Penslen - Revision history

Vector at 23:28, 28 April 2026

2026-04-28T23:28:55Z

← Older revision		Revision as of 23:28, 28 April 2026
Line 3:		Line 3:
	'''Penslen''' (pattern msLsmLsmLsmsLmsL) is an [[aberrisma\|aberrismic]] ternary scale with structure 5L5m6s and the sole [[MOS substitution]] scale of type 6s(5L5m).		'''Penslen''' (pattern msLsmLsmLsmsLmsL) is an [[aberrisma\|aberrismic]] ternary scale with structure 5L5m6s and the sole [[MOS substitution]] scale of type 6s(5L5m).
	== 11-limit penslen ==		== 11-limit penslen ==
			''todo: explain what the heck the mode names are''
	{\| class="wikitable"		{\| class="wikitable"
	\|+ Interval Table (just-2.3.5; mode A3, msLsmLsmLsmsLmsL; 2.3.5 and 2.3.7 triads highlighted)		\|+ Interval Table (just-2.3.5; mode A3, msLsmLsmLsmsLmsL; 2.3.5 and 2.3.7 triads highlighted)

Inthar at 23:34, 5 April 2026

2026-04-05T23:34:18Z

← Older revision		Revision as of 23:34, 5 April 2026
Line 2:		Line 2:

	'''Penslen''' (pattern msLsmLsmLsmsLmsL) is an [[aberrisma\|aberrismic]] ternary scale with structure 5L5m6s and the sole [[MOS substitution]] scale of type 6s(5L5m).		'''Penslen''' (pattern msLsmLsmLsmsLmsL) is an [[aberrisma\|aberrismic]] ternary scale with structure 5L5m6s and the sole [[MOS substitution]] scale of type 6s(5L5m).
			== 11-limit penslen ==
	{\| class="wikitable"		{\| class="wikitable"
	\|+ Interval Table (just-2.3.5; mode A3, msLsmLsmLsmsLmsL; 2.3.5 and 2.3.7 triads highlighted)		\|+ Interval Table (just-2.3.5; mode A3, msLsmLsmLsmsLmsL; 2.3.5 and 2.3.7 triads highlighted)
Line 41:		Line 42:
	\|}		\|}

	~~== 11-limit penslen ==~~
	Portent (Slendric + Keenanismic)-tempered penslen is one of the best scale structures with which to access the 7-limit by tempering out 1029/1024 (equating (8/7)^3 to 3/2), and 11-limit by tempering out 385/384 (equating 6/5 * 8/7 to 11/8). These commas are both small and low-complexity. (Together with [[Aberschismic]], Portent implies 11-limit [[Rodan]], making Rodan uniquely useful in the [[aberrismic theory]] of edos 41 and larger.)		Portent (Slendric + Keenanismic)-tempered penslen is one of the best scale structures with which to access the 7-limit by tempering out 1029/1024 (equating (8/7)^3 to 3/2), and 11-limit by tempering out 385/384 (equating 6/5 * 8/7 to 11/8). These commas are both small and low-complexity. (Together with [[Aberschismic]], Portent implies 11-limit [[Rodan]], making Rodan uniquely useful in the [[aberrismic theory]] of edos 41 and larger.)

