Penslen
In aberrismic theory, penslen (from pentawood and slendric; in aberrismic systematic nomenclature slen5m) is the 16-note ternary scale step pattern LmsLmsLsmLsmLsms with step signature 5L5m6s. It is the unique even-regular scale with this step signature (since the even-regular scale with a given step signature is always unique if it exists).
Penslen is comprised of two 8-note generator arcs. Each generator is a 3-step supermajor second (L + m + s), interpreted as 8/7, and the offset is an 8-step interval. The fifth is 9 steps and is a stack of three 8/7 generators. When you temper out 1029/1024, this fifth is interpreted as 3/2.
Interpretations
Portent
Portent is the temperament 11-lim[1029/1024, 385/384], and interprets the 8-step interval as an ultrafourth 48/35 or 11/8.
A 7-limit JI detempering of Portent penslen (the mode msLsmLsmLsmsLmsL) is:
36/35 21/20 8/7 7/6 6/5 21/16 4/3 48/35 3/2 32/21 63/40 8/5 7/4 9/5 64/35 2/1
The prime interpretations are:
- 3/2 is 9 scale steps
- 5/4 is 4 scale steps
- 7/4 is 13 scale steps
- 11/8 is 8 scale steps
Example edo tunings are 46edo's 6:2:1 and 72edo's 9:3:2 tunings.
2.3.5.7.13.17.23[46&67]
In this temperament, the 8-step offset is ~23/16 tempered together with 10/7 by tempering out 161/160.
A 7-limit JI detempering of this penslen (the mode msLmsLsmLsmLsmsL) is:
21/20 16/15 8/7 6/5 49/40 21/16 4/3 7/5 3/2 32/21 8/5 12/7 7/4 147/80 28/15 2/1
(However, Inthar recommends interpreting the scale in 2.3.7.13.17.23 for higher accuracy, interpreting the ~5/4 as ~64/51 and not as ~5/4.)
Penslen in this temperament is represented by 46edo's 5:3:1 and 67edo's 7:4:2 tunings.