In measures 29-33 of Bach's Invention No.4 (BWV 775), there is a trill in the left hand. My book (Schirmir Masterworks Intermediate) notates it as tr#, indicating it should be between E and F#. However I've seen some people play it between E and F on Youtube.

To my ear, the E-F sounds harsh and dissonant, whereas the E-F# trill fits in nicely with the E major scale which that section of the piece seems to be in. Which trill should be played, and why? Either from the music theory perspective or from a definitive source regarding the composer's intent.

Trill in the bass pedal:

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  • It's always worth having a look at different scores in imslp -- imslp.org/wiki/… just to see if it's notated differently or there are editor/arranger notes. – Carl Witthoft Oct 16 '19 at 14:20
  • @CarlWitthoft, good point. I looked at a few and posted the autograph. None that I saw showed a sharp on the trill. Either way, there is something to explain about the cross relationship. – Michael Curtis Oct 16 '19 at 16:19

The Bach autograph on IMSLP shows...

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...the mark above the E is hard to see as a wavy line - it looks more like a long dash - but there isn't a sharp on it.

In terms of intent, I think the standard thing is to play the trill diatonically so that would be using an F natural.

In terms of music theory the clashing of the F natural in the bass trill and the F# in the treble is a cross relationship. Sometimes those cross relationships are avoided, other times they are exploited.

From an aesthetic point of view you can have two reactions: the dissonance is strong and upsetting, on the other hand it is strong and intensely dramatic.

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The Harvard Dictionary of Music Willi Apel


A nice discussion of a very similar trill, but from the cello suites is available here...

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Trills in the Bach Cello Suites: A Handbook for Performers By Jerome Carrington

The part that catches my eye is: "...the prevailing concensus favors playing this trill without chromatic alteration..."


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    "but there isn't a sharp on it": this implies a question about whether Bach wrote accidentals on trills and similar marks. I am not aware that he did. If he didn't, then the absence of a sharp on this trill does not help us decide whether to play an F or F#. – phoog Oct 16 '19 at 17:00
  • So make an artistic choice on your own. I would play F natural, because I like the dissonance, and because the line doesn't continue up the scale, it changes octave and goes down. It's pretty well known that musicians disagreed about how to embellish even during Bach's time so there isn't an absolute law, not everyone will be pleased. The performer has to make choices. – Michael Curtis Oct 16 '19 at 18:53

It is certainly e - f.

This section is in a- minor, the dominant is E, the movement of the the right hand is up and down using the tones of the E major scale (respectively e-minor upwards while the left hand is playing in the downward mode. Thats quite usual in counterpoint: Look at the line of the end of the trill ignoring the octava step (bars 34-36). In bar 36 we have again a F# (r.h.) and a F (l.h.)

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