LIE scales: Composing with scales of linear intervallic expansion

Abstract

This thesis includes a portfolio of scored compositions with written commentaries and a list of all completed pieces (2017–2024) composed using LIE scalic principle. All compositions use extended fixed pitch fields (FPFs) as source scales and are primarily scored for acoustic instruments. LIE scales (scales of Linear Intervallic Expansion) were initially derived from my discovery of a unique correspondence between consecutive counting numbers (+1, +2, +3...) and Messiaen's “mode 2” scale ,0, 1, 3, 4, 6, 7, 9, 10-. In brief, this compound-chromatic theory of scales combines Non-Octave-Repeating Scales (beyond interval cycles) with Axiomatic scale theory. I explain my development of LIE scales, addresses some of the perceptual aspects of these FPFs, catalogue numerous scales and draw a compositional conclusion. My structural methodology is informed by the work of Webern, Bartók, Schillinger and Slonimsky, for example, but transcends 12-tone theory per se and suggests an alternative approach to harmonic dualism, whilst providing a rich generative vein for compositional development. I explore abstract harmonic polarity by using extended anti/complimentary scales, treating melody and timbre as emergent entities rather than structural prerequisites, and research how harmonic meaning and our awareness of octave equivalence can be enhanced or avoided through composing with compound LIE scalic structures. This thesis should be of interest to any composers working with synthetic mathematically derived patterns, and musicologists specialising in early 20th Century compositional approaches. LIE scales could also be used as a repository of alternative scalic ideas for improvisational purposes. Future research might explore LIE scalic principles microtonally and with regard to granulation, a spectral centroid, and a-spatial (or medial) theories of auditory perception.