Juggernaut - Revision history

Lériendil: Text replacement - "(unchanged-interval)" to "(unchanged interval)"

2025-06-21T06:59:33Z

Text replacement - "(unchanged-interval)" to "(unchanged interval)"

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	! ED5 generator		! ED5 generator
	! [[Eigenmonzo]] (unchanged-interval)		! [[Eigenmonzo]] (unchanged interval)
	! Cents		! Cents
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FloraC: Collect non-octave temperaments in one category

2025-04-29T09:24:39Z

Collect non-octave temperaments in one category

← Older revision		Revision as of 09:24, 29 April 2025
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	[[Category:Juggernaut\| ]] <!-- main article -->		[[Category:Juggernaut\| ]] <!-- main article -->
	[[Category:Rank-2 temperaments]]		[[Category:Rank-2 temperaments]]
	[[Category:~~Subgroup~~ temperaments]]		[[Category:Non-octave temperaments]]
	~~[[Category:Nonoctave]]~~
	~~[[Category:Pentave~~]]

FloraC: - parent category

2025-04-28T14:18:11Z

- parent category

Show changes

Lériendil at 23:10, 19 April 2025

2025-04-19T23:10:32Z

← Older revision		Revision as of 23:10, 19 April 2025
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	[[Category:Temperaments]]		[[Category:Temperaments]]
			[[Category:Rank-2 temperaments]]
	[[Category:Nonoctave]]		[[Category:Nonoctave]]
	[[Category:Pentave]]		[[Category:Pentave]]

BudjarnLambeth: Link to technical data

2024-11-02T04:54:00Z

Link to technical data

← Older revision		Revision as of 04:54, 2 November 2024
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	Juggernaut contains multi-[[MOS scale]]s of the families [[4L 2s (5/1-equivalent)\|4L 2s]], [[4L 6s (5/1-equivalent)\|4L 6s]], [[10L 4s (5/1-equivalent)\|10L 4s]], [[14L 10s (5/1-equivalent)\|14L 10s]], and [[24L 14s (5/1-equivalent)\|24L 14s]]. The 6-note MOS is rendered unusable because it has very large melodic steps (it corresponds to to 6*log(2)/log(5) ≈ 2.6 note octave-repeating scale) and contains too little 5:7:11 chords for the usage in no-twos-or-threes harmony.		Juggernaut contains multi-[[MOS scale]]s of the families [[4L 2s (5/1-equivalent)\|4L 2s]], [[4L 6s (5/1-equivalent)\|4L 6s]], [[10L 4s (5/1-equivalent)\|10L 4s]], [[14L 10s (5/1-equivalent)\|14L 10s]], and [[24L 14s (5/1-equivalent)\|24L 14s]]. The 6-note MOS is rendered unusable because it has very large melodic steps (it corresponds to to 6*log(2)/log(5) ≈ 2.6 note octave-repeating scale) and contains too little 5:7:11 chords for the usage in no-twos-or-threes harmony.

			Technical data: [[No-twos subgroup temperaments#Juggernaut]].

	== Intervals ==		== Intervals ==

Lériendil at 04:15, 6 September 2024

2024-09-06T04:15:00Z

← Older revision		Revision as of 04:15, 6 September 2024
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	'''Juggernaut''' is a 5.7.11 [[nonoctave]] [[regular temperament]], first documented by [[User:CompactStar]], tempering out 125/121. Its subgroup does not contain harmonics 2 and 3 and so it uses the [[5/1\|pentave]] (5/1) as its equivalence instead of the more common [[2/1\|octave]] or even [[3/1\|tritave]]. It has a period of 1\[[2ed5]] (1393 cents) representing [[11/5]], and a generator representing [[7/5]] (in fact, in the [[CTE tuning]] it is exactly 7/5). This gives juggernaut an extremely low [[complexity]] with 5th, 7th, and 11th harmonics all reachable within just 1 generator, while still having only a moderately high error. It is one of the lowest-[[badness]] 5/1-equivalent or "no-twos-or-threes" temperaments, similar to [[meantone]] and [[BPS]]/lambda in their respective spheres. [[14ed5]] (practically the same as [[6edo]]) is the first ed5 offering a workable tuning of juggernaut with the generator as 3\14ed5, while [[24ed5]] offers a more accurate tuning with the generator of 5\24ed5.		'''Juggernaut''' is a 5.7.11 [[nonoctave]] [[regular temperament]], first documented by [[User:CompactStar]], tempering out [[125/121]]. Its subgroup does not contain harmonics 2 and 3 and so it uses the [[5/1\|pentave]] (5/1) as its equivalence instead of the more common [[2/1\|octave]] or even [[3/1\|tritave]]. It has a period of 1\[[2ed5]] (1393 cents) representing [[11/5]], and a generator representing [[7/5]] (in fact, in the [[CTE tuning]] it is exactly 7/5). This gives juggernaut an extremely low [[complexity]] with 5th, 7th, and 11th harmonics all reachable within just 1 generator, while still having only a moderately high error. It is one of the lowest-[[badness]] 5/1-equivalent or "no-twos-or-threes" temperaments, similar to [[meantone]] and [[BPS]]/lambda in their respective spheres. [[14ed5]] (practically the same as [[6edo]]) is the first ed5 offering a workable tuning of juggernaut with the generator as 3\14ed5, while [[24ed5]] offers a more accurate tuning with the generator of 5\24ed5.

	The best extension of juggernaut to the no-twos-or-threes 13-limit, named "cuthbernaut", splits the 7/5 generator into two [[13/11]] by tempering out [[847/845]]. The next best extension has been named "tridecimal juggernaut" since it preserves the original 7/5 generator, mapping [[13/5]] to -2 generators by tempering out 637/625. Tridecimal juggernaut favors a flatter 7/5 (in the vicinity of 570 cents) for the least error.		The best extension of juggernaut to the no-twos-or-threes 13-limit, named "cuthbernaut", splits the 7/5 generator into two [[13/11]] by tempering out [[847/845]]. The next best extension has been named "tridecimal juggernaut" since it preserves the original 7/5 generator, mapping [[13/5]] to -2 generators by tempering out 637/625. Tridecimal juggernaut favors a flatter 7/5 (in the vicinity of 570 cents) for the least error.

Lériendil: /* Tuning spectrum */

2024-08-27T19:41:22Z

Tuning spectrum

← Older revision		Revision as of 19:41, 27 August 2024
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	!Cents		!Cents
	\|-		\|-
			\|
	\|91/25		\|91/25
	\|549.588		\|549.588

Lériendil: your'e

2024-08-27T10:58:17Z

your'e

← Older revision		Revision as of 10:58, 27 August 2024
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	'''Juggernaut''' is a 5.7.11 [[nonoctave]] [[regular temperament]], first documented by [[User:CompactStar]], tempering out 125/121. ~~It's~~ subgroup does not contain harmonics 2 and 3 and so it uses the [[5/1\|pentave]] (5/1) as its equivalence instead of the more common [[2/1\|octave]] or even [[3/1\|tritave]]. It has a period of 1\[[2ed5]] (1393 cents) representing [[11/5]], and a generator representing [[7/5]] (in fact, in the [[CTE tuning]] it is exactly 7/5). This gives juggernaut an extremely low [[complexity]] with 5th, 7th, and 11th harmonics all reachable within just 1 generator, while still having only a moderately high error. It is one of the lowest-[[badness]] 5/1-equivalent or "no-twos-or-threes" temperaments, similar to [[meantone]] and [[BPS]]/lambda in their respective spheres. [[14ed5]] (practically the same as [[6edo]]) is the first ed5 offering a workable tuning of juggernaut with the generator as 3\14ed5, while [[24ed5]] offers a more accurate tuning with the generator of 5\24ed5.		'''Juggernaut''' is a 5.7.11 [[nonoctave]] [[regular temperament]], first documented by [[User:CompactStar]], tempering out 125/121. Its subgroup does not contain harmonics 2 and 3 and so it uses the [[5/1\|pentave]] (5/1) as its equivalence instead of the more common [[2/1\|octave]] or even [[3/1\|tritave]]. It has a period of 1\[[2ed5]] (1393 cents) representing [[11/5]], and a generator representing [[7/5]] (in fact, in the [[CTE tuning]] it is exactly 7/5). This gives juggernaut an extremely low [[complexity]] with 5th, 7th, and 11th harmonics all reachable within just 1 generator, while still having only a moderately high error. It is one of the lowest-[[badness]] 5/1-equivalent or "no-twos-or-threes" temperaments, similar to [[meantone]] and [[BPS]]/lambda in their respective spheres. [[14ed5]] (practically the same as [[6edo]]) is the first ed5 offering a workable tuning of juggernaut with the generator as 3\14ed5, while [[24ed5]] offers a more accurate tuning with the generator of 5\24ed5.

	The best extension of juggernaut to the no-twos-or-threes 13-limit, named "cuthbernaut", splits the 7/5 generator into two [[13/11]] by tempering out [[847/845]]. The next best extension has been named "tridecimal juggernaut" since it preserves the original 7/5 generator, mapping [[13/5]] to -2 generators by tempering out 637/625. Tridecimal juggernaut favors a flatter 7/5 (in the vicinity of 570 cents) for the least error.		The best extension of juggernaut to the no-twos-or-threes 13-limit, named "cuthbernaut", splits the 7/5 generator into two [[13/11]] by tempering out [[847/845]]. The next best extension has been named "tridecimal juggernaut" since it preserves the original 7/5 generator, mapping [[13/5]] to -2 generators by tempering out 637/625. Tridecimal juggernaut favors a flatter 7/5 (in the vicinity of 570 cents) for the least error.

CompactStar at 07:13, 22 August 2023

2023-08-22T07:13:20Z

← Older revision		Revision as of 07:13, 22 August 2023
Line 1:		Line 1:
	'''Juggernaut''' is a 5.7.11 [[nonoctave]] [[regular temperament]], first documented by [[User:CompactStar]], tempering out 125/121. It ~~eliminates~~ harmonics 2 and 3 and so it uses the [[5/1\|pentave]] (5/1) as its equivalence instead of the more common [[2/1\|octave]] or even [[3/1\|tritave]]. It has a period of 1\[[2ed5]] (1393 cents) representing [[11/5]], and a generator representing [[7/5]] (in fact, in the [[CTE tuning]] it is exactly 7/5). This gives juggernaut an extremely low [[complexity]] with 5th, 7th, and 11th harmonics all reachable within just 1 generator, while still having only a moderately high error. It is one of the lowest-[[badness]] 5/1-equivalent or "no-twos-or-threes" temperaments, similar to [[meantone]] and [[BPS]]/lambda in their respective spheres. [[14ed5]] (practically the same as [[6edo]]) is the first ed5 offering a workable tuning of juggernaut with the generator as 3\14ed5, while [[24ed5]] offers a more accurate tuning with the generator of 5\24ed5.		'''Juggernaut''' is a 5.7.11 [[nonoctave]] [[regular temperament]], first documented by [[User:CompactStar]], tempering out 125/121. It's subgroup does not contain harmonics 2 and 3 and so it uses the [[5/1\|pentave]] (5/1) as its equivalence instead of the more common [[2/1\|octave]] or even [[3/1\|tritave]]. It has a period of 1\[[2ed5]] (1393 cents) representing [[11/5]], and a generator representing [[7/5]] (in fact, in the [[CTE tuning]] it is exactly 7/5). This gives juggernaut an extremely low [[complexity]] with 5th, 7th, and 11th harmonics all reachable within just 1 generator, while still having only a moderately high error. It is one of the lowest-[[badness]] 5/1-equivalent or "no-twos-or-threes" temperaments, similar to [[meantone]] and [[BPS]]/lambda in their respective spheres. [[14ed5]] (practically the same as [[6edo]]) is the first ed5 offering a workable tuning of juggernaut with the generator as 3\14ed5, while [[24ed5]] offers a more accurate tuning with the generator of 5\24ed5.

