On Parsimonious Sequences as Scales in Western Music

Richard Hermann and Jack Douthett
Renaissance Banff: Mathematics, Music, Art, Culture (2005)
Pages 293–300

Abstract

Musicians have narrowed the continuous range of frequency into discrete sequences of frequencies, interpreted as pitches, of various types called scales from the earliest writings on music onwards. This study provides some answers as to scope and relationships between modes and scales in areas where, surprisingly, little systematic study has been done. The approach reveals that the Fibonacci sequence provides the key to unlocking the question of scope. Techniques from post-tonal and modal music theory provide answers to relational questions.

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