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 may have
been emphasizing the “color” of each key.