3.1 Past Research

[1] Most claims about chord-tone doubling probably arise from inspection of musical scores. To our knowledge, however, only two theorists have supported their claims with quantitative evidence. McHose, in 1947, tallied the doubling of vocal parts and triad members in Bach’s chorale harmonizations. Huron, in 1993, modeled the doubling of scale degrees in the same repertoire.

McHose (1947)

[2] McHose studied doubling in the chorale harmonizations of Bach. His results, presented as statistical summaries, showed, for instance, that the root is most often doubled in root-position chords and that the soprano is most often doubled in first inversion.⁽⁷⁰⁾ Our analyses provide limited support for his findings.

Huron (1993)

[3] In contrast to McHose, the doubling rules Huron chose to study were of the scale-degree variety.⁽²⁰⁾ The repertoire under examination was similar, however: 50 chorale harmonizations by Bach—44 in major mode, and 6 in minor.

[4] To test the idea that Bach’s doublings favored strong or key-enhancing scale degrees, Huron quantified key enhancement using the Krumhansl-Kessler key profiles. (See §6.2.1.) Whereas traditional scale-degree rules are quite broad—e.g., don’t double the leading tone—the Krumhansl-Kessler profiles suggest finer distinctions; for example, the profiles suggest that the mediant will be doubled more often than the subdominant.

[5] Huron found that the Krumhansl-Kessler profiles provided a very close match to the distribution of doubled scale degrees. Although the non-doubled scale degrees also fit the profile, the fit of the doubled scale degrees was consistently better.

[6] Huron interpreted these results to mean that Bach intended to enhance key perception, and did so by doubling tones with a high score in the Krumhansl-Kessler profiles. Although Huron’s interpretation was reasonable, at least two alternatives can be proposed:

1. Perhaps Bach sought to double certain chord members—which often happened to coincide with tones that had high Krumhansl-Kessler scores.
2. On the other hand, perhaps Bach avoided doubling tendency tones, because doubling them would lead to clumsy voice-leading. Tendency tones—the leading tone and chromatics—invariably have low scores in the Krumhansl-Kessler profiles.

[7] In light of our own results, the last interpretation seems the most plausible account of Huron’s findings. (See §6.2.)

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