Bendy Pitches

A brief new tuning study for the 232-key piano of my imagination: Romance Postmoderne. As I was playing it, my wife said, “Boy, the pitches in that are really bendy.” Then she looked at me suspiciously and added, “You can’t hear it, can you?” And I had to admit I couldn’t. It sounds so normal to me; I’d love to hear how weird it sounds to other people, but I’ve just grown too accustomed to thirteenth harmonics. The tuning is really elegant, all harmonics of Eb: the odd numbers from 1 to 15 multiplied by each other, an 8 x 8 grid comprising 33 different pitches once the duplicates are accounted for (7 x 11 = 11 x 7, for instance). In other words, eight harmonic series’ each up to the 15th harmonic, based on the 1st, 3rd, 5th, 7th, 9th, 11th, 13th, and 15th harmonics of Eb. Hate the piece if you want, but admit that if musicians could learn to hear these intervals, there’d be enough new material here to invigorate new music for at least the next century. UPDATE: complete tuning chart here.

AFTERTHOUGHT: The main difference between this and impressionism, or bebop harmony, is that there are fewer pivot notes between chords. Except for the 3rd harmonic (V chord), which is a special case and I don’t use it much, any two (potentially eight-note) chords tend to contain only one pitch in common. Of course, the result of that is parsimonious voice-leading heaven.

(Incidentally, I tried to turn the file into an mp3 in iTunes, as usual, and the aiff – which had sounded fine when I made it in Logic – got all distorted. I looked around the internet and found that everyone’s complaining about distortion in iTunes in the latest Mac OS. I had to find an internet audio converter to change the file. What a pain. Damn you, iTunes!)


  1. says

    “You can’t hear it, can you?” Oh, how I understand that comment, and not just with respect to tunings. I realized many years ago that I no longer had any idea how normal people experienced the music that I found normal.

    So, for what it is worth, the piece sounds beautiful to me. I like your description of the tuning as elegant. It has a great clarity and transparency of sound.

    KG replies: Thanks, Erling. Like Ives, our ears are on wrong.

  2. PWT says

    This is the same tuning (cross set of harmonics 8-15) that David Cope used in several pieces in the 1980’s. He built several acoustical instruments for this and also synthesized it using both a mainframe computer at Stanford and an Apple II. One reason this tuning is interesting is that it can be very centered on a tonic or use a large number of centerless combination-product set structures called hexanies.

  3. says

    You’ve filled the Hudson River with warm bubble bath. Inexplicably I mean this as a compliment.

    As a possible solution to your mp3 issue, you can bounce to mp3 straight out of Logic.

    KG replies: Ah, I see – it’s in a different window from aiff and wav, hard to notice.

  4. Barry says


    I listen to all sorts of music, from noise to gamelan to pop to jazz. I have no music training and not a clue about the 13th harmonic of e flat. I cannot hear intervals. I think the piece sounds really neat, interesting, intriguing, like another world (I think of Cage’s Haunted Landscape). The one thing I do notice is the lousy sound of an mp3 file of an electronic keyboard! It makes the piece grey and flat and annoying. Maybe I have Cage on my mind because you just wrote about him–I am reminded about his experience writing music he thought expressed one feeling and listeners heard another. You can’t control what your listeners will hear! (As a teacher, you must experience this every day!)


    KG replies: Well, it is an mp3. I don’t tend to hear the difference except in music of more than average sonic complexity. And it is an electronically produced piano, but it’s Pianoteq, which is supposedly the best piano simulator available at the moment. I will say, since Pianoteq sounds pretty realistic when playing Chopin, that I’ve come to the conclusion that the weird tuning tends to make people think the piano sound is less realistic than it is. I’ve certainly had people complain about my Disklavier that it doesn’t sound as good as an acoustic piano – and it *is* an acoustic piano! And they’ve figured out that the lightning-fast riffs just don’t sound like a real piano because they’re not used to a real piano sounding like that. I’ve become convinced that the discomfort with the tuning turns a lot of people off who blame the problem on the sound instead. After all, people sometimes also think La Monte Young’s Well-Tuned Piano isn’t a real piano, too. Like Cage, I suppose I will spend the rest of my life beating my head against that wall. Anyway, it’s a scored piece, this is a realization of it, and it’s the best realization I know how to make under current circumstances. I’m glad no one who finds it annoying is required to listen to it.

    To quote Charles Ives: The waiter brings out the only fresh egg he has, and the customer sends it back because it doesn’t fit his egg cup!

    • Barry says


      I look forward to listening to the CD of the pieces that come out of your current studies!


  5. says

    Truly lovely piece. I think the piano was quite realistic. I agree that it’s the pitches that confused Barry.

    The title to the post had me thinking you were going to bend some pitches like a whammy bar. Maybe next time. Do the tools you use allow glissando?

    KG replies: Boy, Prent, if I could figure out how to glissando piano pitches the way you do in your pieces, I’d do it all over the place. I’ve actually managed to do it in Digital Performer before, but it’s been a lot of work and trial and error. I’ll gladly accept any tips. And thanks, I’m glad you like it. In addition to the unfamiliar harmonics, even the major triads are purely in tune, which must have some effect on the perception of the piano timbre.

  6. George Secor says

    Beautifully soothing! I love the way you voiced the chords, with numerous instances of first-order difference tones in 1:1 (or 1:2) ratios. (This, I believe, is the “secret” ingredient for getting consonant harmony out of those 11’s and 13’s in your pitch-toolbox.) As for “bendy” pitches being perceived as abnormal by “normal” folks, I find that listening to most music equates to hearing the same old “normal” chord changes — in a word, boring. Let’s keep our minds flexible with more “bending” exercises!

    KG replies: Thanks very much, George, just the kind of detailed comment I’ve been yearning for.

  7. says

    Lovely piece, Kyle. Your tunings and harmonic practice really bring out one of the most important (IMO) distinctions between 12ET and richer palettes: multiple planes of consonance against which tension and release can interact, diverging and resolving. