The Zehetmair String Quartet delivered an invigorating performance in
Kansas City tonight.
- Mozart String Quartet in G Major, KV 156
- Hindemith String Quartet No. 4, Op. 22
- Schumann String Quartet No. 1 in A Minor, Op. 41
For entirely personal and idiosyncratic reasons, I found the Schumann Op. 41. No.1 quartet especially intriguing. There are passages in it that reminded me of a piece of software I had recently written, involving reflection and recursion in C# (.NET)—particularly the Quartet’s last movement, the Presto. My code is parallelized, to be run on a multi-CPU parallel multiprocessor in ‘sections’ that ‘rendezvous’ with each other to produce the final result. And so here I am, listening to the Zehetmairs, thrilled to notice sections of the Schumann quartet No. 1 with identical durations are treated as ‘privileged’—much in the manner that my software works—with the violins against the viola and ‘cello. The Zehetmairs’ orienting themselves physically on the stage as they did—in two parallel columns, with the cello directly facing the viola and the second violin directly facing the first violin—is what really ‘made’ the analogy to my code and how it works. As with so many compositions, there is a bias toward hierarchical and ‘nested’ structures in the piece. And there is the ‘repeat’—what programmers would call a loop or iteration. But there are also ‘reflection’ and ‘recursion’ in this quartet—phrases that invoke new instances of themselves, “passing in” new arguments whose values are set by what has gone before, and these invocations in turn invoke yet more instances/replicas. How cool!
Recursion, exemplified by calculation of N! (the factorial of a number, N) as you may remember from high-school maths, is a fundamental concept for expressing algorithms in computer science. Recursive algorithms are typically more elegant and have far more concise code than those whose flow-of-control is implemented in iterative and conditional loops. Recently K-nets and recursive structures have been receiving attention from mathematical musicologists and music theoreticians. But, as far as I’m aware, nobody up to now has looked at algorithmic recursion and reflection in Schumann’s compositions.
How did these quartets come to be? By way of history and background, in 1842 after Clara Schumann’s return home from her tour performing in Hamburg and Copenhagen, Robert composed furiously. This probably was one of the manic episodes of his bipolar disorder. He started in April and by the end of July he’d finished the three string quartets of his Opus 41. He was 32 years old.
It’s curious that Schumann, who’d never before composed a string quartet, would explode into the idiom with three all at once. It’s even odder that these quartets turned out to be his only chamber music works without piano. And why did he never return to this project? Why did he never write more string quartets?
This Op. 41 reflects Schumann’s rapid assimilation of technique and ideas from Bach’s ‘Well Tempered Klavier’. Over the course of the previous year he’d ‘inhaled’ the quartets by the Viennese composers; grasped their mechanics; understood their architecture and flow-of-control. He’d acquired the skills to be a “hacker” in a new idiom. The Quartet No. 1 is not emblematic of ‘borrowing’ as with Brahms and others but, instead, is emblematic of ‘acumen’.
In that regard, the thematic development and counterpoint in Quartet No.1, to me, bears the hallmarks of an eager “patch” contributed to a software open-source project by a ‘newbie’ who’s acquired a reasonable fluency by quietly ‘lurking’ in the project community for some months. Some of Schumann’s writing here is clearly pianistic. His usage is ‘opportunistic’, but it is not ad hoc. His style in this Quartet is ‘modest’ yet self-assured. Schumann is applying compositional techniques and gestures that he knows ‘work’, just as any [software] developer would do. He is generalizing design-patterns from his previous [software] projects. Yes, some of the writing is maybe technically awkward for the violins, as several violinist-writers have said over the years—the Scherzo maybe more so than the Presto. And maybe this alien, pianistic quality in fact conspires to create a certain hyperkinetic/kinesthetic ‘thrill’ for the violins—and for us listeners. It’s unsettling: that’s part of its meaning and charm, and undoubtedly as Schumann intended. This is the work of an adventurous developer, not some casual bricoleur.
