Penslen

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

Portent penslen

It 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, Portent (Slendric + 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