The Limited and The Limitless: Harmonic Voltas and Puns in the Third Movement of Ben Johnston’s Seventh String Quartet

Abstract

Abstract Extended just intonation confronts us with musical problems arising from the sheer array and variety of pitch relationships that can be written, played, and heard. Through an analysis of Ben Johnston’s Seventh String Quartet as a case study, this essay addresses the diversity of these pitch relationships by suggesting a three-way categorization of just intonation ratios: primary intervals (simple integer ratios), ectopic intervals (ratios with no primary interval analogue), and intermediary intervals (ratios with a close primary interval analogue). I suggest a listening strategy based on the categorization resulting in two analytical models. A voltaic analysis recognizes changes in the pitch domain indicated by the differences between primary and intermediary intervals. A pitch pun analysis emphasizes the small magnitude of the differences between primary and intermediary intervals and the slow drift away from a secure sense of pitch place. Finally, I combine these views to compare the two analytical strategies as applied to the last measures of Johnston’s Seventh String Quartet and speculate on the implications of these strategies for hearing and conceiving of pitch intervals.