Widening Unequal Tempered Microtonal Pitch Space for Metaphoric and Cognitive Purposes with New Prime Number Scales

Abstract

I define a new set of microtonal scales based on the prime number series, and containing 41 to 91 pitches spread over the whole audible range, rather than subdividing the octave. I designed these scales for metaphorical purposes, and applied one within my performance piece Ubasuteyama (2008), written with Hazel Smith, for speaker, computer sound and digital processing. Simple timbres using partials bearing prime number ratios to their fundamental were also used to embody the scale. The scales and timbres will be amongst the subjects of cognitive studies of pitch combinations, of large and unbroken pitch intervals in melodies, and of the relation between scale and timbre.