Penslen - Revision history

Inthar: /* 11-limit penslen */

2026-04-05T09:05:48Z

11-limit penslen

← Older revision		Revision as of 09:05, 5 April 2026
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	== 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
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	'''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
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	'''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>

Inthar at 05:58, 6 March 2026

2026-03-06T05:58:45Z

← Older revision		Revision as of 05:58, 6 March 2026
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	{{problematic}}		{{problematic}}

	'''Penslen''' 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.		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.

Inthar: /* Portent penslen */

2026-01-07T22:15:50Z

Portent penslen

← Older revision		Revision as of 22:15, 7 January 2026
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	'''Penslen''' is an [[aberrisma\|aberrismic]] ternary scale with structure 5L5m6s and the sole [[MOS substitution]] scale of type 6s(5L5m).		'''Penslen''' is an [[aberrisma\|aberrismic]] ternary scale with structure 5L5m6s and the sole [[MOS substitution]] scale of type 6s(5L5m).
	== ~~Portent~~ 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.		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.

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	\|1200.0		\|1200.0
	\|}		\|}

	== 23/16-offset penslen ==		== 23/16-offset penslen ==
	In this version of penslen, the 8-step offset is ~23/16 tempered together with 10/7 by tempering out 161/160. You can also add prime 17 by tempering out 8211/8192 = (3717*23)/2^13.		In this version of penslen, the 8-step offset is ~23/16 tempered together with 10/7 by tempering out 161/160. You can also add prime 17 by tempering out 8211/8192 = (3717*23)/2^13.

Inthar: /* 23/16-offset penslen */

2026-01-06T14:51:34Z

23/16-offset penslen

← Older revision		Revision as of 14:51, 6 January 2026
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	\|}		\|}
	== 23/16-offset penslen ==		== 23/16-offset penslen ==
	In this ~~temperament~~, the 8-step offset is ~23/16 tempered together with 10/7 by tempering out 161/160. You can also add prime 17 by tempering out 8211/8192 = (3717*23)/2^13.		In this version of penslen, the 8-step offset is ~23/16 tempered together with 10/7 by tempering out 161/160. You can also add prime 17 by tempering out 8211/8192 = (3717*23)/2^13.

	Tuning shown is just 2.3.23, and		Tuning shown is just 2.3.23, and

Inthar: /* 23/16-offset penslen */

2026-01-06T14:45:52Z

23/16-offset penslen

← Older revision		Revision as of 14:45, 6 January 2026
Line 108:		Line 108:
	\|}		\|}
	== 23/16-offset penslen ==		== 23/16-offset penslen ==
	In this temperament, the 8-step offset is ~23/16 tempered together with 10/7 by tempering out 161/160. You can also add 17 by tempering out 8211/8192 = (3717*23)/2^13.		In this temperament, the 8-step offset is ~23/16 tempered together with 10/7 by tempering out 161/160. You can also add prime 17 by tempering out 8211/8192 = (3717*23)/2^13.

	Tuning shown is just 2.3.23, and		Tuning shown is just 2.3.23, and

Inthar: /* 23/16-offset penslen */

2026-01-06T14:45:20Z

23/16-offset penslen

← Older revision		Revision as of 14:45, 6 January 2026
Line 108:		Line 108:
	\|}		\|}
	== 23/16-offset penslen ==		== 23/16-offset penslen ==
	In this temperament, the 8-step offset is ~23/16 tempered together with 10/7 by tempering out 161/160.		In this temperament, the 8-step offset is ~23/16 tempered together with 10/7 by tempering out 161/160. You can also add 17 by tempering out 8211/8192 = (3717*23)/2^13.

	Tuning shown is just 2.3.23, and		Tuning shown is just 2.3.23, and

Inthar: /* 23/16-offset penslen */

2026-01-06T14:41:02Z

23/16-offset penslen

← Older revision		Revision as of 14:41, 6 January 2026
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	\|}		\|}

	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 tuning.
	{{Cat\|Ternary scales		{{Cat\|Ternary scales
	MOS substitution scales		MOS substitution scales
	}}		}}