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 ~~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 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 ~~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 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]].

A 7-limit JI detempering of penslen is:

== Interpretations ==

=== 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]]. This is the interpretation originally found by groundfault.

A 7-limit JI detempering of Portent penslen (the mode msLsmLsmLsmsLmsL) is:

36/35

Line 21:

Line 25:

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:

Line 31:

Line 32:

* 11/8 is 8 scale steps

Example edo tunings are [[46edo]]'s 6:2:1 ~~and~~ [[72edo]]'s 9:3:2 ~~tunings~~.

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.)

~~==== 17-lim~~[~~46 & 72~~] ~~====~~

Penslen in this temperament is represented by [[46edo]]'s 5:3:1 and [[67edo]]'s 7:4:2 tunings.

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

== 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 ===

* [https://www.youtube.com/watch?v=8p40itH3fg4 Gordon ~~Wrey~~ stream 1]

* [https://www.youtube.com/watch?v=8p40itH3fg4 Gordon Wery stream 1]

* [https://www.youtube.com/watch?v=FYDlDKZTtVg Gordon ~~Wrey~~ stream 2]

* [https://www.youtube.com/watch?v=FYDlDKZTtVg Gordon Wery stream 2]

* [https://www.youtube.com/watch?v=KK5ER1GvCr0 Gordon ~~Wrey~~ stream 3]

* [https://www.youtube.com/watch?v=KK5ER1GvCr0 Gordon Wery stream 3]

* [https://www.youtube.com/watch?v=sauNE8CApz8 Gordon ~~Wrey~~ stream 4]

* [https://www.youtube.com/watch?v=sauNE8CApz8 Gordon Wery stream 4]

[[Category:Aberrismic theory]]

[[Category:Rank-3 scales]]

@@ Line 1: / Line 1: @@
-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).
+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 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 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]].
-A 7-limit JI detempering of penslen is:
+== Interpretations ==
+=== 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]]. This is the interpretation originally found by groundfault.
+A 7-limit JI detempering of Portent penslen (the mode msLsmLsmLsmsLmsL) is:
 /35
@@ Line 21: / Line 25: @@
 /35
 /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:
@@ Line 31: / Line 32: @@
 * 11/8 is 8 scale steps
-Example edo tunings are [[46edo]]'s 6:2:1 and [[72edo]]'s 9:3:2 tunings.
+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:
+/20
+/15
+/7
+/5
+/40
+/16
+/3
+/5
+/2
+/21
+/5
+/7
+/4
+/80
+/15
+/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.)
-==== 17-lim[46 & 72] ====
+Penslen in this temperament is represented by [[46edo]]'s 5:3:1 and [[67edo]]'s 7:4:2 tunings.
-This temperament is a half-octave rank-2 temperament, equal to 17-lim[385/384, 441/440, 561/560, 595/594].
 == 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 ===
-* [https://www.youtube.com/watch?v=8p40itH3fg4 Gordon Wrey stream 1]
+* [https://www.youtube.com/watch?v=8p40itH3fg4 Gordon Wery stream 1]
-* [https://www.youtube.com/watch?v=FYDlDKZTtVg Gordon Wrey stream 2]
+* [https://www.youtube.com/watch?v=FYDlDKZTtVg Gordon Wery stream 2]
-* [https://www.youtube.com/watch?v=KK5ER1GvCr0 Gordon Wrey stream 3]
+* [https://www.youtube.com/watch?v=KK5ER1GvCr0 Gordon Wery stream 3]
-* [https://www.youtube.com/watch?v=sauNE8CApz8 Gordon Wrey stream 4]
+* [https://www.youtube.com/watch?v=sauNE8CApz8 Gordon Wery stream 4]
 [[Category:Aberrismic theory]]
 [[Category:Rank-3 scales]]