Dynamic Transposition of Melodic Sequences on Digital Devices

TL;DR

This paper introduces a novel method for musical composition using hierarchical transposition of melodic sequences, enabling flexible harmonic structures and simplifying score writing on digital devices.

Contribution

It presents a transposition-based approach with hierarchical sequences and scales, facilitating complex harmonic progressions and instrument-specific tuning in digital music composition.

Findings

Enables hierarchical transposition sequences for musical composition.

Supports various tuning scales like chromatic and just intonation.

Simplifies multi-instrument score writing with independent harmonic sequences.

Abstract

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.