I like making charts
Creating visual diagrams is one way I process information, both in and out of a musical context (I think David Byrne’s “mental maps” in Arboretum are super cool, and I’ve been making my own little integration sketches). Charting and graphing out concepts is also part of my early compositional process, especially as I’ve become more interested in the proportions of music.
I decided to do some basic analysis of the first movement, “Ludus,” from Arvo Pärt’s Tabula Rasa by charting the form. Tabula Rasa is a two-movement work for two solo violins, string orchestra, and prepared piano. Because the piece has such clear structural points (the silence of the grand pauses and the distinct musical material of the two solo violin lines), I wanted to investigate the proportional relationships within and between the phrases. The piece unfolds beautifully, and that has everything to do with pacing and proportion.
I used Google Sheets to keep track of the information (which ended up not being the right medium for what I wanted to do—lesson learned). I charted the piece beat-by-beat rather than by measure because the solo violin lines enter in the middle of measures sometimes, and I wanted to see this. I also wanted the chart to account for all the time signature changes. Having a quarter note as the base unit allowed me to see the time difference between 4/4, 5/4, and 6/4 measures (and the varying grand pauses). Essentially, I tracked what instruments were playing when with a bit of coloring to show pitch and textural material. You can view my final Sheet here (complete with rehearsal markings, measure numbers, color explanations, etc.).
Here’s the chart:
What did I learn about “Ludus” throughout this project?
There are many processes happening at the same time. I can categorize these into five types: expansion, subtraction, alternation, variation, and stasis.
Examples of expansion: each phrase (grand pause to grand pause) increases by approximately 20 quarter notes with each iteration; the layered string orchestra accompaniment increases by exactly 4 beats each iteration (seen in the red and blue layered “V’s”)
Examples of subtraction: the grand pauses are 2 beats shorter every time (the first one is 16 beats, the last one is 2 beats)
Examples of alternation: the layered string orchestra accompaniment alternates between having 3 and 4 M-voices (look at the “V’s”—they alternate between having 3 and 4 blue layers); the M-voice of the solo violins (the blue lines after the yellow lines) switch between Solo Violin 1 and Solo Violin 2
Examples of variation: the entrances of the solo violins’ a material (purple)—I couldn’t find a system that explained when the soloists entered in context of the accompaniment or each other; I tried counting the beats and saw no pattern
Examples of stasis: the piano has an attack at every entrance of the b material of the solo violins (notice the gray block under the start of each green line)
Expansion and contraction can happen indefinitely, but subtraction creates arrival. There is essentially nothing stopping musical material from expanding or contracting forever; however, subtraction will always lead to nothing. Arriving at nothing is definitely a structural point in music.
I listened to a bunch of recordings of “Ludus” throughout this project, and one stood out to me: Jean-Jacques Kantorow with the Tapiola Sinfonietta (Jan Soderblom and Tero Latvala on the solo violin parts; Jouko Laivuori on piano). Kantorow’s interpretation has incredible momentum, and the timbre of the prepared piano was hauntingly gentle.