Two articles on jazz rhythm

I came across two articles by Matthew Butterfield, a professor of music theory at Franklin & Marshall College, that should be interesting for us in surveying analyses of jazz, and in resorting to observations or measurements using waveforms as evidence.

One of the articles is titled “Why Do Jazz Musicians Swing their Eighth Notes,” and, while the question can hardly ever be answered definitively, it is a good one to be asking in analyzing jazz rhythm. Here is the citation:

Butterfield, Matthew W. “Why Do Jazz Musicians Swing Their Eighth Notes?” Music Theory Spectrum – The Journal of the Society for Music Theory 33. 1 (Spring 2011): 3-26, 107.

Butterfield makes some convincing points on a subject, jazz rhythm, that often seems to produce vague generalities and mysticism in the literature on jazz. Carefully examining ratios between different parts of soloists’ and drummers’ patterns of eighth notes, or eighth notes and quarter notes (which he calls the “Beat/Upbeat Ratio”), he goes on to show how soloists use minute variations in the ratios to embellish their phrases. That in turn suggests that they do so in distinctive ways, and that a particular artist’s expressive effects in this realm might be profiled, a possibility we should discuss further.

But my chief concern in this post is where and how Butterfield derives his evidence. He investigates audio waveforms for the nuances of timing he seeks to observe. Here is a footnote from the above article, p. 166, on his method for observing changes in the Beat/Upbeat ratio:

“BUR values in all musical examples included in this study were calculated by the author. The digital sound-editing program Audacity was used on a Macintosh computer to identify the onset of each note from a visual and aural analysis of its waveform. From these figures, IOIs between successive notes were defined and then employed to calculate the BUR values. There is inevitably some degree of uncertainty in identifying the attack point of each note, as noise and other onset ambiguities can render an exact determination impossible. By employing a consistent set of criteria to resolve ambiguities, I am confident that my figures are accurate to within ±.5 milliseconds, which translates into a BUR value accuracy of ±.05 at the tempos shown in Examples 4 and 5.”

Butterfield’s claims depend on his ability to identify onsets of given parts of the beat in a soloists’ performance. How can he be so sure he is that accurate? Because he is simply looking at a single point in musical time, aided by listening to the recording itself at that point, without aggregating it statistically (which we must do to characterize whole files)? What are his “criteria for resolving ambiguities”? is his manner of determining an onset useful to us in some fashion?

I have similar questions in another equally interesting article by this author. This one is open access:

Butterfield, Matthew. “Participatory Discrepancies and the Perception of Beats in Jazz,” Music Perception: An Interdisciplinary Journal, Vol. 27, No. 3 (February 2010): 157-176. URL:

This piece tests the contribution of “participatory discrepancies,” or subtle rhythmic changes ahead or behind the beat, to the effect of swing in jazz. The idea has weight in ethnomusicology, based on widely known work of Charles Keil, who sees the inherent asynchronicity and rhythmic in music as an attraction to is, an invitation to become part and shape the interaction. (See Keil, Charles, “Participatory discrepancies and the power of Music,” Cultural Anthropology, 2, pp. 275-283.) Discrepancies between instruments have also been a central concern of ours, even if our agenda was to ask how they might affect beat-tracking software and identifying individual artists (especially drummers), rather than delving into how they fuel the fundamental human experience of playing or listening to music.

Butterfield’s main concern is whether listeners, even ones with limited musical training, can perceive these discrepancies, and he describes some elaborate tests with real subjects. His answer seems to be “not much.” His conclusion may be valid within the terms of his own research design, but it is a straw man: a misguided attempt to directly and empirically test what for Keil was more of a philosophical argument and musical manifesto. Average listeners may not be able to accurately tell whether a bass is behind a drummer, but the practice of playing ahead or behind itself is beyond question, in more kinds of music than jazz (and listeners may sense it even if they cannot articulate or analyze what they hear). Arguing this point more carefully would take us too far afield.(Butterfield himself makes some very valid points toward the end of this article, once he leaves testing with human subjects behind and proceeds from his own observations on the performance discrepancies themselves, which deserves another post here.)

What is most important here is that, on page 163, Butterfield once again refers to his own observations using waveforms in a rendering of a jazz recording in Audacity. In this case, he is interested identifying lags between the accompanying bass and drums, and determining who might be ahead, so that he can test whether listeners perceive the discrepancies.

Here Butterfield claims not only to be able to tell where an onset is, but to distinguish different instruments within a waveform:

“Cymbal strikes in particular tend to be well defined and easy to spot—they appear ‘furry.’ Bass onsets, by contrast, are characterized by a substantial burst in wave amplitude.”

See the diagram on p. 163 to visualize this “furriness” and “burst.” Butterfield then seems to veer toward, or call out for, a beat-tracking methodology in the next passage:

“[Bass onsets] are not as clear as cymbal strikes, however, and this required formulation of a consistent procedure to define them. To this end, determination of each bass onset would begin with an onset hypothesis, placing it tentatively at the peak of the first wave whose amplitude departed significantly from the prevailing shape preceding it. A careful aural analysis of the beat ensued, working backwards and forwards from that point and adjusting it in accordance with aural evidence for an earlier or later onset until it could be determined with confidence to within ±5 ms. Any beat where the bass onset could not be determined with confidence to within this interval was omitted from analysis.”

He seems to acknowledge the need to adjust moment to moment rhythmic events to a virtual or average beat, but then proceeds to do intuitively or ad hoc, it seems to me.

So there are some common points of approach between Butterfield’s work and ours. If these methods of gathering evidence are in question, what would it say in the end about his otherwise compelling arguments about rhythmic dynamics in jazz? Are there quantitative terms or observations about jazz practices that could be useful for us in profiling certain artists, or analyzing whole performances, or major structural parts?


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