Penslen

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Penslen (pattern msLsmLsmLsmsLmsL) is an aberrismic ternary scale with structure 5L5m6s and the sole MOS substitution scale of type 6s(5L5m).

11-limit penslen

Portent (Slendric + Keenanismic)-tempered penslen is one of the best scale structures with which to access the 7-limit by tempering out 1029/1024 (equating (8/7)^3 to 3/2), and 11-limit by tempering out 385/384 (equating 6/5 * 8/7 to 11/8). These commas are both small and low-complexity.

The simplest tuning is 31edo, which tempers out both of the relevant commas.

Tuning shown is just 2.3.5, Slendric 7, Keenanismic 11, i.e.

$T(7)=(2^{10}/3{)}^{\frac{1}{3}}$

$T(11)=\frac{384}{5\cdot T(7)}$

T() denotes applying the tuning map.

Mode A3 (msLsmLsmLsmsLmsL) Just-2.3.5 Tuning

	0	1
3	702.0	51.6
2	468.0	1017.6
1	234.0	783.6
0	0.0	549.6
-1	966.0	315.6
-2	732.0	81.7
-3	498.0	1047.7
-4	264.1	813.7

Example Untempered Intervals

36/35	48.8
21/20	84.5
8/7	231.2
7/6	266.9
6/5	315.6
21/16	470.8
4/3	498.0
48/35	546.8
3/2	702.0
32/21	729.2
63/40	786.4
8/5	813.7
7/4	968.8
9/5	1017.6
64/35	1044.9
2/1	1200.0

23/16-offset penslen

In this version of penslen, the 8-step offset is ~23/16 tempered together with 10/7 by tempering out 161/160. You can also add prime 17 by tempering out 8211/8192 = (3*7*17*23)/2^13.

Tuning shown is just 2.3.23, and

$T(7)=(2^{10}/3{)}^{\frac{1}{3}},$

$T(5)=\frac{23\cdot T(7)}{2^5}.$

Mode G6 (LsmsLmsLmsLsmLsm) Just-2.3.23 Tuning

	0	1
3	702.0	130.2
2	468.0	1096.2
1	234.0	862.3
0	0.0	628.3
-1	966.0	394.3
-2	732.0	160.3
-3	498.0	1126.3
-4	264.1	892.3

Penslen in this temperament is represented by 46edo's 5:3:1 tuning.