Pentadacus - Revision history

CompactStar at 04:13, 16 October 2026

2026-10-16T04:13:52Z

← Older revision		Revision as of 04:13, 16 October 2026
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	Properly-tuned pentadacus generates the [[5/1]]-equivalent [[MOS scales]] [[1L 1s (5/1-equivalent)\|1L 1s<5/1>]], [[1L 2s (5/1-equivalent)\|1L 2s<5/1>]], etc. until ending the monolarge mos chain at [[1L 13s (5/1-equivalent)\|1L 13s<5/1>]], followed by [[14L 1s (5/1-equivalent)\|14L 1s<5/1>]], [[14L 15s (5/1-equivalent)\|14L 15s<5/1>]]. Pentadacus has both low [[complexity]] (especially by the standards of the 5/1-equivalent world, where scales have lots of notes) and low [[error]] if tuned correctly, providing an [[efficiency\|efficient]] traversal of the 5.7.11 subgroup. It was first discovered and named by [[User:CompactStar\|CompactStar]] in 2026.		Properly-tuned pentadacus generates the [[5/1]]-equivalent [[MOS scales]] [[1L 1s (5/1-equivalent)\|1L 1s<5/1>]], [[1L 2s (5/1-equivalent)\|1L 2s<5/1>]], etc. until ending the monolarge mos chain at [[1L 13s (5/1-equivalent)\|1L 13s<5/1>]], followed by [[14L 1s (5/1-equivalent)\|14L 1s<5/1>]], [[14L 15s (5/1-equivalent)\|14L 15s<5/1>]]. Pentadacus has both low [[complexity]] (especially by the standards of the 5/1-equivalent world, where scales have lots of notes) and low [[error]] if tuned correctly, providing an [[efficiency\|efficient]] traversal of the 5.7.11 subgroup. It was first discovered and named by [[User:CompactStar\|CompactStar]] in 2026.

	Pentadacus can be thought of as a compressed [[14ed5]] until you hit [[5/1]], as is best exemplified by the [[1L 13s (5/1-equivalent)\|1L 13s<5/1>]] Pentadacus[14] mos. Because of this, many good smaller pentadacus tunings are of the form (14''n'' + 1)ed5 such as [[29ed5]], [[43ed5]], and [[57ed5]]. In this respect, it is similar to a [[cluster temperament]], but does not seem to exactly meet the definition of a cluster temperament. 14ed5 is also close to [[6edo]], the familiar whole-tone scale with octaves, so pentadacus is very alien (being a step above even tritave-equivalent temperaments) but can lapse into sounding like the familiar whole-tone scale at times. 6 generators in pentadacus can sound a bit like a [[stretched and compressed tuning\|compressed octave]] but it is usually inaccurate unless you are using a very sharp tuning like 14ed5. It should also be noted that -2 generators pentave-reduced can sound close to [[4/1]].		Pentadacus can be thought of as a compressed [[14ed5]] until you hit [[5/1]], as is best exemplified by the [[1L 13s (5/1-equivalent)\|1L 13s<5/1>]] Pentadacus[14] mos. Because of this, many good smaller pentadacus tunings are of the form (14''n'' + 1)ed5 such as [[29ed5]], [[43ed5]], and [[57ed5]]. In this respect, it is similar to a [[cluster temperament]], but does not seem to exactly meet the definition of a cluster temperament. 14ed5 is also close to [[6edo]], the familiar whole-tone scale with octaves, so pentadacus is very alien (being a step above even tritave-equivalent temperaments) but can lapse into sounding like the familiar whole-tone scale at times. 6 generators in pentadacus can sound a bit like a [[stretched and compressed tuning\|compressed octave]] but it is usually inaccurate unless you are using a very sharp tuning like 14ed5. It should also be noted that -2 generators pentave-reduced can sound very close to [[4/1]].

	Pentadacus is connected to the octave-repeating [[didacus]] temperament as both have a small whole tone generator for which 3 stack to 7/5, and [[didacus\|undecimal didacus]] can actually be viewed not only as an [[extension]] of didacus to include the 11th harmonic, but also a [[weak extension]] of pentadacus to include octaves, with 2/1 being mapped to half a pentave minus one generator. Pentadacus's connection to [[14ed5]] (which is effectively 6edo with a just 5/1) is a lot like Didacus's connection to [[6edo]].		Pentadacus is connected to the octave-repeating [[didacus]] temperament as both have a small whole tone generator for which 3 stack to 7/5, and [[didacus\|undecimal didacus]] can actually be viewed not only as an [[extension]] of didacus to include the 11th harmonic, but also a [[weak extension]] of pentadacus to include octaves, with 2/1 being mapped to half a pentave minus one generator. Pentadacus's connection to [[14ed5]] (which is effectively 6edo with a just 5/1) is a lot like Didacus's connection to [[6edo]].

