Penslen: Difference between revisions
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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 | 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]]. | 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]]. | ||
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== Interpretations == | == Interpretations == | ||
=== Portent === | === Portent === | ||
[[Portent]] is the temperament 11-lim[1029/1024, 385/384], and interprets the 8-step interval as an [[Interseptimal interval|ultrafourth]] [[48/35]] or [[11/8]]. | [[Portent]] is the temperament 11-lim[1029/1024, 385/384], and interprets the 8-step interval as an [[Interseptimal interval|ultrafourth]] [[48/35]] or [[11/8]]. This is the interpretation originally found by groundfault. | ||
A 7-limit JI detempering of Portent penslen is: | A 7-limit JI detempering of Portent penslen (the mode msLsmLsmLsmsLmsL) is: | ||
36/35 | 36/35 | ||
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* 11/8 is 8 scale steps | * 11/8 is 8 scale steps | ||
Example edo tunings are [[46edo]] | 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& | === 2.3.5.7.13.17.23[46&67] === | ||
In this temperament, | 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 is: | A 7-limit JI detempering of this penslen (the mode msLmsLsmLsmLsmsL) is: | ||
21/20 | 21/20 | ||
16/15 | 16/15 | ||
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28/15 | 28/15 | ||
2/1 | 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. | Penslen in this temperament is represented by [[46edo]]'s 5:3:1 and [[67edo]]'s 7:4:2 tunings. | ||
== External links == | == External links == | ||
* [https://scaleworkshop.plainsound.org/scale/r4mvOJneC 46edo tuning] | * [https://scaleworkshop.plainsound.org/scale/r4mvOJneC 46edo (6:2:1) tuning] | ||
* [https://scaleworkshop.plainsound.org/scale/r4mRDJvg2 72edo tuning] | * [https://scaleworkshop.plainsound.org/scale/r4mRDJvg2 72edo (9:3:2) tuning] | ||
* [https://sw3.lumipakkanen.com/scale/bsm1wb-7E 46edo (5:3:1) tuning] | |||
* [https://sw3.lumipakkanen.com/scale/bsmQ3gcGX 67edo (7:4:2) tuning] | |||
=== Streams === | === Streams === | ||
* [https://www.youtube.com/watch?v=8p40itH3fg4 Gordon Wery stream 1] | * [https://www.youtube.com/watch?v=8p40itH3fg4 Gordon Wery stream 1] | ||
Latest revision as of 15:58, 27 March 2025
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:
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.