Ground at 15:34, 5 April 2026

2026-04-05T15:34:43Z

← Older revision		Revision as of 15:34, 5 April 2026
Line 3:		Line 3:
	'''Penslen''' (pattern msLsmLsmLsmsLmsL) is an [[aberrisma\|aberrismic]] ternary scale with structure 5L5m6s and the sole [[MOS substitution]] scale of type 6s(5L5m).		'''Penslen''' (pattern msLsmLsmLsmsLmsL) is an [[aberrisma\|aberrismic]] ternary scale with structure 5L5m6s and the sole [[MOS substitution]] scale of type 6s(5L5m).
	{\| class="wikitable"		{\| class="wikitable"
	\|+ Interval Table (just-2.3.5, mode A3, msLsmLsmLsmsLmsL)		\|+ Interval Table (just-2.3.5; mode A3, msLsmLsmLsmsLmsL; 2.3.5 and 2.3.7 triads highlighted)
	! A3 !! G3 !! G8 !! A2 !! A7 !! G7 !! A1 !! A6 !! G6 !! A0 !! A5 !! G5 !! G10 !! A4 !! G4 !! G9		! A3 !! G3 !! G8 !! A2 !! A7 !! G7 !! A1 !! A6 !! G6 !! A0 !! A5 !! G5 !! G10 !! A4 !! G4 !! G9
	\|-		\|-
	\| 1200 \|\| 1148 \|\| 1118 \|\| 966 \|\| 936 \|\| 884 \|\| 732 \|\| 702 \|\| 650 \|\| 498 \|\| 468 \|\| 416 \|\| 386 \|\| 234 \|\| 182 \|\| 152		\| 1200 \|\| 1148 \|\| 1118 \|\| 966 \|\| 936 \|\| 884 \|\| 732 \|\|class="thl"\| 702 \|\| 650 \|\| 498 \|\| 468 \|\| 416 \|\|class="thl"\| 386 \|\| 234 \|\| 182 \|\| 152
	\|-		\|-
	\| 1048 \|\| 996 \|\| 966 \|\| 814 \|\| 784 \|\| 732 \|\| 580 \|\| 550 \|\| 498 \|\| 346 \|\| 316 \|\| 264 \|\| 234 \|\| 82 \|\| 30 \|\| 0		\| 1048 \|\| 996 \|\| 966 \|\| 814 \|\| 784 \|\| 732 \|\| 580 \|\| 550 \|\| 498 \|\| 346 \|\|class="thl"\| 316 \|\|class="thl"\| 264 \|\| 234 \|\| 82 \|\| 30 \|\|class="thl"\| 0
	\|-		\|-
	\| 1018 \|\| 966 \|\| 936 \|\| 784 \|\| 754 \|\| 702 \|\| 550 \|\| 520 \|\| 468 \|\| 316 \|\| 286 \|\| 234 \|\| 204 \|\| 52 \|\| 0 \|\| 1170		\| 1018 \|\| 966 \|\| 936 \|\| 784 \|\| 754 \|\|class="thl"\| 702 \|\| 550 \|\| 520 \|\| 468 \|\|class="thl"\| 316 \|\| 286 \|\| 234 \|\| 204 \|\| 52 \|\|class="thl"\| 0 \|\| 1170
	\|-		\|-
	\| 966 \|\| 914 \|\| 884 \|\| 732 \|\| 702 \|\| 650 \|\| 498 \|\| 468 \|\| 416 \|\| 264 \|\| 234 \|\| 182 \|\| 152 \|\| 0 \|\| 1148 \|\| 1118		\| 966 \|\| 914 \|\| 884 \|\| 732 \|\|class="thl"\| 702 \|\| 650 \|\| 498 \|\| 468 \|\| 416 \|\|class="thl"\| 264 \|\| 234 \|\| 182 \|\| 152 \|\|class="thl"\| 0 \|\| 1148 \|\| 1118
