Penslen: Difference between revisions
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In [[aberrismic theory]], '''penslen''' (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). | 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 [[Interseptimal interval|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]]. | 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 [[Interseptimal interval|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]]. | ||
Revision as of 01:09, 2 December 2024
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 steps
- 5/4 is 4 steps
- 7/4 is 13 steps
- 11/8 is 8 steps
Example edo tunings are 46edo's 6:2:1 and 72edo's 9:3:2 tunings.