  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.