CompactStar at 03:55, 16 October 2026

2026-10-16T03:55:58Z

← Older revision		Revision as of 03:55, 16 October 2026
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	Properly-tuned pentadacus generates the [[5/1]]-equivalent [[MOS scales]] [[1L 1s (5/1-equivalent)\|1L 1s<5/1>]], [[1L 2s (5/1-equivalent)\|1L 2s<5/1>]], etc. until ending the monolarge mos chain at [[1L 13s (5/1-equivalent)\|1L 13s<5/1>]], followed by [[14L 1s (5/1-equivalent)\|14L 1s<5/1>]], [[14L 15s (5/1-equivalent)\|14L 15s<5/1>]]. Pentadacus has both low [[complexity]] (especially by the standards of the 5/1-equivalent world, where scales have lots of notes) and low [[error]] if tuned correctly, providing an [[efficiency\|efficient]] traversal of the 5.7.11 subgroup. It was first discovered and named by [[User:CompactStar\|CompactStar]] in 2026.		Properly-tuned pentadacus generates the [[5/1]]-equivalent [[MOS scales]] [[1L 1s (5/1-equivalent)\|1L 1s<5/1>]], [[1L 2s (5/1-equivalent)\|1L 2s<5/1>]], etc. until ending the monolarge mos chain at [[1L 13s (5/1-equivalent)\|1L 13s<5/1>]], followed by [[14L 1s (5/1-equivalent)\|14L 1s<5/1>]], [[14L 15s (5/1-equivalent)\|14L 15s<5/1>]]. Pentadacus has both low [[complexity]] (especially by the standards of the 5/1-equivalent world, where scales have lots of notes) and low [[error]] if tuned correctly, providing an [[efficiency\|efficient]] traversal of the 5.7.11 subgroup. It was first discovered and named by [[User:CompactStar\|CompactStar]] in 2026.

	Pentadacus can be thought of as a compressed [[14ed5]] until you hit [[5/1]], as is best exemplified by the [[1L 13s (5/1-equivalent)\|1L 13s<5/1>]] Pentadacus[14] mos. Because of this, many good smaller pentadacus tunings are of the form (14''n'' + 1)ed5 such as [[29ed5]], [[43ed5]], and [[57ed5]]. In this respect, it is similar to a [[cluster temperament]], but does not seem to exactly meet the definition of a cluster temperament. 14ed5 is also close to [[6edo]], the familiar whole-tone scale with octaves, so pentadacus is very alien (being a step above even tritave-equivalent temperaments) but can lapse into sounding like the familiar whole-tone scale at times. 6 generators in pentadacus can sound a bit like a [[stretched and compressed tuning\|compressed octave]] but it is usually inaccurate unless you are using a very sharp tuning like 14ed5.		Pentadacus can be thought of as a compressed [[14ed5]] until you hit [[5/1]], as is best exemplified by the [[1L 13s (5/1-equivalent)\|1L 13s<5/1>]] Pentadacus[14] mos. Because of this, many good smaller pentadacus tunings are of the form (14''n'' + 1)ed5 such as [[29ed5]], [[43ed5]], and [[57ed5]]. In this respect, it is similar to a [[cluster temperament]], but does not seem to exactly meet the definition of a cluster temperament. 14ed5 is also close to [[6edo]], the familiar whole-tone scale with octaves, so pentadacus is very alien (being a step above even tritave-equivalent temperaments) but can lapse into sounding like the familiar whole-tone scale at times. 6 generators in pentadacus can sound a bit like a [[stretched and compressed tuning\|compressed octave]] but it is usually inaccurate unless you are using a very sharp tuning like 14ed5. It should also be noted that -2 generators pentave-reduced can sound close to [[4/1]].

