Dynamic Transposition of Melodic Sequences on Digital Devices
  A method is proposed which enables one to produce musical compositions by using transposition in place of harmonic progression. A transposition scale is introduced to provide a set of intervals commensurate with the musical scale, such as chromatic or just intonation scales. A sequence of intervals selected from the transposition scale is used to shift instrument frequency at predefined times during the composition which serves as a harmonic sequence of a composition. A transposition sequence constructed in such a way can be extended to a hierarchy of sequences. The fundamental sound frequency of an instrument is obtained as a product of the base frequency, instrument key factor, and a cumulative product of respective factors from all the harmonic sequences. The multiplication factors are selected from subsets of rational numbers, which form instrument scales and transposition scales of different levels. Each harmonic sequence can be related to its own transposition scale, or a single scale can be used for all levels. When composing for an orchestra of instruments, harmonic sequences and instrument scales can be assigned independently to each musical instrument. The method solves the problem of using just intonation scale across multiple octaves as well as simplifies writing of instrument scores. 
Andrei V Smirnov
cs.SD