Many of you know the distinction between pure and applied mathematics. The pure mathematician selects problems for their truth and beauty and tries to solve them within the laws of mathematical logic. The applied mathematician also respects those laws, but his primary focus is using mathematics to look at, understand, and improve the world.
Through the centuries, there have been many achievements in “pure music.” The fugues of J.S. Bach and, before him, the canons of Josquin des Prez express truths in counterpoint, the art of combining two or more melodies in a sonorous manner. Beethoven’s sonatas show that many structures besides the traditional ones can hold a piece together as a unit. Experiments in the twentieth century have aimed at functional harmony without triads (Ravel, jazz), tonality without functional harmony (Hindemith), and coherence without tonality (Schoenberg), and have successfully achieved all these aims, whatever one’s opinion of the aesthetic qualities of the pieces and styles thus created. See Elkies’ Steganographic Étude for a modern piece that sets a unique aim and achieves it within the confines of late Baroque/early Classical style.
Although I have a great appreciation for pure music, it has been made clear through the years that it should not become my primary focus. Much progress in musical art has come about through the striving toward practical, that is to say emotional, aims. The simplicity and insistency of much dance music invites all to put aside their differences and share in a festival celebrating a common joy. Gregorian chant and Renaissance polyphony are styles honed to draw people away from their personal cares and into the presence of God. Mozart’s lone sonata in A minor and, jumping to modern times, Lauridsen’s Lux Aeterna were written (at least in part) to console the respective composers after their mothers’ deaths.
Which brings us to the present piece. “Grand Croggon Rhapsody” is an improvisation that has been a pleasure to transcribe because it was played entirely uð imlâža manîr (as a pathway to calmness). The situation was this. At the beginning of the academic year, I was attending a conference at the IAS, a half hour’s walk from Princeton’s campus. After the end of the conference, a professor, whom I will leave unnamed, kindly offered me a ride back to campus as well as some advice, including that I should attend tea at the department more often. What angered me so much about this advice was not so much that it was brusque and unsolicited as that it might be wise. Thus it was that I rushed to the piano and, fortunately, had the presence of mind to turn on the recording function on the phone before plunging the tumult of the day into the keys.
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