	\|-		\|-
	\| 814 \|\| 762 \|\| 732 \|\| 580 \|\| 550 \|\| 498 \|\| 346 \|\| 316 \|\| 264 \|\| 112 \|\| 82 \|\| 30 \|\| 0 \|\| 1048 \|\| 996 \|\| 966		\| 814 \|\| 762 \|\| 732 \|\| 580 \|\| 550 \|\| 498 \|\| 346 \|\|class="thl"\| 316 \|\|class="thl"\| 264 \|\| 112 \|\| 82 \|\| 30 \|\|class="thl"\| 0 \|\| 1048 \|\| 996 \|\| 966
	\|-		\|-
	\| 784 \|\| 732 \|\| 702 \|\| 550 \|\| 520 \|\| 468 \|\| 316 \|\| 286 \|\| 234 \|\| 82 \|\| 52 \|\| 0 \|\| 1170 \|\| 1018 \|\| 966 \|\| 936		\| 784 \|\| 732 \|\|class="thl"\| 702 \|\| 550 \|\| 520 \|\| 468 \|\|class="thl"\| 316 \|\| 286 \|\| 234 \|\| 82 \|\| 52 \|\|class="thl"\| 0 \|\| 1170 \|\| 1018 \|\| 966 \|\| 936
	\|-		\|-
	\| 732 \|\| 680 \|\| 650 \|\| 498 \|\| 468 \|\| 416 \|\| 264 \|\| 234 \|\| 182 \|\| 30 \|\| 0 \|\| 1148 \|\| 1118 \|\| 966 \|\| 914 \|\| 884		\| 732 \|\| 680 \|\| 650 \|\| 498 \|\| 468 \|\| 416 \|\|class="thl"\| 264 \|\| 234 \|\| 182 \|\| 30 \|\|class="thl"\| 0 \|\| 1148 \|\| 1118 \|\| 966 \|\| 914 \|\| 884
	\|-		\|-
	\| 702 \|\| 650 \|\| 620 \|\| 468 \|\| 438 \|\| 386 \|\| 234 \|\| 204 \|\| 152 \|\| 0 \|\| 1170 \|\| 1118 \|\| 1088 \|\| 936 \|\| 884 \|\| 854		\|class="thl"\| 702 \|\| 650 \|\| 620 \|\| 468 \|\|class="thl"\| 438 \|\|class="thl"\| 386 \|\| 234 \|\| 204 \|\| 152 \|\|class="thl"\| 0 \|\| 1170 \|\| 1118 \|\| 1088 \|\| 936 \|\| 884 \|\| 854
	\|-		\|-
	\| 550 \|\| 498 \|\| 468 \|\| 316 \|\| 286 \|\| 234 \|\| 82 \|\| 52 \|\| 0 \|\| 1048 \|\| 1018 \|\| 966 \|\| 936 \|\| 784 \|\| 732 \|\| 702		\| 550 \|\| 498 \|\| 468 \|\|class="thl"\| 316 \|\| 286 \|\| 234 \|\| 82 \|\| 52 \|\|class="thl"\| 0 \|\| 1048 \|\| 1018 \|\| 966 \|\| 936 \|\| 784 \|\| 732 \|\|class="thl"\| 702
	\|-		\|-
	\| 498 \|\| 446 \|\| 416 \|\| 264 \|\| 234 \|\| 182 \|\| 30 \|\| 0 \|\| 1148 \|\| 996 \|\| 966 \|\| 914 \|\| 884 \|\| 732 \|\| 680 \|\| 650		\| 498 \|\| 446 \|\| 416 \|\|class="thl"\| 264 \|\| 234 \|\| 182 \|\| 30 \|\|class="thl"\| 0 \|\| 1148 \|\| 996 \|\| 966 \|\| 914 \|\| 884 \|\| 732 \|\| 680 \|\| 650
	\|-		\|-
	\| 468 \|\| 416 \|\| 386 \|\| 234 \|\| 204 \|\| 152 \|\| 0 \|\| 1170 \|\| 1118 \|\| 966 \|\| 936 \|\| 884 \|\| 854 \|\| 702 \|\| 650 \|\| 620		\| 468 \|\| 416 \|\|class="thl"\| 386 \|\| 234 \|\| 204 \|\| 152 \|\|class="thl"\| 0 \|\| 1170 \|\| 1118 \|\| 966 \|\| 936 \|\| 884 \|\| 854 \|\|class="thl"\| 702 \|\| 650 \|\| 620
