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. This is the interpretation originally found by groundfault.

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:

• 41edo, 5:2:1
• 46edo, 6:2:1
• 72edo, 9:3:2
• 87edo, 11:4:2
• 159edo, 20:7:4

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.

External links

• 46edo (6:2:1) tuning
• 72edo (9:3:2) tuning
• 46edo (5:3:1) tuning
• 67edo (7:4:2) tuning

Streams

• Gordon Wery stream 1
• Gordon Wery stream 2
• Gordon Wery stream 3
• Gordon Wery stream 4