Piano Study in Mixed Accents

Statistical and Morphological Measures

Larry Polansky

scans of transparencies
pages 1-3, 8 of The Casten Variation

Originally, this was a talk given at the Society for Music Theory in November, 1993. It was 10 minutes long, and given as a "response" to an excellent presentation by Seeger scholar Joseph Strauss, about atonal analysis of RCS' work. The one work he did not discuss was the Piano Study..., so I decided to explore that (it was a piece that I'd long had a great interest in).

The talk takes the Crawford piano piece, incidentally, a piece which had yet to receive a kind of standard atonal analysis, and uses it as a basis to explore new techniques in computer-based visual, statistical, morphological and multi-dimensional scaling analyses. The talk is in the form of a set of "verbal captions" to a series of graphic analysis which try to progressively elucidate morphological structure in the work, while at the same time bringing up general issues in analysis and music theory themselves.

Part of my intent was, having at the time been very influenced by the work of Edward Tufte in statistical visualization, to try and present an an enormous trajectory of analytical possibilities in a very short time. There are some 50 or so charts of the piece, ranging from the simple statistical representations (a time series of the notes!) to counting intervals in lots of different ways, towards more morphological measures (using some of my morphological metrics). The talk ended with a set of multi-dimensional scaling charts of the pairwise morphological similarities of the different phrase groupings, under different similarity measures (and for different sections of the piece).

The original paper made use of a lot of HMSL software to do the analyses, Excel to plot the data, and in the final stages, a combination of HMSL and the statistical program Systat to do the MDS plots.

This talk has since been given many times (to students at my own institution, at conferences, as a guest lecture at other schools, etc.). There were three fundamental goals in the original talk: to explore visualization, to explore the piece, to explore the difference between morphological and statistical measures.

Soon after the first talk, being somewhat dissatisfied with the "outcome", I decided to take the project one, perhaps more positive, step further. I took the MDS analyses and decided to "resynthesize" the piece. The result was a work for ensemble or solo piano, The Casten Variation (the piano version has been played many times, and is being recorded by pianist Sarah Cahill, who often pairs it with the original). My colleague Charles Dodge suggested that what I had done was classic "analysis/resynthesis" and I like that description: the original RCS piece is indeed "time-stretched" and "pitch-stretched" in a sort of classic phase vocoder manner, but in this case, rather than use the FFT as the analysis/resynthesis tool, I used a kind of simplified multi-dimensional fitting algorithm based on my morphological metric sofftware.

The piece (Casten...) is available from Frog Peak Music. A number of the MDS plots from the original talk appeared in slightly altered form in my article on morphological metrics in the Journal of New Music Research. The notes for the original talk, and the many charts, remain unpublished (someday, I hope to return to it, fix a few minor problems, and make it available).