Systematic Variation and Microtoming in Rhythmic Performance of Bach and its relation to Polyphony

Question: What systematic deviations from a mechanical norm can be found in the performance of the solo cello work of Bach?  How do these deviations relate to the underlying polyphonic structure of the piece and what tendencies can be derived from the analysis?

As a performer, I am particularly interested in how to interpret the music that I play.  This question allows me to look closely at how the finest perfomers interpret the music of Bach and to see what deviations they all have in common.  This experiment deals mainly with the performance of musical rhythm.  This question is important because, through data analysis, I expect to find standard variation in timing which correlates with a change of voice in the polyphonic structure.

“Systematic deviation” refers to consistent and recurring deviations from the mechanical norm Bengtsson & Gabrielsson (1980).

For data analysis, I will choose 8 performers interpretations of 4 specific measures of polyphony from the Allegro portion of the Prelude to Bach’s Suite for Cello No. 5 in C minor.  Using Davis (2006) analytical system, I can provide proof of where the lines change voices using her numbered score system.  I chose to use only 4 measures because of the issue of time.

The duration analysis will be carried out in the following fashion, as it was in Bengtsson & Gabrielsson (1980):

“The durations measured and analyzed in this paper refer
to the duration from the beginning (onset) of one tone
sound event to the beginning of the next tone sound event”

I will present my findings in a paper format with data inserts.

As Bengtsson and Gabrielsson (1980) found, I expect that the analysis of systematic variations or SYSVAR will elucidate important and relevant perceptual data with respect to the cognition of polyphonic music..


Bengtsson, Ingmar, & Gabrielsson, A. L. F. (1980). Methods for analyzing performance of musical rhythm. Scandinavian Journal of Psychology, 21(1), 257-268. doi: 10.1111/j.1467-9450.1980.tb00369.x     (ARTICLES+)

Stacey Davis. (2006). Implied Polyphony in the Solo String Works of J. S. Bach: A Case for the Perceptual Relevance of Structural Expression. Music Perception: An Interdisciplinary Journal, 23(5), 423-446. doi: 10.1525/mp.2006.23.5.423   (GOOGLE SCHOLAR)



One thought on “Systematic Variation and Microtoming in Rhythmic Performance of Bach and its relation to Polyphony

  1. I do think this is a more manageable and potentially more interesting project than the one about timbre, but then I might just be biased!

    A few things to clarify as you start working:
    1. What do you mean by “what tendencies can be derived from the analysis”?
    2. By referring to “systematic” deviations, you are in essence, setting up the task to not only find deviations, but pattern of deviations that are representative of several performers. Also of interest, I think, might be to look not only at the patterns that will (at least this is the hope) be similar across performers (means and standard deviations), but also at individual performers that might not conform to this norm (specific IOIs and timespan ratios). In practiacl terms, that means that you can map the average IOIs for all performers on a two-dimensional graph (x-axis = timepoints; y-axis = IOIs) as well as individual timing patterns (look at different representations in performance analysis literature).
    3. “I can provide proof of where the lines change voices using her numbered score system.” The word “proof” is not quite the right one here; maybe “predict where the lines change voices with reasonable accuracy.” Is this the part where you will be applying Davis’s method?
    4. Since you are interested in specific moments within the timespan of the excerpt, you might also consider comparing IOIs across voice boundaries and within voice boundaries. This will be easiest to do if the IOIs are notated as the same (i.e., within voice quarter vs. across voices quarter).

    In terms of the next steps, there are a few tasks I would suggest:
    1. Get familiarized with Sonic Visualizer as soon as possible and play around with extracted IOIs from one excerpt. Once you have some strategy/method worked out, then apply the same method to all your excerpts. You will need to decide on some criteria for when you determine that the sound starts. It might seem trivial, but since you will be measuring in milliseconds, you will need to decide exactly where you will consider a sound to have started.
    2. Make a table of Davis’s method for determining voice boundaries. Apply it to your except and send me the analysis as soon as it is done for review.3
    3. Read the core articles more closely and identify a few secondary articles of interest.

    Let me know if you have any questions.

Leave a Reply

Your email address will not be published. Required fields are marked *