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 only diregular scale with this step signature (since the diregular 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 can be interpreted as an ultrafourth 48/35 or 11/8. 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.

A 7-limit JI detempering of penslen 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 

Interpretations

Portent

Portent is the temperament 11-lim[1029/1024, 385/384], and equates the 8-step interval interpreted as 48/35 to 11/8.

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.

17-lim[46 & 72]

This temperament is a half-octave rank-2 temperament, equal to 17-lim[385/384, 441/440, 561/560, 595/594].

External links

• 46edo tuning
• 72edo tuning