jwilzewske: New Quantitative Ways to Look at Small-Scale Variability in Meter and Rhythm

A pianist friend of mine says that the 2-part Inventions are merely ‘steep hills’ but that the 3-part Sinfonias are ‘craggy mountains whose paths have lots of twists and turns’. Having lived with these pieces most of my life, I have to agree.”
— Lee Ridgway, harpsichordist, BEMF 2011 Fringe Recital.

H arpsichordist Lee Ridgway performed all 15 of J.S. Bach’s 2-part Inventions and all 15 of the 3-part Sinfonias yesterday, in one of the ‘fringe’ recitals at the Boston Early Music Festival. He performed them in the sequence in which they originally appeared in W.F. Bach’s clavier-büchlein. His masterful and sensitive treatment of each provoked a number of reveries for me, for which I am grateful.

A mong these was a reflection on how the moment-to-moment agogic metric accents might be analyzed with mathematical and statistical signal processing and spectrum-analytic methods similar to those that have been applied over the past 20 years in cardiology, to understand heart rate variability (HRV) and develop predictive models of cardiac disorders. The pulse quickens; the pulse also slows! Quantitative details of small-scale dispersion of meter—and the abnormal, motoric diminution of HRV that occurs in stress and in disease states—can tell us so much! Just to see what interesting things may turn up, I begin with one of the simplest ‘variability’ measures—the root-mean-square standard deviation, RMSSD:

I look in the music theory literature and recent doctoral dissertations, and so far I am unable to find anybody who has pursued this sort of thing. If I am wrong, please email me or add a comment below.

O vernight, I download some MP3s of others’ performances of the 2-part Inventions and begin to run some analyses using the MATLAB signal processing toolbox software—the same modules that I use for analyzing digital electrocardiograms. I pick off beat-by-beat interbeat intervals in the left-hand part and the right-hand part. I exclude marked ritardando/accelerando bars; also exclude fermatas.

T here is more or less constant variation in articulation and timing... successive notes are crafted with varying durations—this is especially true on harpsichord more than other keyboard instruments, but it would be true as well for winds, voice, any instrument. The plot above is a composite across 2-part variations—a quick exploratory ‘look’ only; not what we would do for a proper analysis.

D etached releases ranging from ‘sharp’ ones to ‘lingering’ ones… this all shows up in the RMSSD and other time-domain variability measures. It also shows up in frequency-domain power-spectrum and other FFT- and wavelet-transform-based measures.

A nd, naturally, the variability and rhythmic power-spectrum measures change throughout the course of each piece. The power spectrum has ‘shoulders’ on it, on both the left (slower, longer IBI) and right (faster, shorter IBI) side of the median interbeat interval or rhythmic frequency. In principle, we would watch and measure the time-evolution of the power-spectrum from the beginning of a piece to the end of a piece—look at these evolutions or trajectories for different performers whose interpretations and styles differ. Then we would be better able to account objectively and quantitatively for how they do what they do!

L inkages across the bar-line are frequent, often involving small melodic voice-leading in one part (hand). These were particularly prominent in Ridgway’s accounts of the C-major, F-major, G-major, and C-minor 2-part variations. Beautiful, truly.

T hrough thoughtful, passionate application of agogic variations in small-scale timing, we get an acute sense of tension between (1) propulsion from ordinary and extraordinary accents in the metric frame and (2) propulsion from motivic and other phrase units. It is a major source of musical drama and beauty—not just in Bach but, I think, in all music. It was simply Ridgway’s fantastic playing yesterday that makes me think of these mathematical ways of explaining and understanding how it works.

R idgway is a solo organ and harpsichord performer, has performed for more than 40 years throughout North America and Europe. A native of Oklahoma, he received his Bachelor of Arts from the University of Oklahoma and Master of Arts from New England Conservatory of Music. Presently the organist and choir director at St. Chrysostom[s Episcopal Church in Quincy, MA, he is also Dean of the Boston Chapter of the American Guild of Organists. The instrument on which he performed yesterday at Emmanuel Church is one made by Boston’s Allan Winkler, a 2-manual adaptation of a 1716 design by Carl Conrad Fleischer… gorgeous sound.

B eyond their pedagogical applications, the Inventions and Sinfonias offer us wonderful, individual pieces of music… The similarities or contrasts between pieces in the same key; the [affective] characteristics of different keys; the characteristics of individual themes; … how the voices engage in dialogue or games of chase...”
— Lee Ridgway, harpsichordist, BEMF 2011 Fringe Recital.

jwilzewske

Tuesday, June 14, 2011

New Quantitative Ways to Look at Small-Scale Variability in Meter and Rhythm

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