BPS: Difference between revisions
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Sharp tunings generally possess a more convenient 13th harmonic than 11th, by tempering out [[637/625]] and identifying (25/21)<sup>2</sup> with [[13/9]], which is optimal near the 30edt tuning. It is then very easy to insert in 19 by tempering [[247/245]], and identifying [[13/9]] with [[27/19]], therefore placing the 19th harmonic 10 generators down; this extension is optimal near the 56edt tuning. | Sharp tunings generally possess a more convenient 13th harmonic than 11th, by tempering out [[637/625]] and identifying (25/21)<sup>2</sup> with [[13/9]], which is optimal near the 30edt tuning. It is then very easy to insert in 19 by tempering [[247/245]], and identifying [[13/9]] with [[27/19]], therefore placing the 19th harmonic 10 generators down; this extension is optimal near the 56edt tuning. | ||
=== Prime 2 === | |||
''Main article: [[Relationship between Bohlen-Pierce and octave-ful temperaments#Relationship of rank-2 Bohlen-Pierce-Stearns temperament to octave-ful temperaments|Relationship between Bohlen-Pierce and octave-ful temperaments]]. | |||
It is also possible to incorporate octaves into the BPS temperament. The logical choices for a mapping of 2 are 7 generators up (equating [[2/1]] to [[125/63]]), which produces [[sensi]] temperament, and 6 generators down (equating 2/1 to [[49/25]]), which produces [[hedgehog]] temperament. | |||
== Interval chains == | == Interval chains == | ||