Tempering the clavier: Examining the intervallic content of Bach's Well-Tempered Clavier through the lens of historical temperaments
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Date
2021-12-16
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Ohio State University. Libraries
Abstract
While it is understood today that J.S. Bach's Well-Tempered Clavier was intended for a system of "well temperament," which (if any) specific temperament remains unknown. Excerpts from the work have been analyzed in the context of Werkmeister-III (Gann, 2019), but also within other tuning frameworks (Lehman, 1995). This study addressed the question of temperament from a computational standpoint – in other words, the aim was to determine whether a certain temperament would be a better "fit" for Bach's WTC when frequency of harmonic intervals and deviation from pure (just) intonation are considered. This study examined accented (simultaneous onset) imperfect consonances' frequencies as a proportion of all accented harmonic intervals in the WTC fugues, weighting each according to its notated duration in the score. The average expected frequency for each interval was calculated on a basis of key (e.g. major third between tonic and mediant) to control for differences in usage arising from tonal function. Intervallic "emphasis," then, was used as a metric. This study found no significant correlation between intervallic emphasis for Werkmeister-III, and a small yet significant positive correlation for Bach-Lehman. This indicates that Bach was not avoiding less purely-tuned intervals in these fugues, and emphasizing the "color" of each key.
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Keywords
Bach, Temperament, Well-Tempered Clavier, Werkmeister, Bach-Lehman
Citation
Future Directions of Music Cognition (2021), pp. 33-37