Volume 10, Number 2, June 2004
Copyright © 2004 Society for Music Theory
Bret Aarden and Paul T. von Hippel
Rules for Chord Doubling (and Spacing): Which Ones Do We Need?
 When voice-doubling rules require information about the scale degrees of the PCs, the local key at that moment must also be determined. The method we adopted was to sample only from regions of music that were clearly in the home key. Our conservative approach was to assume that this occurs from the beginning of the piece to the first point of modulation; and, if the analysis ends in the home key, from the last modulation to the end of the piece. This technique forced us to ignore large portions of the scores, but many clear statements of triads could still be found in most of the scores.
 We used the Melisma harmonic analysis software(73) to assist in the process of identifying home key regions. In the end, 126 chorales and 86 string quartet movements were available for sampling. The total number of measures in each piece that were clearly in the home key ranged from 1 to 134 (the latter found in Mozart's string quartet K. 285, third movement), with an average of 22 measures per piece.(74)
 We employed several checks to ensure the analyses were reasonably accurate. The most serious error possible with an harmonic analysis is the assignment of a completely wrong home key. Melisma's analyses of individual triads were not used in this study, but its analyses of keys were essential. An analysis that begins in an incorrect key is likely to indicate modulations at a wildly different point than one beginning in the correct key.
 The easiest check for key misattributions is in the score itself, in the form of the key signature. Errors in most semi-intelligent software will probably displace the key by a third or fifth, which would render the key incompatible with the key signature. Even after taking enharmonics into account, about two-fifths of the 299 analyses were discarded for starting in an unlikely key.(75)
 An analysis may also mistakenly begin in the relative major or minor, which is a more difficult error to identify. The presence of a raised fifth in major or a lowered seventh in minor is a possible indicator of a substituted relative key. These flags were found in the home-key regions of 115 of the movements. Proof-listening to these resulted in the discovery of 20 more movements with incorrect analyses.
 Further key complexity is created because some of the Bach chorales appear to be modal rather than tonal. Scale degree information in these pieces could either be qualitatively different than that in tonal works, or simply wrong. Rather than worrying about how to integrate tonal and modal practice, these pieces were dropped. Following the guidelines outlined by Burns,(76) 45 of the chorales were excluded from the sample.
 The Melisma Music Analyzer happens to be a very capable choice for this project, but as with all harmonic analysis software, there were some problems. For various reasons, partly due to metric complexity, 4 of the chorales and 221of the string quartet movements failed to be analyzed.
 It is true that hand analysis would have allowed a greater role for intuition. On the other hand, the results would have been harder to reproduce. Furthermore, it would not have been possible to analyze as much music. Using this method, we were able to sample from 207 distinct pieces, for a total of over 4500 measures of music.
Brent Yorgason, Managing Editor
Updated 03 June 2004