Learning About Harmony with Harmony Space: An Overview

Recent developments are presented in the evolution of Harmony Space, a highly enabling interface designed to encourage and facilitate rapid learning, especially by beginners, about the practical use and theory of tonal harmony, especially as applied to composition and analysis. The interface exploits both cognitive theories of tonal harmony and principles of human-computer interaction. In particular, the design of the interface draws on Balzano's and Longuet-Higgins' theories of tonal harmony. The interface allows entities of interest (notes, chords, chord progressions, key areas, modulations) to be manipulated via direct manipulation techniques using a single principled spatial metaphor. This makes it possible for novices to learn to perform a wide range of musical tasks involving harmony relatively quickly. The interface can also be used by experienced musicians to gain new insights and perform certain tasks much more easily than with conventional tools and notations. The interface is highly interactive and multi-modal, using two pointing devices and spatial, aural and kinaesthetic cues that all map uniformly into the underlying representation. Some recent implementations of Harmony Space are discussed, together with some of the musical tasks which they make tractable for beginners and experienced musicians. Aspects of the simple, consistent, principled framework behind the interface are outlined. 1 Introduction Harmony Space is a highly interactive interface for exploring harmony and a means of learning about certain aspects of music composition. The interface draws on two cognitive theories of harmony. It exploits artificial intelligence and human computer interaction methodologies to help beginners learn about and make use of tonal harmony. The interface was originally inspired by Longuet-Higgins (1962) theory of the perception of harmony, and some current versions of the interface still strongly reflect this influence. However, for many purposes, it has turned out to be more appropriate to use Balzano's 1982 group theoretic characterisation of the perception of harmony as a grounding for the interface. In this paper we will focus on the use of the interface for tonal and modal harmony: most versions of this interface (constructed during a series of research projects) employ a 12-fold equal-tempered division of the octave, though other implemented versions employ just intonation (Holland 1989) in order to facilitate the exploration of harmonic ideas and aspects of modulation using this tuning. Versions of the interface have also been constructed for 6-fold, 20-fold 30-fold, 42-fold 56-fold, and 72-fold divisions of the octave, to facilitate the exploration of microtonal scales …