	Pentadacus is connected to the octave-repeating [[didacus]] temperament as both have a small whole tone generator for which 3 stack to 7/5, and [[didacus\|undecimal didacus]] can actually be viewed not only as an [[extension]] of didacus to include the 11th harmonic, but also a [[weak extension]] of pentadacus to include octaves, with 2/1 being mapped to half a pentave minus one generator. Pentadacus's connection to [[14ed5]] (which is effectively 6edo with a just 5/1) is a lot like Didacus's connection to [[6edo]].		Pentadacus is connected to the octave-repeating [[didacus]] temperament as both have a small whole tone generator for which 3 stack to 7/5, and [[didacus\|undecimal didacus]] can actually be viewed not only as an [[extension]] of didacus to include the 11th harmonic, but also a [[weak extension]] of pentadacus to include octaves, with 2/1 being mapped to half a pentave minus one generator. Pentadacus's connection to [[14ed5]] (which is effectively 6edo with a just 5/1) is a lot like Didacus's connection to [[6edo]].

CompactStar at 02:21, 16 October 2026

2026-10-16T02:21:58Z

← Older revision		Revision as of 02:21, 16 October 2026
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	Pentadacus is connected to the octave-repeating [[didacus]] temperament as both have a small whole tone generator for which 3 stack to 7/5, and [[didacus\|undecimal didacus]] can actually be viewed not only as an [[extension]] of didacus to include the 11th harmonic, but also a [[weak extension]] of pentadacus to include octaves, with 2/1 being mapped to half a pentave minus one generator. Pentadacus's connection to [[14ed5]] (which is effectively 6edo with a just 5/1) is a lot like Didacus's connection to [[6edo]].		Pentadacus is connected to the octave-repeating [[didacus]] temperament as both have a small whole tone generator for which 3 stack to 7/5, and [[didacus\|undecimal didacus]] can actually be viewed not only as an [[extension]] of didacus to include the 11th harmonic, but also a [[weak extension]] of pentadacus to include octaves, with 2/1 being mapped to half a pentave minus one generator. Pentadacus's connection to [[14ed5]] (which is effectively 6edo with a just 5/1) is a lot like Didacus's connection to [[6edo]].

			For technical data, see [[No-2s subgroup temperaments#Pentadacus]].
	== Etymology ==		== Etymology ==
	It is named as a play on [[didacus]], with the "di-" part being rebracketed as the Greek prefix for 2 and changed to "penta-" (5).		It is named as a play on [[didacus]], with the "di-" part being rebracketed as the Greek prefix for 2 and changed to "penta-" (5).

CompactStar at 01:11, 16 October 2026

2026-10-16T01:11:42Z

← Older revision		Revision as of 01:11, 16 October 2026
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	It is suitable for a harmonic system based exclusively on [https://oeis.org/wiki/5-rough_numbers 5-rough numbers] (numbers not divisible by 2 or 3), similar to how [[Bohlen-Pierce]]/[[BPS]] is suitable for a harmonic system based on odd numbers. 5:7:11(:25) could be used as the fundamental consonant chord in such a system, in the place of 3:5:7(:9) in BPS or of 4:5:6(:8) in meantone.		It is suitable for a harmonic system based exclusively on [https://oeis.org/wiki/5-rough_numbers 5-rough numbers] (numbers not divisible by 2 or 3), similar to how [[Bohlen-Pierce]]/[[BPS]] is suitable for a harmonic system based on odd numbers. 5:7:11(:25) could be used as the fundamental consonant chord in such a system, in the place of 3:5:7(:9) in BPS or of 4:5:6(:8) in meantone.


	Properly-tuned pentadacus generates the [[5/1]]-equivalent [[MOS scales]] [[1L 1s (5/1-equivalent)\|1L 1s<5/1>]], [[1L 2s (5/1-equivalent)\|1L 2s<5/1>]], etc. until ending the monolarge mos chain at [[1L 13s (5/1-equivalent)\|1L 13s<5/1>]], followed by [[14L 1s (5/1-equivalent)\|14L 1s<5/1>]], [[14L 15s (5/1-equivalent)\|14L 15s<5/1>]]. Pentadacus has both low [[complexity]] (especially by the standards of the 5/1-equivalent world, where scales have lots of notes) and low [[error]] if tuned correctly, providing an [[efficiency\|efficient]] traversal of the 5.7.11 subgroup. It was first discovered and named by [[User:CompactStar\|CompactStar]] in 2026.		Properly-tuned pentadacus generates the [[5/1]]-equivalent [[MOS scales]] [[1L 1s (5/1-equivalent)\|1L 1s<5/1>]], [[1L 2s (5/1-equivalent)\|1L 2s<5/1>]], etc. until ending the monolarge mos chain at [[1L 13s (5/1-equivalent)\|1L 13s<5/1>]], followed by [[14L 1s (5/1-equivalent)\|14L 1s<5/1>]], [[14L 15s (5/1-equivalent)\|14L 15s<5/1>]]. Pentadacus has both low [[complexity]] (especially by the standards of the 5/1-equivalent world, where scales have lots of notes) and low [[error]] if tuned correctly, providing an [[efficiency\|efficient]] traversal of the 5.7.11 subgroup. It was first discovered and named by [[User:CompactStar\|CompactStar]] in 2026.

CompactStar: /* Tuning spectrum */

2026-10-16T00:53:35Z

Tuning spectrum

← Older revision		Revision as of 00:53, 16 October 2026
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	\|		\|
	\|		\|
	\| 0.000		\| '''0.000'''
	\| '''Lower bound of 5.7.11 tonality diamond monotone'''		\| '''Lower bound of 5.7.11 tonality diamond monotone'''
	\|-		\|-
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	\| '''1\[[14ed5]]'''		\| '''1\[[14ed5]]'''
	\|		\|
	\| 199.022		\| '''199.022'''
	\| '''Upper bound of 5.7.11 tonality diamond monotone'''		\| '''Upper bound of 5.7.11 tonality diamond monotone'''
	\|-		\|-

CompactStar: /* Tuning spectrum */

2026-10-16T00:53:04Z

Tuning spectrum

← Older revision		Revision as of 00:53, 16 October 2026
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	! Generator (¢)		! Generator (¢)
	! Comments		! Comments
			\|-
			\|
			\|
			\| 0.000
			\| '''Lower bound of 5.7.11 tonality diamond monotone'''
	\|-		\|-
	\| 1\[[15ed5]]		\| 1\[[15ed5]]
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	\|		\|
	\|-		\|-
	\| 1\[[14ed5]]		\| '''1\[[14ed5]]'''
	\|		\|
	\| 199.022		\| 199.022
	\|		\| '''Upper bound of 5.7.11 tonality diamond monotone'''
	\|-		\|-
	\|		\|

CompactStar at 00:47, 16 October 2026

2026-10-16T00:47:37Z

← Older revision		Revision as of 00:47, 16 October 2026
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	It is suitable for a harmonic system based exclusively on [https://oeis.org/wiki/5-rough_numbers 5-rough numbers] (numbers not divisible by 2 or 3), similar to how [[Bohlen-Pierce]]/[[BPS]] is suitable for a harmonic system based on odd numbers. 5:7:11(:25) could be used as the fundamental consonant chord in such a system, in the place of 3:5:7(:9) in BPS or of 4:5:6(:8) in meantone.		It is suitable for a harmonic system based exclusively on [https://oeis.org/wiki/5-rough_numbers 5-rough numbers] (numbers not divisible by 2 or 3), similar to how [[Bohlen-Pierce]]/[[BPS]] is suitable for a harmonic system based on odd numbers. 5:7:11(:25) could be used as the fundamental consonant chord in such a system, in the place of 3:5:7(:9) in BPS or of 4:5:6(:8) in meantone.

CompactStar at 22:26, 15 October 2026

2026-10-15T22:26:22Z

← Older revision		Revision as of 22:26, 15 October 2026
Line 12:		Line 12:
	}}		}}

	'''Pentadacus''' is a [[nonoctave]] [[regular temperament]] in the 5.7.11 [[subgroup]] which tempers out the comma [[831875/823543]]. It is even more exotic than [[Bohlen-Pierce]], lacking both [[2/1]] and [[3/1]], and typically it would be used with an [[equave]] of [[5/1]], also known as the pentave. ~~Essentially it~~ is suitable for a harmonic system based exclusively on [https://oeis.org/wiki/5-rough_numbers 5-rough numbers] (numbers not divisible by 2 or 3), similar to how Bohlen-Pierce is suitable for a harmonic system based on odd numbers. ~~It is generated by~~ a ~~[[meantone]]-esque small whole tone interval that represents [[55/49]]. Stacking~~ 3 ~~of these tones gives [[7/~~5~~]] and~~ 7 of ~~them give [[11/~~5]].		'''Pentadacus''' is a [[nonoctave]] [[regular temperament]] in the 5.7.11 [[subgroup]] which tempers out the comma [[831875/823543]]. It is even more exotic than [[Bohlen-Pierce]], lacking both [[2/1]] and [[3/1]], and typically it would be used with an [[equave]] of [[5/1]], also known as the pentave.. It is generated by a [[meantone]]-esque small whole tone interval that represents [[55/49]]. Stacking 3 of these tones gives [[7/5]] and 7 of them give [[11/5]].

			It is suitable for a harmonic system based exclusively on [https://oeis.org/wiki/5-rough_numbers 5-rough numbers] (numbers not divisible by 2 or 3), similar to how [[Bohlen-Pierce]]/[[BPS]] is suitable for a harmonic system based on odd numbers. 5:7:11(:25) could be used as the fundamental consonant chord in such a system, in the place of 3:5:7(:9) in BPS or of 4:5:6(:8) in meantone.



	Properly-tuned pentadacus generates the [[5/1]]-equivalent [[MOS scales]] [[1L 1s (5/1-equivalent)\|1L 1s<5/1>]], [[1L 2s (5/1-equivalent)\|1L 2s<5/1>]], etc. until ending the monolarge mos chain at [[1L 13s (5/1-equivalent)\|1L 13s<5/1>]], followed by [[14L 1s (5/1-equivalent)\|14L 1s<5/1>]], [[14L 15s (5/1-equivalent)\|14L 15s<5/1>]]. Pentadacus has both low [[complexity]] (especially by the standards of the 5/1-equivalent world, where scales have lots of notes) and low [[error]] if tuned correctly, providing an [[efficiency\|efficient]] traversal of the 5.7.11 subgroup. It was first discovered and named by [[User:CompactStar\|CompactStar]] in 2026.		Properly-tuned pentadacus generates the [[5/1]]-equivalent [[MOS scales]] [[1L 1s (5/1-equivalent)\|1L 1s<5/1>]], [[1L 2s (5/1-equivalent)\|1L 2s<5/1>]], etc. until ending the monolarge mos chain at [[1L 13s (5/1-equivalent)\|1L 13s<5/1>]], followed by [[14L 1s (5/1-equivalent)\|14L 1s<5/1>]], [[14L 15s (5/1-equivalent)\|14L 15s<5/1>]]. Pentadacus has both low [[complexity]] (especially by the standards of the 5/1-equivalent world, where scales have lots of notes) and low [[error]] if tuned correctly, providing an [[efficiency\|efficient]] traversal of the 5.7.11 subgroup. It was first discovered and named by [[User:CompactStar\|CompactStar]] in 2026.

CompactStar at 22:24, 15 October 2026

2026-10-15T22:24:20Z

← Older revision		Revision as of 22:24, 15 October 2026
Line 12:		Line 12:
	}}		}}

	'''Pentadacus''' is a [[nonoctave]] [[regular temperament]] in the 5.7.11 [[subgroup]] which tempers out the comma [[831875/823543]]. It is even more exotic than [[Bohlen-Pierce]], lacking both [[2/1]] and [[3/1]], and typically it would be used with an [[equave]] of [[5/1]], also known as the pentave. Essentially it is suitable for a harmonic system based exclusively on [https://oeis.org/wiki/5-rough_numbers 5-rough numbers] (numbers ~~that have no prime factors less than 5~~), similar to how Bohlen-Pierce is suitable for a harmonic system based on odd numbers. It is generated by a [[meantone]]-esque small whole tone interval that represents [[55/49]]. Stacking 3 of these tones gives [[7/5]] and 7 of them give [[11/5]].		'''Pentadacus''' is a [[nonoctave]] [[regular temperament]] in the 5.7.11 [[subgroup]] which tempers out the comma [[831875/823543]]. It is even more exotic than [[Bohlen-Pierce]], lacking both [[2/1]] and [[3/1]], and typically it would be used with an [[equave]] of [[5/1]], also known as the pentave. Essentially it is suitable for a harmonic system based exclusively on [https://oeis.org/wiki/5-rough_numbers 5-rough numbers] (numbers not divisible by 2 or 3), similar to how Bohlen-Pierce is suitable for a harmonic system based on odd numbers. It is generated by a [[meantone]]-esque small whole tone interval that represents [[55/49]]. Stacking 3 of these tones gives [[7/5]] and 7 of them give [[11/5]].

