Pentadacus: Difference between revisions

Line 16:

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, but 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]]. Because of this, many pentadacus tunings are of the form (14n+1)ed5 such as [[15ed5]] (although that one is barely a tuning, being even worse than 14ed5), [[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 can often be very alien (being a step above even tritave-equivalent temperaments) but also lapse into sounding like the familiar whole-tone scale at times. 6 generators in pentadacus can sound a bit like a [[~~tempered~~ octave]] but it’s usually inaccurate unless you're using a very sharp tuning like 14ed5.

[[14ed5]] is an inaccurate but important tuning of Pentadacus, because in 14ed5, the whole tone generator corresponds to a single step of 14ed5, but 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]]. Because of this, many pentadacus tunings are of the form (14n+1)ed5 such as [[15ed5]] (although that one is barely a tuning, being even worse than 14ed5), [[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 can often be very alien (being a step above even tritave-equivalent temperaments) but also lapse into sounding like the familiar whole-tone scale at times. 6 generators in pentadacus can sound a bit like a [[Octave stretching|compressed octave]] but it’s usually inaccurate unless you're using a very sharp tuning like 14ed5.

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>]].

@@ Line 16: / Line 16: @@
 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, but 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]]. Because of this, many pentadacus tunings are of the form (14n+1)ed5 such as [[15ed5]] (although that one is barely a tuning, being even worse than 14ed5), [[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 can often be very alien (being a step above even tritave-equivalent temperaments) but also lapse into sounding like the familiar whole-tone scale at times. 6 generators in pentadacus can sound a bit like a [[tempered octave]] but it’s usually inaccurate unless you're using a very sharp tuning like 14ed5.
+[[14ed5]] is an inaccurate but important tuning of Pentadacus, because in 14ed5, the whole tone generator corresponds to a single step of 14ed5, but 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]]. Because of this, many pentadacus tunings are of the form (14n+1)ed5 such as [[15ed5]] (although that one is barely a tuning, being even worse than 14ed5), [[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 can often be very alien (being a step above even tritave-equivalent temperaments) but also lapse into sounding like the familiar whole-tone scale at times. 6 generators in pentadacus can sound a bit like a [[Octave stretching|compressed octave]] but it’s usually inaccurate unless you're using a very sharp tuning like 14ed5.
 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>]].