	The best extension of juggernaut to the no-twos-or-threes 13-limit, named "cuthbernaut", splits the 7/5 generator into two [[13/11]] by tempering out [[847/845]]. The next best extension has been named "tridecimal juggernaut" since it preserves the original 7/5 generator, mapping [[13/5]] to -2 generators by tempering out 637/625. Tridecimal juggernaut favors a flatter 7/5 (in the vicinity of 570 cents) for the least error.		The best extension of juggernaut to the no-twos-or-threes 13-limit, named "cuthbernaut", splits the 7/5 generator into two [[13/11]] by tempering out [[847/845]]. The next best extension has been named "tridecimal juggernaut" since it preserves the original 7/5 generator, mapping [[13/5]] to -2 generators by tempering out 637/625. Tridecimal juggernaut favors a flatter 7/5 (in the vicinity of 570 cents) for the least error.

CompactStar at 07:13, 22 August 2023

2023-08-22T07:13:07Z

← Older revision		Revision as of 07:13, 22 August 2023
Line 1:		Line 1:
	'''Juggernaut''' is a 5.7.11 [[nonoctave]] [[regular temperament]], first documented by [[User:CompactStar]], tempering out 125/121. It uses the [[5/1\|pentave]] (5/1) as its equivalence instead of the more common [[2/1\|octave]] or even [[3/1\|tritave]]. It has a period of 1\[[2ed5]] (1393 cents) representing [[11/5]], and a generator representing [[7/5]] (in fact, in the [[CTE tuning]] it is exactly 7/5). This gives juggernaut an extremely low [[complexity]] with 5th, 7th, and 11th harmonics all reachable within just 1 generator, while still having only a moderately high error. It is one of the lowest-[[badness]] 5/1-equivalent or "no-twos-or-threes" temperaments, similar to [[meantone]] and [[BPS]]/lambda in their respective spheres. [[14ed5]] (practically the same as [[6edo]]) is the first ed5 offering a workable tuning of juggernaut with the generator as 3\14ed5, while [[24ed5]] offers a more accurate tuning with the generator of 5\24ed5.		'''Juggernaut''' is a 5.7.11 [[nonoctave]] [[regular temperament]], first documented by [[User:CompactStar]], tempering out 125/121. It eliminates harmonics 2 and 3 and so it uses the [[5/1\|pentave]] (5/1) as its equivalence instead of the more common [[2/1\|octave]] or even [[3/1\|tritave]]. It has a period of 1\[[2ed5]] (1393 cents) representing [[11/5]], and a generator representing [[7/5]] (in fact, in the [[CTE tuning]] it is exactly 7/5). This gives juggernaut an extremely low [[complexity]] with 5th, 7th, and 11th harmonics all reachable within just 1 generator, while still having only a moderately high error. It is one of the lowest-[[badness]] 5/1-equivalent or "no-twos-or-threes" temperaments, similar to [[meantone]] and [[BPS]]/lambda in their respective spheres. [[14ed5]] (practically the same as [[6edo]]) is the first ed5 offering a workable tuning of juggernaut with the generator as 3\14ed5, while [[24ed5]] offers a more accurate tuning with the generator of 5\24ed5.

	The best extension of juggernaut to the no-twos-or-threes 13-limit, named "cuthbernaut", splits the 7/5 generator into two [[13/11]] by tempering out [[847/845]]. The next best extension has been named "tridecimal juggernaut" since it preserves the original 7/5 generator, mapping [[13/5]] to -2 generators by tempering out 637/625. Tridecimal juggernaut favors a flatter 7/5 (in the vicinity of 570 cents) for the least error.		The best extension of juggernaut to the no-twos-or-threes 13-limit, named "cuthbernaut", splits the 7/5 generator into two [[13/11]] by tempering out [[847/845]]. The next best extension has been named "tridecimal juggernaut" since it preserves the original 7/5 generator, mapping [[13/5]] to -2 generators by tempering out 637/625. Tridecimal juggernaut favors a flatter 7/5 (in the vicinity of 570 cents) for the least error.