	Properly-tuned pentadacus generates the [[5/1]]-equivalent [[MOS scales]] [[1L 1s (5/1-equivalent)\|1L 1s<5/1>]], [[1L 2s (5/1-equivalent)\|1L 2s<5/1>]], etc. until ending the monolarge mos chain at [[1L 13s (5/1-equivalent)\|1L 13s<5/1>]], followed by [[14L 1s (5/1-equivalent)\|14L 1s<5/1>]], [[14L 15s (5/1-equivalent)\|14L 15s<5/1>]]. Pentadacus has both low [[complexity]] (especially by the standards of the 5/1-equivalent world, where scales have lots of notes) and low [[error]] if tuned correctly, providing an [[efficiency\|efficient]] traversal of the 5.7.11 subgroup. It was first discovered and named by [[User:CompactStar\|CompactStar]] in 2026.		Properly-tuned pentadacus generates the [[5/1]]-equivalent [[MOS scales]] [[1L 1s (5/1-equivalent)\|1L 1s<5/1>]], [[1L 2s (5/1-equivalent)\|1L 2s<5/1>]], etc. until ending the monolarge mos chain at [[1L 13s (5/1-equivalent)\|1L 13s<5/1>]], followed by [[14L 1s (5/1-equivalent)\|14L 1s<5/1>]], [[14L 15s (5/1-equivalent)\|14L 15s<5/1>]]. Pentadacus has both low [[complexity]] (especially by the standards of the 5/1-equivalent world, where scales have lots of notes) and low [[error]] if tuned correctly, providing an [[efficiency\|efficient]] traversal of the 5.7.11 subgroup. It was first discovered and named by [[User:CompactStar\|CompactStar]] in 2026.

CompactStar at 22:24, 15 October 2026

2026-10-15T22:24:07Z

← Older revision		Revision as of 22:24, 15 October 2026
Line 12:		Line 12:
	}}		}}

	'''Pentadacus''' is a [[nonoctave]] [[regular temperament]] in the 5.7.11 [[subgroup]] which tempers out the comma [[831875/823543]]. It is even more exotic than [[Bohlen-Pierce]], lacking both [[2/1]] and [[3/1]], and typically it would be used with an [[equave]] of [[5/1]], also known as the pentave. It is generated by a [[meantone]]-esque small whole tone interval that represents [[55/49]]. Stacking 3 of these tones gives [[7/5]] and 7 of them give [[11/5]].		'''Pentadacus''' is a [[nonoctave]] [[regular temperament]] in the 5.7.11 [[subgroup]] which tempers out the comma [[831875/823543]]. It is even more exotic than [[Bohlen-Pierce]], lacking both [[2/1]] and [[3/1]], and typically it would be used with an [[equave]] of [[5/1]], also known as the pentave. Essentially it is suitable for a harmonic system based exclusively on [https://oeis.org/wiki/5-rough_numbers 5-rough numbers] (numbers that have no prime factors less than 5), similar to how Bohlen-Pierce is suitable for a harmonic system based on odd numbers. It is generated by a [[meantone]]-esque small whole tone interval that represents [[55/49]]. Stacking 3 of these tones gives [[7/5]] and 7 of them give [[11/5]].

	Properly-tuned pentadacus generates the [[5/1]]-equivalent [[MOS scales]] [[1L 1s (5/1-equivalent)\|1L 1s<5/1>]], [[1L 2s (5/1-equivalent)\|1L 2s<5/1>]], etc. until ending the monolarge mos chain at [[1L 13s (5/1-equivalent)\|1L 13s<5/1>]], followed by [[14L 1s (5/1-equivalent)\|14L 1s<5/1>]], [[14L 15s (5/1-equivalent)\|14L 15s<5/1>]]. Pentadacus has both low [[complexity]] (especially by the standards of the 5/1-equivalent world, where scales have lots of notes) and low [[error]] if tuned correctly, providing an [[efficiency\|efficient]] traversal of the 5.7.11 subgroup. It was first discovered and named by [[User:CompactStar\|CompactStar]] in 2026.		Properly-tuned pentadacus generates the [[5/1]]-equivalent [[MOS scales]] [[1L 1s (5/1-equivalent)\|1L 1s<5/1>]], [[1L 2s (5/1-equivalent)\|1L 2s<5/1>]], etc. until ending the monolarge mos chain at [[1L 13s (5/1-equivalent)\|1L 13s<5/1>]], followed by [[14L 1s (5/1-equivalent)\|14L 1s<5/1>]], [[14L 15s (5/1-equivalent)\|14L 15s<5/1>]]. Pentadacus has both low [[complexity]] (especially by the standards of the 5/1-equivalent world, where scales have lots of notes) and low [[error]] if tuned correctly, providing an [[efficiency\|efficient]] traversal of the 5.7.11 subgroup. It was first discovered and named by [[User:CompactStar\|CompactStar]] in 2026.

