The Expectancy Dynamics of Anti-Tonal Twelve-Tone Rows: A Commentary and Reanalysis of von Hippel & Huron (2020)

Niels Chr. Hansen


This commentary provides two methodological expansions of von Hippel and Huron's (2020) empirical report on (anti-)tonality in twelve-tone rows by Arnold Schoenberg, Anton Webern, and Alban Berg. First, motivated by the theoretical importance of equality between all pitch classes in twelve-tone music, a full replication of their findings of "anti-tonality" in rows by Schoenberg and Webern is offered using a revised tonal fit measure which is not biased towards row-initial and row-final sub-segments. Second, motivated by a long-standing debate in music cognition research between distributional and sequential/dynamic tonality concepts, information-theoretic measures of entropy and information content are estimated by a computational model and pitted against distributional tonal fit measures. Whereas Schoenberg's rows are characterized by low distributional tonal fit, but do not strongly capitalize on tonal expectancy dynamics, Berg's rows exhibit tonal traits in terms of low unexpectedness, and Webern's rows achieve anti-tonal traits by combining high uncertainty and low unexpectedness through prominent use of the semitone interval. This analysis offers a complementary–and arguably more nuanced–picture of dodecaphonic compositional practice.


dodecaphony; twelve-tone music; tonality; expectation; entropy; probability; information theory

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