# 5L 5s

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 Brightest mode LsLsLsLsLs Period 1\5 Range for bright generator 0\5 (0.0¢) to 1\10 (120.0¢) Range for dark generator 1\10 (120.0¢) to 1\5 (240.0¢) Parent MOS 5edo Daughter MOSes 10L 5s, 5L 10s Sister MOS 5L 5s TAMNAMS name pentawood Equal tunings Supersoft (L:s = 4:3) 3\35 (102.9¢) Soft (L:s = 3:2) 2\25 (96.0¢) Semisoft (L:s = 5:3) 3\40 (90.0¢) Basic (L:s = 2:1) 1\15 (80.0¢) Semihard (L:s = 5:2) 2\35 (68.6¢) Hard (L:s = 3:1) 1\20 (60.0¢) Superhard (L:s = 4:1) 1\25 (48.0¢)

5L 5s is an octave-equivalent MOS scale pattern built with five repeating "Ls" (or "sL").

## As a temperament

There is only one significant harmonic entropy minimum with this MOS pattern: blackwood, in which intervals of the prime numbers 3 and 7 are all represented using steps of 5edo, and the generator gets you to intervals of 5 like 6/5, 5/4, or 7/5.

The true MOS, LsLsLsLsLs, is always proper because there is only one small step per period, but because there are 5 periods in an octave, there are a wealth of near-MOSes in which multiples of the period (that is, intervals of an even number of steps) are the only generic intervals that come in more than two different flavors. Specifically, there are 6 others: LLssLsLsLs, LLssLLssLs, LLsLssLsLs, LLsLssLLss, LLsLsLssLs, LLsLsLsLss. In the blackwood temperament, these are right on the boundary of being proper (because 1\15 is in the middle of the range of good blackwood generators).

## Scale tree

Generator Cents L s L/s Comments
Chroma-positive Chroma-negative
1\10 120.000 120.000 1 1 1.000
6\55 130.909 109.091 6 5 1.200 Qintosec↑
5\45 133.333 106.667 5 4 1.250
9\80 135.000 105.000 9 7 1.286
4\35 137.143 102.857 4 3 1.333
11\95 138.947 101.053 11 8 1.375
7\60 140.000 100.000 7 5 1.400 Warlock
10\85 141.176 98.824 10 7 1.428
3\25 144.000 96.000 3 2 1.500 L/s = 3/2
11\90 146.667 93.333 11 7 1.571
8\65 147.692 92.308 8 5 1.600
13\105 148.571 91.429 13 8 1.625 Unnamed golden tuning
5\40 150.000 90.000 5 3 1.667
12\95 151.579 88.421 12 7 1.714
7\55 152.727 87.273 7 4 1.750 Quinkee
9\70 154.286 85.714 9 5 1.800
2\15 160.000 80.000 2 1 2.000 Basic pentawood
Blacksmith is optimal around here
9\65 166.154 73.846 9 4 2.250 Trisedodge
7\50 168.000 72.000 7 3 2.333
12\85 169.412 70.588 12 5 2.400
5\35 171.429 68.571 5 2 2.500
13\90 173.333 66.667 13 5 2.600 Unnamed golden tuning
8\55 174.545 65.455 8 3 2.667
11\75 176.000 64.000 11 4 2.750
3\20 180.000 60.000 3 1 3.000 L/s = 3/1
10\65 184.615 55.385 10 3 3.333
7\45 186.667 53.333 7 2 3.500
11\70 188.571 51.429 11 3 3.667
4\25 192.000 48.000 4 1 4.000
9\55 196.364 43.636 9 2 4.500
5\30 200.000 40.000 5 1 5.000
6\35 205.714 34.286 6 1 6.000 Cloudtone↓
1\5 240.000 0.000 1 0 → inf