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)



Individual Project Proposal

In Huron (1989), an experiment is carried out to determine trained musicians ability to denumerate individual lines from a polyphonic musical texture.  The examples used were played using homogenous timbre.  This experiment led me to the idea that I could possibly alter its structure, and create an entirely new experiment, only this time with respect to timbre.  Timbre, as it relates to this proposal, can be defined as “that attribute of auditory sensation in terms of which a listener can judge that two sounds similarly presented and having the same loudness and pitch are dissimilar” Brancucci (1999).  My proposal is to use the musical examples from Gregory (1990) in order to test a participants ability to denumerate, or count the number of voices active in a polyphonic structure.  These examples would be altered using different timbres in order to observe what effect this might have on a participants ability to attend to concurrent and independent stimuli.  This question could lead to further studies about the perception of music and how timbre can effect our ability to attend to simultaneously occurring independent auditory streams.

Using the 5 polyphonic examples from Gregory (1990) the stimuli will be randomly organized and presented to participants.  As a rule, no one will hear the same excerpt twice.  The control timbre will be a standard grand piano sound.  I will alternate using tuba and oboe in order to get a good sense of the high and low ends of the pitch spectrum.  I will then analyze the results with respect to timbre and example number, doing a side by side comparison.

My prediction is that timbre will have an effect on the listener’s ability to denumerate individual lines in a polyphonic texture.  Specifically, I expect to observe a higher rate of success in identification with the oboe.  The tuba’s timbre quality I expect will make it more difficult to attend to separate audio streams.



Gregory, A. H.  Listening to Polyphonic Music. Psychology of Music, October 1990; vol. 18,

2: pp. 163-170. Article DOI: 10.1177/0305735690182005.

I used the musical examples in this article.


Huron, D. Voice Denumerability in Polyphonic Music of Homogeneous Timbres

Music Perception: An Interdisciplinary Journal, Vol. 6, No. 4 (Summer, 1989), pp. 361-382

Published by: University of California Press. Article DOI: 10.2307/40285438.

I used this article as a model for my current experiment.



Pietro, S.M. and Brancucci, A. Laterality in the perception of temporal cues of musical

timbre. Neuropsychologia, Volume 37, Issue 13, December 1999, Pages 1445–


I used this article to help define timbre as it relates to this experiment.


Risset J.C. and Wessel D.L. Exploration of timbre by analysis and

synthesis. In: Deutsch D, editor. The psychology of music. New

York: Academic Press, 1982. p. 25±58.

I used this chapter to further clarify my definition of timbre as it relates to this experiment.