	\|-		\|-
	\| 316 \|\| 264 \|\| 234 \|\| 82 \|\| 52 \|\| 0 \|\| 1048 \|\| 1018 \|\| 966 \|\| 814 \|\| 784 \|\| 732 \|\| 702 \|\| 550 \|\| 498 \|\| 468		\|class="thl"\| 316 \|\|class="thl"\| 264 \|\| 234 \|\| 82 \|\| 52 \|\|class="thl"\| 0 \|\| 1048 \|\| 1018 \|\| 966 \|\| 814 \|\| 784 \|\| 732 \|\|class="thl"\| 702 \|\| 550 \|\| 498 \|\| 468
	\|-		\|-
	\| 264 \|\| 212 \|\| 182 \|\| 30 \|\| 0 \|\| 1148 \|\| 996 \|\| 966 \|\| 914 \|\| 762 \|\| 732 \|\| 680 \|\| 650 \|\| 498 \|\| 446 \|\| 416		\|class="thl"\| 264 \|\| 212 \|\| 182 \|\| 30 \|\|class="thl"\| 0 \|\| 1148 \|\| 996 \|\| 966 \|\| 914 \|\| 762 \|\| 732 \|\| 680 \|\| 650 \|\| 498 \|\| 446 \|\| 416
	\|-		\|-
	\| 234 \|\| 182 \|\| 152 \|\| 0 \|\| 1170 \|\| 1118 \|\| 966 \|\| 936 \|\| 884 \|\| 732 \|\| 702 \|\| 650 \|\| 620 \|\| 468 \|\| 416 \|\| 386		\| 234 \|\| 182 \|\| 152 \|\|class="thl"\| 0 \|\| 1170 \|\| 1118 \|\| 966 \|\| 936 \|\| 884 \|\| 732 \|\|class="thl"\| 702 \|\| 650 \|\| 620 \|\| 468 \|\| 416 \|\|class="thl"\| 386
	\|-		\|-
	\| 82 \|\| 30 \|\| 0 \|\| 1048 \|\| 1018 \|\| 966 \|\| 814 \|\| 784 \|\| 732 \|\| 580 \|\| 550 \|\| 498 \|\| 468 \|\| 316 \|\| 264 \|\| 234		\| 82 \|\| 30 \|\|class="thl"\| 0 \|\| 1048 \|\| 1018 \|\| 966 \|\| 814 \|\| 784 \|\| 732 \|\| 580 \|\| 550 \|\| 498 \|\| 468 \|\|class="thl"\| 316 \|\|class="thl"\| 264 \|\| 234
	\|-		\|-
	\| 52 \|\| 0 \|\| 1170 \|\| 1018 \|\| 988 \|\| 936 \|\| 784 \|\| 754 \|\| 702 \|\| 550 \|\| 520 \|\| 468 \|\| 438 \|\| 286 \|\| 234 \|\| 204		\| 52 \|\|class="thl"\| 0 \|\| 1170 \|\| 1018 \|\| 988 \|\| 936 \|\| 784 \|\| 754 \|\|class="thl"\| 702 \|\| 550 \|\| 520 \|\| 468 \|\|class="thl"\| 438 \|\| 286 \|\| 234 \|\| 204
	\|-		\|-
	\| 0 \|\| 1148 \|\| 1118 \|\| 966 \|\| 936 \|\| 884 \|\| 732 \|\| 702 \|\| 650 \|\| 498 \|\| 468 \|\| 416 \|\| 386 \|\| 234 \|\| 182 \|\| 152		\|class="thl"\| 0 \|\| 1148 \|\| 1118 \|\| 966 \|\| 936 \|\| 884 \|\| 732 \|\|class="thl"\| 702 \|\| 650 \|\| 498 \|\| 468 \|\| 416 \|\|class="thl"\| 386 \|\| 234 \|\| 182 \|\| 152
	\|}		\|}

