Pentadacus: Difference between revisions

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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.

[[14ed5]] is an inaccurate but important tuning of Pentadacus, because in 14ed5, the whole tone generator corresponds to a single step of 14ed5, although ~~the whole tone~~ is ~~bigger~~ than usual ~~being around [[9/8]]-sized, causing the~~ approximations ~~of 7/5 and 11/5 to be bad~~. Basically, pentadacus can be thought of as a compressed 14ed5, at least until you hit [[5/1]]. 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, and 6 generators in pentadacus can sound like a tempered octave but it’s usually quite inaccurate and dissonant. 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>]]. After this it branches into.

[[14ed5]] is an inaccurate but important tuning of Pentadacus, because in 14ed5, the whole tone generator corresponds to a single step of 14ed5, although it is a much larger than usual Pentadacus generator which results in poor approximations. Basically, pentadacus can be thought of as a compressed 14ed5, at least until you hit [[5/1]]. 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, and 6 generators in pentadacus can sound like a tempered octave but it’s usually quite inaccurate and dissonant. 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>]]. After this it branches into.

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	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.		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.

	[[14ed5]] is an inaccurate but important tuning of Pentadacus, because in 14ed5, the whole tone generator corresponds to a single step of 14ed5, although ~~the whole tone~~ is ~~bigger~~ than usual ~~being around [[9/8]]-sized, causing the~~ approximations ~~of 7/5 and 11/5 to be bad~~. Basically, pentadacus can be thought of as a compressed 14ed5, at least until you hit [[5/1]]. 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, and 6 generators in pentadacus can sound like a tempered octave but it’s usually quite inaccurate and dissonant. 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>]]. After this it branches into.		[[14ed5]] is an inaccurate but important tuning of Pentadacus, because in 14ed5, the whole tone generator corresponds to a single step of 14ed5, although it is a much larger than usual Pentadacus generator which results in poor approximations. Basically, pentadacus can be thought of as a compressed 14ed5, at least until you hit [[5/1]]. 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, and 6 generators in pentadacus can sound like a tempered octave but it’s usually quite inaccurate and dissonant. 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>]]. After this it branches into.