← Older revision		Revision as of 04:13, 16 October 2026
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	Properly-tuned pentadacus generates the [[5/1]]-equivalent [[MOS scales]] [[1L 1s (5/1-equivalent)\|1L 1s<5/1>]], [[1L 2s (5/1-equivalent)\|1L 2s<5/1>]], etc. until ending the monolarge mos chain at [[1L 13s (5/1-equivalent)\|1L 13s<5/1>]], followed by [[14L 1s (5/1-equivalent)\|14L 1s<5/1>]], [[14L 15s (5/1-equivalent)\|14L 15s<5/1>]]. Pentadacus has both low [[complexity]] (especially by the standards of the 5/1-equivalent world, where scales have lots of notes) and low [[error]] if tuned correctly, providing an [[efficiency\|efficient]] traversal of the 5.7.11 subgroup. It was first discovered and named by [[User:CompactStar\|CompactStar]] in 2026.		Properly-tuned pentadacus generates the [[5/1]]-equivalent [[MOS scales]] [[1L 1s (5/1-equivalent)\|1L 1s<5/1>]], [[1L 2s (5/1-equivalent)\|1L 2s<5/1>]], etc. until ending the monolarge mos chain at [[1L 13s (5/1-equivalent)\|1L 13s<5/1>]], followed by [[14L 1s (5/1-equivalent)\|14L 1s<5/1>]], [[14L 15s (5/1-equivalent)\|14L 15s<5/1>]]. Pentadacus has both low [[complexity]] (especially by the standards of the 5/1-equivalent world, where scales have lots of notes) and low [[error]] if tuned correctly, providing an [[efficiency\|efficient]] traversal of the 5.7.11 subgroup. It was first discovered and named by [[User:CompactStar\|CompactStar]] in 2026.

	Pentadacus can be thought of as a compressed [[14ed5]] until you hit [[5/1]], as is best exemplified by the [[1L 13s (5/1-equivalent)\|1L 13s<5/1>]] Pentadacus[14] mos. Because of this, many good smaller pentadacus tunings are of the form (14''n'' + 1)ed5 such as [[29ed5]], [[43ed5]], and [[57ed5]]. In this respect, it is similar to a [[cluster temperament]], but does not seem to exactly meet the definition of a cluster temperament. 14ed5 is also close to [[6edo]], the familiar whole-tone scale with octaves, so pentadacus is very alien (being a step above even tritave-equivalent temperaments) but can lapse into sounding like the familiar whole-tone scale at times. 6 generators in pentadacus can sound a bit like a [[stretched and compressed tuning\|compressed octave]] but it is usually inaccurate unless you are using a very sharp tuning like 14ed5. It should also be noted that -2 generators pentave-reduced can sound close to [[4/1]].		Pentadacus can be thought of as a compressed [[14ed5]] until you hit [[5/1]], as is best exemplified by the [[1L 13s (5/1-equivalent)\|1L 13s<5/1>]] Pentadacus[14] mos. Because of this, many good smaller pentadacus tunings are of the form (14''n'' + 1)ed5 such as [[29ed5]], [[43ed5]], and [[57ed5]]. In this respect, it is similar to a [[cluster temperament]], but does not seem to exactly meet the definition of a cluster temperament. 14ed5 is also close to [[6edo]], the familiar whole-tone scale with octaves, so pentadacus is very alien (being a step above even tritave-equivalent temperaments) but can lapse into sounding like the familiar whole-tone scale at times. 6 generators in pentadacus can sound a bit like a [[stretched and compressed tuning\|compressed octave]] but it is usually inaccurate unless you are using a very sharp tuning like 14ed5. It should also be noted that -2 generators pentave-reduced can sound very close to [[4/1]].

	Pentadacus is connected to the octave-repeating [[didacus]] temperament as both have a small whole tone generator for which 3 stack to 7/5, and [[didacus\|undecimal didacus]] can actually be viewed not only as an [[extension]] of didacus to include the 11th harmonic, but also a [[weak extension]] of pentadacus to include octaves, with 2/1 being mapped to half a pentave minus one generator. Pentadacus's connection to [[14ed5]] (which is effectively 6edo with a just 5/1) is a lot like Didacus's connection to [[6edo]].		Pentadacus is connected to the octave-repeating [[didacus]] temperament as both have a small whole tone generator for which 3 stack to 7/5, and [[didacus\|undecimal didacus]] can actually be viewed not only as an [[extension]] of didacus to include the 11th harmonic, but also a [[weak extension]] of pentadacus to include octaves, with 2/1 being mapped to half a pentave minus one generator. Pentadacus's connection to [[14ed5]] (which is effectively 6edo with a just 5/1) is a lot like Didacus's connection to [[6edo]].

