Volume 10, Number 3, September 2004
Copyright 2004 Society for Music Theory
Paul T. von Hippel and Bret Aarden
Rules for Chord Doubling (and Spacing): A Reply To Wibberley

Sample size

[1]Wibberley challenges our conclusions on the grounds that we looked at "only" 2643 triads from the Bach chorales. This puzzles us, since 2643 far exceeds the number used in previous studies, and of course we also looked at 960 triads from the string quartets of Haydn and Mozart. By contrast, the norm in textbooks is to demonstrate doubling and spacing rules with a handful of illustrations. Wibberley's own paper focuses on ten chords and four chorale phrases.

[2]Wibberley complains that readers "do not know...upon what basis this selection [of chords] was made." Actually, we described the selection criteria in section 4.1 of our paper. We are happy, however, to provide more detail. We began with the Bach chorale section of the MuseData database, which contains "only those [185] chorales for which there is a distinct BWV number (BV 253-438)." (1) After excluding modal chorales and chorales without Melisma harmonic analyses, 126 chorales remained, containing 7616 distinct sonorities, many of which are not functional triads. After restricting the sample to complete strong-beat triads in tonally unambiguous passages, we arrived at the 2643 chorale triads used in our study. In a back-of-the-envelope calculation, Wibberley suggests that there are "at least 11,872 chords" in the Bach chorales, but he begins with the 371 chorales in the Riemenschneider collection, which is not available in computer-readable format, and he does not restrict himself to complete strong-beat triads in tonally unambiguous passages.

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1. Center for Computer-Assisted Research in the Humanities. MuseData editions of Bach's works. http://www.musedata.org/encodings/bach. Palo Alto, CA.
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Prepared by
Brent Yorgason, Managing Editor
Updated 17 September 2004