Musical Offerings, Fall 2018

Musical Offerings ⦁ 2018 ⦁ Volume 9 ⦁ Number 2 71 consonances [are] those produced with the first six integers.” 34 With this understanding, aural perception better corresponds with theory. This was a big deal; the mathematical description of consonance influenced the way composers sought to complete the musical circle. Problems of tuning and temperament affected all keyboard works, including books I and II of J. S. Bach’s Well-Tempered Clavier (WTC). Yet, Bach seems to have mastered the issue of temperament in these collections by including a piece in every key. How did he do it? According to Thomas Donahue, “The question of temperament and the music of J. S. Bach is complicated…. Bach’s music does not seem to be ‘supported’ by a single temperament.” 35 Donahue indicates that history offers varying perspectives on which temperament Bach may have preferred. The only thing known for certain is that Bach preferred his major thirds tuned slightly sharp. 36 Rudolf Rasch writes that until the 1950s, “The WTC was considered to be one of the first examples of what could be done with the tonal system when all twelve semitones were of equal size [ET], so that all keys sounded the same.” 37 Conversely, some authors argue that the WTC is best performed with unequal temperament—not technically equal or meantone. Along this line of thought, since Bach composed in different styles for different keys, perhaps he also desired some type of unequal temperament to highlight distinctive elements of each key. As a result, “The tonal relationships are exciting: C major and F major remain the best in tune, E major is the most brilliant key, and there is no harshness anywhere.” 38 However, despite much research, Bach’s choice of temperament remains shrouded in uncertainty. Although historians will continue to debate the authentic temperament for Bach’s music, the ground-breaking truth of the WTC clearly remains today; it is possible to perform an aurally pleasing piece in all twenty-four musical keys on a keyboard instrument . 39 Such an 34 Roger Mathew Grant, “Ad infinitum: Numbers and Series in Early Modern Music Theory,” Music Theory Spectrum no. 1 (2013): 67, do i: 10.1525/mts.2013.35.1.62 . 35 Donahue, A Guide to Musical Temperament , 117. 36 John O’Donnell, “Bach’s Temperament, Occam’s Razor, and the Neidhardt Factor,” Early Music 34, no. 4 (2006): 632, do i: 10.1093/em/cal101 . 37 Rudolf Rasch, Bach, Handel, Scarlatti: Tercentenary Essays , ed. Peter Williams, (New York: Cambridge University Press, 2008), 293. 38 Bradley Lehman, “Bach’s Extraordinary Temperament: Our Rosetta Stone—2,” Early Music 33, no. 2 (2005): 211, do i: 10.1093/em/cah067 . 39 Ibid.