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As you may have heard, Robert Schneider of The Apples in Stereo recently composed a score for a play written by mathematician Andrew Granville and his sister Jennifer Granville, entitled MSI (Mathematical Sciences Investigation): The Anatomy of Integers and Permutations. In late December Robert wrote Optical Atlas, “I composed a score for a play, and played on December 12 at the Institute for Advanced Study in Princeton, NJ, which is probably the most famous mathematical college in the world (along with Trinity College in Cambridge, England) – there are no students, only professors doing research. Einstein lived on the campus, and many of the world’s most famous mathematicians, physicists, historians and such have been on the faculty or lived there – very exclusive. I actually had the band take me by there just to see the place, earlier this year when we played at Princeton University. Anyway, this very well-known mathematician Andrew Granville, who is a top expert in number theory and especially in prime number distribution (which is what I am really into, and for that topic, Andrew is the man), asked me to compose a musical score for a mathematical mystery play he had written – he is experimenting with different formats for writing math papers. This is the first time in the Institute’s history that a theatrical performance has been given. So I wrote a composition called ‘Reverie in Prime Time Signatures,’ that is obviously written in prime time signatures, that is, only prime numbers of beats per measure. Also the piece has kind of a sophisticated middle section that encodes some ancient Greek mathematics related to prime numbers in musical form, that I am proud of. It was extremely private and hush-hush, only produced for Institute members and by invitation – [the] audience populated by Nobel recipients and Fields Prize winners (the Nobel equivalent for mathematics). I met all sorts of amazing people and got to stay in the campus apartments for visiting faculty, designed by a Bauhaus architect… The piece was composed for clarinet, cello, and harpsichord, sort of a baroque sound – Heather McIntosh [Circulatory System, The Instruments] came up from Athens to play, and also a clarinetist/mathematician Alex Kontorovich… It was awesome!”

In the photo above, taken by C.J. Mozzochi, you can see in rehearsal Alex Kontorovich on clarinet, Robert on Roland JX-3P synthesizer, and Heather on cello. “During the performance, we all wore black orchestra attire, but I also wore a lab coat.” Which would be the signature Robbert Bobbert and the Bubble Machine garb.

Robert’s interest in mathematics began to merge with his obsession with pop music around the release of the last Apples in Stereo album, New Magnetic Wonder, which featured the unveiling of his Non-Pythagorean musical scale and a number of short instrumental compositions ultilizing it. (The latest Apples album, Travellers in Space and Time [April 20], includes a full song, “C.P.U.,” based upon the scale.) Robert has also given talks at the Mathematical Association of America’s MathFest conference, has been interviewed in New Scientist, and has taken undergraduate classes in mathematics at the University of Kentucky (Robert lives in Lexington).

Below you can listen to a piano demo Robert composed for the play, featuring the three parts of the composition. The middle section, Robert states, is “based on the Sieve of Eratosthenes (look it up, a very simple, beautiful way to identify which numbers are prime, and it was also the first mathematical theorem I ever ‘discovered,’ before I found out it was basically one of the first things ever known about primes).” You can also read his extract on the piece, and even download the sheet music, below.

Robert Schneider – Reverie in Prime Time Signatures (demo)

Reverie in Prime Time Signatures – Score (.pdf file)

The MAA’s review of the play, which features more detail on the plot and characters.

An interview with Andrew Granville on the play.

ON “REVERIE IN PRIME TIME SIGNATURES”
Robert Peter Schneider

As the title indicates, the piece is written in prime-numbered time signatures—which is to say, there is a prime number of beats in each measure. The main theme plays in the time signature 7/4, which indicates 7 beats per measure, with an interlude that passes through the signatures 2/4, 3/4, and 5/4 as well. From the constraints imposed by these rhythmic patterns, melodies emerged naturally as I composed, special to each prime. A second interlude happens in 29/4 time, occurring, by a pleasing coincidence, at the 29th measure of the composition—a musical rendition of the sieve of Eratosthenes, an ancient Greek method for identifying prime numbers. Here, a high keyboard note pulses on every beat, rising in pitch at the perfect squares; while the cello plays a note on every other beat, the clarinet every third beat, and the keyboard plays a chord on every fifth beat—that every fifth beat is marked by a chord instead of a single note, is intended as a nod to the golden ratio, which is related to the square root of 5, and has historically been considered a model of aesthetic perfection by some writers. Notice how the cello marks beats that are multiples of 2, the clarinet marks multiples of 3, and the chords mark multiples of 5. Clearly, the beats on which none of these instruments play must not be multiples of 2, 3 or 5, which is enough to identify them as primes among the integers relevant to the composition, accompanied by only the high pulse; until the cello, clarinet, and keyboard chords sound together on the 30th beat (30 is the first multiple of all three primes 2, 3 and 5), resolving before returning to the main theme. In this tangled interlude, not quite random, our ears experience the formation of the sequence of the primes. I have read that Leonardo Da Vinci may have hidden a musical composition in his painting “The Last Supper,” and that Roslyn Chapel in Scotland has musical notation encoded in the masonry. As a variation on this theme, I sought to encode a hint of real mathematics within this musical composition: Eratosthenes’ first step toward understanding the primes.