Ground at 15:26, 5 April 2026

2026-04-05T15:26:48Z

@@ Line 2: / Line 2: @@
 '''Penslen''' (pattern msLsmLsmLsmsLmsL) is an [[aberrisma|aberrismic]] ternary scale with structure 5L5m6s and the sole [[MOS substitution]] scale of type 6s(5L5m).
 == 11-limit penslen ==
 Portent (Slendric + Keenanismic)-tempered penslen is one of the best scale structures with which to access the 7-limit by tempering out 1029/1024 (equating (8/7)^3 to 3/2), and 11-limit by tempering out 385/384 (equating 6/5 * 8/7 to 11/8). These commas are both small and low-complexity. (Together with [[Aberschismic]], Portent implies 11-limit [[Rodan]], making Rodan uniquely useful in the [[aberrismic theory]] of edos 41 and larger.)

Inthar: /* 11-limit penslen */

2026-04-05T09:06:34Z

11-limit penslen

← Older revision		Revision as of 09:06, 5 April 2026
Line 3:		Line 3:
	'''Penslen''' (pattern msLsmLsmLsmsLmsL) is an [[aberrisma\|aberrismic]] ternary scale with structure 5L5m6s and the sole [[MOS substitution]] scale of type 6s(5L5m).		'''Penslen''' (pattern msLsmLsmLsmsLmsL) is an [[aberrisma\|aberrismic]] ternary scale with structure 5L5m6s and the sole [[MOS substitution]] scale of type 6s(5L5m).
	== 11-limit penslen ==		== 11-limit penslen ==
	Portent (Slendric + Keenanismic)-tempered penslen is one of the best scale structures with which to access the 7-limit by tempering out 1029/1024 (equating (8/7)^3 to 3/2), and 11-limit by tempering out 385/384 (equating 6/5 * 8/7 to 11/8). These commas are both small and low-complexity.		Portent (Slendric + Keenanismic)-tempered penslen is one of the best scale structures with which to access the 7-limit by tempering out 1029/1024 (equating (8/7)^3 to 3/2), and 11-limit by tempering out 385/384 (equating 6/5 * 8/7 to 11/8). These commas are both small and low-complexity. (Together with [[Aberschismic]], Portent implies 11-limit [[Rodan]], making Rodan uniquely useful in the [[aberrismic theory]] of edos 41 and larger.)

	(Together with [[Aberschismic]], Portent implies 11-limit [[Rodan]], making Rodan uniquely useful in the [[aberrismic theory]] of edos 41 and larger.)

	The simplest tuning is 31edo, which tempers out both of the relevant commas.		The simplest tuning is 31edo, which tempers out both of the relevant commas.

Inthar: /* 11-limit penslen */

2026-04-05T09:06:13Z

11-limit penslen

← Older revision		Revision as of 09:06, 5 April 2026
Line 5:		Line 5:
	Portent (Slendric + Keenanismic)-tempered penslen is one of the best scale structures with which to access the 7-limit by tempering out 1029/1024 (equating (8/7)^3 to 3/2), and 11-limit by tempering out 385/384 (equating 6/5 * 8/7 to 11/8). These commas are both small and low-complexity.		Portent (Slendric + Keenanismic)-tempered penslen is one of the best scale structures with which to access the 7-limit by tempering out 1029/1024 (equating (8/7)^3 to 3/2), and 11-limit by tempering out 385/384 (equating 6/5 * 8/7 to 11/8). These commas are both small and low-complexity.

	(Together with [[Aberschismic]], Portent implies 11-limit [[Rodan]], making Rodan uniquely ~~important~~ in the [[aberrismic theory]] of edos 41 and larger.)		(Together with [[Aberschismic]], Portent implies 11-limit [[Rodan]], making Rodan uniquely useful in the [[aberrismic theory]] of edos 41 and larger.)

	The simplest tuning is 31edo, which tempers out both of the relevant commas.		The simplest tuning is 31edo, which tempers out both of the relevant commas.

Inthar: /* 11-limit penslen */

2026-04-05T09:05:48Z

11-limit penslen

← Older revision		Revision as of 09:05, 5 April 2026
Line 4:		Line 4:
	== 11-limit penslen ==		== 11-limit penslen ==
	Portent (Slendric + Keenanismic)-tempered penslen is one of the best scale structures with which to access the 7-limit by tempering out 1029/1024 (equating (8/7)^3 to 3/2), and 11-limit by tempering out 385/384 (equating 6/5 * 8/7 to 11/8). These commas are both small and low-complexity.		Portent (Slendric + Keenanismic)-tempered penslen is one of the best scale structures with which to access the 7-limit by tempering out 1029/1024 (equating (8/7)^3 to 3/2), and 11-limit by tempering out 385/384 (equating 6/5 * 8/7 to 11/8). These commas are both small and low-complexity.

			(Together with [[Aberschismic]], Portent implies 11-limit [[Rodan]], making Rodan uniquely important in the [[aberrismic theory]] of edos 41 and larger.)

	The simplest tuning is 31edo, which tempers out both of the relevant commas.		The simplest tuning is 31edo, which tempers out both of the relevant commas.

