MEMETERIA by Thomas May

Music & the Arts

Strange Loops and Golden Braids

Last night’s performance of The Musical Offering is a contender for the highlight of the four performances I attended during this summer’s festival presented by the Seattle Chamber Music Society.

Today, by coincidence, as the thema regium occupies my mind, marks the 278th anniversary of the death of J.S. Bach. The performers — violinists James Ehnes and Amy Schwartz Moretti, violist Richard O’Neill, and cellist Edward Arron (the newly reformulated James Ehnes Quartet); violinists Yura Lee and Erin Keefe; violist Che-Yen Chen; cellists Julie Albers and Ronald Thomas; flutist Christie Reside; and harpsichordist Byron Schenkman — sustained a very special atmosphere throughout.

It differed in fascinating ways from the usual SCMS mood, Bach’s intellectual virtuosity holding the capacity audience spellbound, but with the tragic undertone that is also part of this music ever-present. Such a rare pleasure.

A few observations from Douglas Hofstadter’s 1970s classic, Gödel, Escher, Bach:

“The Musical Offering” is a fugue of fugues, a Tangled Hierarchy like those of Escher and Gödel, an intellectual construction which reminds me, in ways I cannot express, of the beautiful many-voiced fugue of the human mind. And that is why in my book the three strands of Gödel, Escher, and Bach are woven into an Eternal Golden Braid.

In [the Canon per Tonos], Bach has given us our first example of the notion of Strange Loops. The “Strange Loop” phenomenon occurs whenever, by moving upwards (or downwards) through the levels of some hierarchical system, we unexpectedly find ourselves right back where we started. (Here, the system is that of musical keys.) … Implicit in the concept of Strange Loops is the concept of infinity, since what else is a loop but a way of representing an endless process in a finite way?

To give an idea of how extraordinary a six-part fugue is, in the entire Well-Tempered Clavier by Bach, containing forty-eight Preludes and Fugues, only two have as many as five parts, and nowhere is there a six-part fugue! One could probably liken the task of improvising a six-part fugue to the playing of sixty simultaneous blindfold games of chess, and winning them all. To improvise an eight-part fugue is really beyond human capability.

“Quaerendo invenietis” is my advice to the reader.

Meanwhile, the Boston Public Library has digitized and put online dozens of Escher’s prints here.

Filed under: Bach, Seattle Chamber Music Society

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