← Older revision		Revision as of 03:55, 16 October 2026
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	Properly-tuned pentadacus generates the [[5/1]]-equivalent [[MOS scales]] [[1L 1s (5/1-equivalent)\|1L 1s<5/1>]], [[1L 2s (5/1-equivalent)\|1L 2s<5/1>]], etc. until ending the monolarge mos chain at [[1L 13s (5/1-equivalent)\|1L 13s<5/1>]], followed by [[14L 1s (5/1-equivalent)\|14L 1s<5/1>]], [[14L 15s (5/1-equivalent)\|14L 15s<5/1>]]. Pentadacus has both low [[complexity]] (especially by the standards of the 5/1-equivalent world, where scales have lots of notes) and low [[error]] if tuned correctly, providing an [[efficiency\|efficient]] traversal of the 5.7.11 subgroup. It was first discovered and named by [[User:CompactStar\|CompactStar]] in 2026.		Properly-tuned pentadacus generates the [[5/1]]-equivalent [[MOS scales]] [[1L 1s (5/1-equivalent)\|1L 1s<5/1>]], [[1L 2s (5/1-equivalent)\|1L 2s<5/1>]], etc. until ending the monolarge mos chain at [[1L 13s (5/1-equivalent)\|1L 13s<5/1>]], followed by [[14L 1s (5/1-equivalent)\|14L 1s<5/1>]], [[14L 15s (5/1-equivalent)\|14L 15s<5/1>]]. Pentadacus has both low [[complexity]] (especially by the standards of the 5/1-equivalent world, where scales have lots of notes) and low [[error]] if tuned correctly, providing an [[efficiency\|efficient]] traversal of the 5.7.11 subgroup. It was first discovered and named by [[User:CompactStar\|CompactStar]] in 2026.

	Pentadacus can be thought of as a compressed [[14ed5]] until you hit [[5/1]], as is best exemplified by the [[1L 13s (5/1-equivalent)\|1L 13s<5/1>]] Pentadacus[14] mos. Because of this, many good smaller pentadacus tunings are of the form (14''n'' + 1)ed5 such as [[29ed5]], [[43ed5]], and [[57ed5]]. In this respect, it is similar to a [[cluster temperament]], but does not seem to exactly meet the definition of a cluster temperament. 14ed5 is also close to [[6edo]], the familiar whole-tone scale with octaves, so pentadacus is very alien (being a step above even tritave-equivalent temperaments) but can lapse into sounding like the familiar whole-tone scale at times. 6 generators in pentadacus can sound a bit like a [[stretched and compressed tuning\|compressed octave]] but it is usually inaccurate unless you are using a very sharp tuning like 14ed5.		Pentadacus can be thought of as a compressed [[14ed5]] until you hit [[5/1]], as is best exemplified by the [[1L 13s (5/1-equivalent)\|1L 13s<5/1>]] Pentadacus[14] mos. Because of this, many good smaller pentadacus tunings are of the form (14''n'' + 1)ed5 such as [[29ed5]], [[43ed5]], and [[57ed5]]. In this respect, it is similar to a [[cluster temperament]], but does not seem to exactly meet the definition of a cluster temperament. 14ed5 is also close to [[6edo]], the familiar whole-tone scale with octaves, so pentadacus is very alien (being a step above even tritave-equivalent temperaments) but can lapse into sounding like the familiar whole-tone scale at times. 6 generators in pentadacus can sound a bit like a [[stretched and compressed tuning\|compressed octave]] but it is usually inaccurate unless you are using a very sharp tuning like 14ed5. It should also be noted that -2 generators pentave-reduced can sound close to [[4/1]].

	Pentadacus is connected to the octave-repeating [[didacus]] temperament as both have a small whole tone generator for which 3 stack to 7/5, and [[didacus\|undecimal didacus]] can actually be viewed not only as an [[extension]] of didacus to include the 11th harmonic, but also a [[weak extension]] of pentadacus to include octaves, with 2/1 being mapped to half a pentave minus one generator. Pentadacus's connection to [[14ed5]] (which is effectively 6edo with a just 5/1) is a lot like Didacus's connection to [[6edo]].		Pentadacus is connected to the octave-repeating [[didacus]] temperament as both have a small whole tone generator for which 3 stack to 7/5, and [[didacus\|undecimal didacus]] can actually be viewed not only as an [[extension]] of didacus to include the 11th harmonic, but also a [[weak extension]] of pentadacus to include octaves, with 2/1 being mapped to half a pentave minus one generator. Pentadacus's connection to [[14ed5]] (which is effectively 6edo with a just 5/1) is a lot like Didacus's connection to [[6edo]].