Bach WTC1 B flat minor Fugue mm. 58-59: Slightly Out of Tune ?

This is concerning measures 58 - 59 from Bach WTC1 B flat minor Fugue:


To my ears, this passage has the effect of sounding “slightly out of tune” - perhaps having to do do with temperament on a modern keyboard instrument with a conventional tuning. Does anyone else hear it that way? Any comments on how to analyze this passage?



Isaac Malitz, Ph.D.



  • Hi Issac, 

    Upon immediate inspection of measures 58 -59 - we have a sequence with a cycle of 4ths pattern in the bass (C- F -Bb - Eb).  We also have descending chromatic lines in the tenor (A - Ab - G) and the skeleton of the top voices in thirds is also a descending chromatic passage [minus the sequential thirds] (eflat/c - - eflat/cflat - dnatural/bflat - - dflat/bflat).  Harmonically we have an Adim7 chord (half diminished) in first inversion followed by a Db7 chord in first inversion resolving to a Bb7 (with that passing minor Db) resolving to the Cdim7 in first inversion as well (with a passing tone flat 9th [Db], then moving to another Adim7(half diminished) chord in measure 60.  So we have cross relations, irregular resolutions, unstable harmony structurally resulting from the descending chromatic movement in the upper voices all moving towards the final cadence through very dissonant territory and irregular resolutions.  

  • For Bach, this fugue was in a re-mi-fa key (see the title page). Using the standard solmization system in use in Bach's part of the world at that time, the only notes that do not belong to the governing scale are C-flat and D-natural in bars 58-59 (they are chromatic inflections, accidentali that do not alter the solmization). THe A-flat to A-natural in the bass is more usual, since the re-scale could incorporate both ut and sharpened ut.

    The melody of bars 58-59 would have been conceived by musicians of Bach's generation as sol fa la sol | fa la sol fa | mi fa | mi re | do.


  • Schenker comments on this passage in Das Meisterwerk in der Musik II, pp. 33-34 of the German edition. He gives the score of bars 55-63 and a reduced example from which, he says, the score is developed. I propose here an intermediary graph, between the score and his reduction, and showing how all lines fill in the intervals of the 7th on E♭ (IV):

    Schenker writes: "The example comes  without a sustained note – and yet, what manner of dissonance arises, especially in bars 58–9, as a result of the linear progressions in the outer voices! (By imagining E♭, the root of IV, as persisting to the upbeat of bar 61, one gains, by insight into the linear progressions, a convincing explanation of all incidental dissonances.)"

    I doubt that the musicians in Bach's circle would have conceived his WTC in terms of solmization. Ut re mi and re mi fa, as Bach writes on the title page, were standard designations of the major and minor scales, but the very idea of presenting 24 Preludes and Fugues, i.e. 12 transpositions of these two scales, is rather contradictory to the principles of solmization (as advocated by Burstett against Mattheson) which remained linked with the idea of six or eight modes.




  • Here is the example:

    (With thanks for the help)



  • I find Schenker's analysis compelling. But I think there is another aspect to the mm 58-59: I tried transposing it into some other keys; in various transpositions it sounds very different (to my ears anyhow).

    - Transposed up one half-step, it sounds very different, I don't know how to describe it.

    - Transposed down from B flat minor to G minor, it sounds (to me) like Bill Evans !

    If various transpositions sound different, doesn't this suggest that something is going on re temperament ?



    Isaac Malitz, Ph.D.


  • Isaac, we have the very common notion that if keys sound different, it must be a matter of temperament, as it did (we think) in Bach's time. Yet equal temperament should make no difference between keys, and we may presume that your piano is good enough and well tuned enough to sound at least roughly in ET. The difference that you experience must therefore have other causes.

    A possible explanation is intertextuality: you may unconciously remind other pieces in B flat minor, or B minor, or G minor – or not so unconsciously, perhaps, when you mention Bill Evans in G minor...

    Another explanation is keyboard fingering: it makes quite a lot of difference playing this passage as an elaboration of e♭/E♭7 or of e/E7, if only because the first requires up to about six flats, the second up to four sharps, a quite different sensation under the fingers. The fact is also that we easily hear flats lower than sharps, even although they are played on the same key. And transposing the fugue in G minor would transform the elaborated chord in one of c/C. Jacques Handschin wrote that the tone C "appears to us as a primal image (Urbild) of 'stability', of 'self-assertion'..." (Der Toncharackter, 1948, p. 16).

    And of course, you might have absolute pitch, which also would make a difference.

    This all to say that I don't believe temperament has much to do with what you resent here.



  • Nicolas, thank you for your comments.

    I have listened to the passage again on several instruments: My Yamaha C7 piano , which I confirmed is ET; an electronic instrument  which allows various alternative tunings. Based on these experiences, I think that you and Schenker elucidate what my experience is of this passage.

    Isaac Malitz, Ph.D.


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