Magazine article Musical Times


Magazine article Musical Times


Article excerpt

Enharmonies in Bach

An extremely significant and still open question is what tuning system Bach used, preferred or considered tolerable. Bach's deployment of sequential enharmonic notes might be useful in addressing this question, since in an equally tempered system enharmonies sound identical, while in other temperaments they do not. Here I should like to present three interesting examples of Bach's use of sequential enharmonic notes that may shed light on Bach's acceptance of equal temperament over non-equal temperament.

The first example comes from the Fantasia and Fugue for organ in G minor BWV 542/1. On the fourth beat of bar 38 of the Fantasia the pedal part consists of two successive quavers, E# and F[natural] (ex.i). The Fantasia is unusual, sectional and richly chromatic, unlike its lively and well-known Fugue. The first 30 bars essentially use flat-key harmonies, which in bars 31-34 intensify, until in bar 35 Bach moves to sharp harmonies before returning enharmonically in bar 38 to flat harmonies.

Beat four of bar 38 also stands out, as it is the only place in the piece where notes as short as quavers (or even crotchets) repeat on the same pitch. While there might exist organs with different pedals for enharmonic notes, and the piece might even have conceivably been written for one, it is likely that, given the rarity of such instruments. Bach must not have been uncomfortable with it being played on an organ where enharmonies sound the same pitch. It follows, then, that Bach cannot have found equal temperament unacceptable. In which case why aren't there more such examples of sequential enharmonies? This may be due to a relative lack of Bach pieces with such a strong delineation into highly flat and sharp sections.

I thank Noam Elides of the Mathematics Department of Harvard University for pointing out the second example to me. Notice that in ex.2 the last note in the pedal in bar 10 of the chorale prelude Durch Adams Fall (BWV 637) is a D#, and the first note in the pedal in bar 11 is an E[musical flat] (one octave higher).

My third example is not strictly a pure sequential enharmonie, but a very close enharmonie. The lowest note in the chord on the first beat of bar 10 of the first movement of the Sonata for solo violin in C Major (BWV 1005/1) is a D#. The lowest note of the chord on the third beat of that bar is an E[musical flat] (ex.3). Again, Bach is using the enharmonic to transition from sharp to flat harmonies. On the violin, especially in a solo piece, it is certainly possible to play these enharmonic notes as different pitches. And it would be an interesting experiment to see if playing them as such greatly improves the piece or not. But in writing the piece Bach must surely have considered that at least some performers would not play the notes as different, thus again illustrating that his comfort level for equal temperament was fairly high. Furthermore, this enharmonic persists in the clavier version of this movement, the Adagio in G major BWV 968, which utilises an A# on beat one and a B[musical flat] in an homologous position on beat three. Harpsichords typically did not have separate half-keys for enharmonic sharp and flat notes, so, again, Bach could not have been too intolerant of the enharmonic notes sounding the same pitch.

More than half a century ago Howard Shanet ('Why did J. S. Bach transpose his arrangements? …

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