So what? How would this resemblance, noticed only because of my own recent work in software development, shed any new light on Schumann or on this Quartet? I think it’s worth posting here because it illuminates a dimension of Schumann and his environment that may go beyond what regular biographers might have noticed. For example, any software developer does what he/she does “in community”, with the knowledge and anticipation that other developers will see and experience the code that he/she has written. So it is between composers—especially between a newbie writing her/his first composition in a particular genre and the community of established composers in that genre. And if my suggestion (that Schumann’s phrasing and pacing and compositional structures and technical fastidiousness resemble those of a modern-day software developer) has plausibility, then we should think about the “community” whose responses Schumann was anticipating. Yes, Schumann was writing these quartets in the shadow of Haydn and Mozart and Beethoven especially. And Boccherini, Cambini, Campagnola, Viotti, and Schubert, Hoffmeister, Spohr, Burgmüller, Kraus, Kramář, Gyrowetz, Hänsel, Rejcha, and Vranický, too. But maybe these quartets’ construction reflects an implicit anticipation of the reception by Mendelssohn, Chopin, Gossec, Vaňhal, Václav Pichl and Robert Volkmann and others.
Schumann in Op. 41 seems to be trying out some of the formal procedures of Beethoven’s late quartets—but with Schumann’s own original transformations. This Quartet No. 1 is no ‘homage’ as such. In fact, as Daniel Chua has suggested, maybe Schumann’s Op. 41 was conceived in somewhat the way that Beethoven’s Op. 127 was conceived—as a means to
influence musical history, rather than to
reflect the musical past. These Op. 41 quartets are advancing new methods of theme construction, movement structure, and quartet orchestration. Here we have Schumann (maybe like Beethoven before him) preferring, socially, to be the musical ‘hammer’ rather than the ‘anvil’.
And so it is as well with open-source software developers. Self-styled hammers they are, never content to be anvils!
More than anything, and knowing as we do that this was Schumann’s first string quartet, what we hear are “transgressive” gestures of a “newbie” to string quartet writing. As a software developer myself, I see evidence in Op. 41 that’s reminiscent of an intense young software developer, one who is new to a particular tool-set and new project architecture / design patterns. To me, this is Schumann bursting in upon the composerly society of quartet writing, much in the manner of a developer making her/his first contribution to an open-source collaboration, such as SourceForge.
R ule 1: Stick to your level of Karma. Open-source is not a democracy. You have heard something different? This is wrong. Always keep in mind: Open-source is not a democracy. Every developer has a certain unexpressed and inexpressable level of Karma, which allows him/her to decide (or even dictate) things and to make use of the infrastructure of the community (like their version control system, their servers, etc.). Think of Karma like your “points level” in a role-playing computer game. The more levels you’ve played and the more riddles you’ve solved, the higher your Karma level grows. But beware: your Karma may be damaged or lost, if you act improperly. If you are new to a community, your Karma level is zero by default. Always keep that in mind. What is Karma? Karma basically means the trust the community has in you. It is not possible to measure Karma or even to guess it. If you have to ask, you’ll never know.”
— Tobias Schlitt, 10 Golden Rules for Open-Source, 19-APR-2007
After this No. 1 fugato Andante espressivo opens in A minor, we get what sounds like a second theme in the relative major. But this turns out in fact to be a first theme: the A-minor section was just a slow introduction. The movement never returns to A minor but instead finishes in F major.
The Adagio is basically a Lied in F major, and the F major evokes further uncertainty about the quartet’s tonal center. The scherzo movement is a normal, ternary form with a contrasting Intermezzo.
The vigorous Presto in A minor closes the quartet. This is the movement that immediately reminded me of my application in C# (.NET).
Schumann iterates a rising-fifth motive. He sets up so-called Kreutzer exercise figurations (Rodolphe Kreutzer’s violin etudes, designed to strengthen the violinist’s left hand) that are not just repetitive iterations but recursive—each successive instance appears to invoke yet more instantiations of the figure, in a cascade inward. The cascades alternate between the violins and the viola and ‘cello. Programmerly recursion! Not whole phrases, but smaller-scale movements within the phrases.
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