Pentadacus: Difference between revisions

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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 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 an extension of pentadacus to include octaves. 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]].

== Etymology ==

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 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 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 an extension of pentadacus to include octaves. 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]].
 == Etymology ==