Juggernaut: Difference between revisions

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'''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]]. 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. Altogether it is one of the best 5/1-equivalent or "no-twos-or-threes" temperaments, comparable to [[meantone]] and [[BPS]] in their respective spheres.

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.

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.

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	'''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]]. 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. Altogether it is one of the best 5/1-equivalent or "no-twos-or-threes" temperaments, comparable to [[meantone]] and [[BPS]] in their respective spheres.		'''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]]. 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. Altogether it is one of the best 5/1-equivalent or "no-twos-or-threes" temperaments, comparable to [[meantone]] and [[BPS]] in their respective spheres.

	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.		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.