A Base-40 Number-line Representation
of Musical Pitch Notation

Walter B. Hewlett
Stanford, California


A base-40 number line representation of pitch notation is suggested which makes it possible to incorporate information on pitch in one number, where the difference between two pitch numbers correctly determines the notated interval name between the corresponding pitches. A general theory of 1:1 representation of pitch notation, taking into consideration the invariance of musical intervals, is suggested. The relations between the representation system suggested in the paper and other systems of pitch representation (Zimmerman's system, Clements' system) are discussed.

1. Introduction

2. The problem of 1:1 pitch-mapping

3. Pitch representation with the base-40 system

4. The problem of interval-invariancy

5. Interval-invariancy: A general theory

6. The base-40 system and the Clements system. Final propositions to the theory