When Keys Collide

I’m rather obsessed with bitonality at the moment, and the three composers who are much on my mind and stereo lately – Charles Ives, Kaikhosru Sorabji, and Darius Milhaud – all have a strong bitonal streak in their music, though that’s not as well known about the first two as it is about Milhaud, who wrote a book on bitonality. My wife Nancy gave me a three-octave toy piano for my recent birthday, and as a kind of sketchbook I wrote a suite for it called Surrealities; of the seven movements, two are atonal, one tonal, three bitonal, and one bi-modal (C harmonic minor in one hand, C Lydian in the other). I’m particularly pleased with the sixth movement, “Incommensurate Quantities,” which is a bitonal canon in A and D-flat, the only canon I know of at the interval of a diminished fourth. More to the point, it follows all the traditional contrapuntal rules, resolving every dissonance correctly, and of course contains an episode in the equidistant key of F (Gbb):




You can hear me play it here. Also another bitonal movement “Deep Denial” (A in one hand, C alternating with F# in the other), and the last (tonal) movement “Mistimed Adieu,” which I’m quite happy with.

In my youth Milhaud was one of my favorite composers, and he’s never quit being, though one doesn’t encounter his name much these days, or get opportunities to write about him. When I last visited San Francisco, Richard Friedman reminded me of a wonderful Milhaud piece I remember well from the 1960s, recorded only on vinyl, called A Frenchman in New York, written to go on the flip side of Gershwin’s American in Paris – and the Milhaud is by far the better work. To allow you to assess that judgment, I temporarily upload the recording he gave me here. I hadn’t heard it in thirty-five years, and with the first notes it all came flooding back from the recesses of my memory. Philip Glass has told me that Milhaud is one of his ongoing influences as well.



  1. says

    Some rhythmic delights take place within peaceful 4/4 pieces! How harder was such a canon to write than a one-key one?

    KG replies: You know, except for one early atonal one, all of my canons (and I write too many of them) have been at such odd intervals (sevenths, sixths, seconds) that I don’t think I’ve ever written one you could call one-key (they usually modulate constantly). But I do usually rather plan out the harmonies, which is cheating a little bit, and this time I didn’t. The left-hand line could never move until its scale was consonant with the right hand. It fell into place almost without effort, as happens occasionally when the gods feel like it.

  2. says

    For those curious, the six movements of the Milhaud (op. 399, 1962) are:

    1) New York with Fog on the Hudson River
    2) Two Cloisters
    3) Horse and Carriage in Central Park
    4) Times Square
    5) Gardens on the Roofs
    6) Baseball in Yankee Stadium

    KG replies: Thanks, Carson.

  3. says

    Love the canon. I used to teach the Corcovado from Saudades do Brasil at the end of my 3d semester harmony course. I still think it’s one of the wittiest pieces I know, and the materials are so (apparently) simple.

  4. Jim Dalton says

    Delightful pieces! The toy piano seems particularly well-suited to the bitonality (or vice versa).

    Could you tell me more about Milhaud’s book on bitonality?

    KG replies: No. I mean, I know it exists, but as far as I’ve been able to research, it doesn’t seem to have been translated into English. I can sort of read French, but I haven’t been able to find the text.

  5. says

    I’m not sure if Milhaud wrote a whole book on the subject. There’s a 1920’s article on polytonality in the collection ‘Notes sur la musique’. I have it but unfortunately it’s packed away at the moment. It has examples in notation. I remember he warns that some ostensibly bitonal chords, such as the one combining C-major and g-minor triads are difficult to hear bitonally as they are familiar from tonal music. It’s rather basic.

    KG replies: Well, there are at least two articles from 1923, one in Le courier musicale, and the other in La revue musicale. And I’ve run across a book in French out there, though it wasn’t clear whether Milhaud was the sole author or it was an annotated compilation of some kind. Still looking.