.000 7 5 1.400
10\68 176.471 123.529 10 7 1.428
3\20 180.000 60.000 3 2 1.500 L/s = 3/2
11\72 183.333 116.667 11 7 1.571
8\52 184.615 115.385 8 5 1.600
13\84 185.714 114.286 13 8 1.625 Golden diminished
5\32 187.500 112.500 5 3 1.667
12\76 189.474 110.526 12 7 1.714
7\44 190.909 109.091 7 4 1.750
9\56 192.857 107.143 9 5 1.800
2\12 200.000 100.000 2 1 2.000 Basic tetrawood
Diminished is optimal around here
9\52 207.692 92.308 9 4 2.250
7\40 210.000 90.000 7 3 2.333
12\68 211.765 88.235 12 5 2.400
5\28 214.286 85.714 5 2 2.500
13\72 216.667 83.333 13 5 2.600 Unnamed golden tuning
8\44 218.182 81.818 8 3 2.667
11\60 220.000 80.000 11 4 2.750
3\16 225.000 75.000 3 1 3.000 L/s = 3/1
10\52 230.769 69.231 10 3 3.333
7\36 233.333 66.667 7 2 3.500
11\56 235.714 64.286 11 3 3.667
4\20 240.000 60.000 4 1 4.000
9\44 245.455 54.545 9 2 4.500
5\24 250.000 50.000 5 1 5.000
6\28 257.143 42.857 6 1 6.000 Quadritikleismic↓
1\4 300.000 0.000 1 0 → inf