Nature has more on the suitably self-recursive premiere of a uniquely mathematical piece of music:
The piece, “The Hilbert Heartbreak Hotel” by Danish composer Niels Marthinsen, was the brainchild of computer scientist Thore Husfeldt of Lund University in Sweden and IT University of Copenhagen. “I probably have some latent frustration about the increasing fragmentation of the arts and sciences,” Husfeldt says, “so maybe it’s an attempt to bring together some strands of culture that I happen to enjoy very much.”
Marthinsen was a student of the Danish composer Per Nørgård, who in the 1960s explored the use of mathematics in composition with, for example, series of notes with the fractal-like property of self-similarity.
So Marthinsen was a natural choice for commissioning the piece. “He said: ‘This is completely insane and I don’t have time at all, but of course we have to do it.’” Husfeldt recalls. “From there, the puzzle was to actually make it work.”
The basis for “The Hilbert Heartbreak Hotel” is a set of axioms about integers, or whole numbers, proposed by the Italian mathematician Giuseppe Peano in the late nineteenth century. The axioms are an attempt to put arithmetic and number theory on formal, logical foundations, starting from some obvious-seeming statements such as: “For every natural number x, x = x” and “If x = y, then y = x”.
To turn Peano’s axioms into music, Marthinsen assigned each logical symbol to a musical note to create short musical phrases, which he calls gödelings. He used several different ‘encodings’ of this sort to create what he calls “musically satisfactory language” — a set of options that does not sound too sterile. Similar encodings of alphabetic or symbol strings into musical notes have been explored by many others, from Bach to the Russian composer Dmitri Shostakovich.
Marthinsen layered these gödelings to produce musical parts that are “complicated but understandable” — reminiscent of the interweaving voices of Bach’s counterpoint. He says that he wanted to ensure that the result worked as music and did not get lost in “numerology”.
On top of this, Marthinsen placed a freely composed soprano vocal. “The soprano sings about Hilbert’s Heartbreak Hotel,” he explains: “how a heartless person entering the hotel is given a human heart from one of the guests on a winter’s night, and how all the guests pass on their hearts to each other until everybody has one.” The scenario alludes to a paradox about infinite sets — conceptualized by Hilbert as a hotel with an infinite number of rooms — as well as to Elvis Presley’s song Heartbreak Hotel.
The composer and mathematician discuss the piece here (click through for subtitles):
But you can’t actually hear it until after the premiere on July 9 in Copenhagen. The music is still notional (and, maybe, incomplete?), at least for us out here in the world.