Inthar: /* 11-limit penslen */

2026-04-05T01:18:54Z

11-limit penslen

← Older revision		Revision as of 01:18, 5 April 2026
Line 3:		Line 3:
	'''Penslen''' (pattern msLsmLsmLsmsLmsL) is an [[aberrisma\|aberrismic]] ternary scale with structure 5L5m6s and the sole [[MOS substitution]] scale of type 6s(5L5m).		'''Penslen''' (pattern msLsmLsmLsmsLmsL) is an [[aberrisma\|aberrismic]] ternary scale with structure 5L5m6s and the sole [[MOS substitution]] scale of type 6s(5L5m).
	== 11-limit penslen ==		== 11-limit penslen ==
	Keenanismic-tempered penslen is one of the best scale structures with which to access the 7-limit by tempering out 1029/1024 (equating (8/7)^3 to 3/2), and 11-limit by tempering out 385/384 (equating 6/5 * 8/7 to 11/8). These commas are both small and low-complexity.		Portent (Slendric + Keenanismic)-tempered penslen is one of the best scale structures with which to access the 7-limit by tempering out 1029/1024 (equating (8/7)^3 to 3/2), and 11-limit by tempering out 385/384 (equating 6/5 * 8/7 to 11/8). These commas are both small and low-complexity.

	The simplest tuning is 31edo, which tempers out both of the relevant commas.		The simplest tuning is 31edo, which tempers out both of the relevant commas.

Inthar: /* 11-limit penslen */

2026-03-06T13:36:55Z

11-limit penslen

← Older revision		Revision as of 13:36, 6 March 2026
Line 3:		Line 3:
	'''Penslen''' (pattern msLsmLsmLsmsLmsL) is an [[aberrisma\|aberrismic]] ternary scale with structure 5L5m6s and the sole [[MOS substitution]] scale of type 6s(5L5m).		'''Penslen''' (pattern msLsmLsmLsmsLmsL) is an [[aberrisma\|aberrismic]] ternary scale with structure 5L5m6s and the sole [[MOS substitution]] scale of type 6s(5L5m).
	== 11-limit penslen ==		== 11-limit penslen ==
	~~Gamelismic~~-tempered penslen is one of the best scale structures with which to access the 7-limit by tempering out 1029/1024 (equating (8/7)^3 to 3/2), and 11-limit by tempering out 385/384 (equating 6/5 * 8/7 to 11/8). These commas are both small and low-complexity.		Keenanismic-tempered penslen is one of the best scale structures with which to access the 7-limit by tempering out 1029/1024 (equating (8/7)^3 to 3/2), and 11-limit by tempering out 385/384 (equating 6/5 * 8/7 to 11/8). These commas are both small and low-complexity.

	The simplest tuning is 31edo, which tempers out both of the relevant commas.		The simplest tuning is 31edo, which tempers out both of the relevant commas.

	Tuning shown is just 2.3.5, Slendric 7, ~~Gamelismic~~ 11, i.e.		Tuning shown is just 2.3.5, Slendric 7, Keenanismic 11, i.e.

	<math>		<math>

Vector: portent is probably to be treated as canonical gamelismic

2026-03-06T06:18:24Z

portent is probably to be treated as canonical gamelismic

← Older revision		Revision as of 06:18, 6 March 2026
Line 3:		Line 3:
	'''Penslen''' (pattern msLsmLsmLsmsLmsL) is an [[aberrisma\|aberrismic]] ternary scale with structure 5L5m6s and the sole [[MOS substitution]] scale of type 6s(5L5m).		'''Penslen''' (pattern msLsmLsmLsmsLmsL) is an [[aberrisma\|aberrismic]] ternary scale with structure 5L5m6s and the sole [[MOS substitution]] scale of type 6s(5L5m).
	== 11-limit penslen ==		== 11-limit penslen ==
	~~Portent~~-tempered penslen is one of the best scale structures with which to access the 7-limit by tempering out 1029/1024 (equating (8/7)^3 to 3/2), and 11-limit by tempering out 385/384 (equating 6/5 * 8/7 to 11/8). These commas are both small and low-complexity.		Gamelismic-tempered penslen is one of the best scale structures with which to access the 7-limit by tempering out 1029/1024 (equating (8/7)^3 to 3/2), and 11-limit by tempering out 385/384 (equating 6/5 * 8/7 to 11/8). These commas are both small and low-complexity.

	The simplest tuning is 31edo, which tempers out both of the relevant commas.		The simplest tuning is 31edo, which tempers out both of the relevant commas.

	Tuning shown is just 2.3.5, Slendric 7, ~~Portent (Slendric + Keenanismic)~~ 11, i.e.		Tuning shown is just 2.3.5, Slendric 7, Gamelismic 11, i.e.

	<math>		<math>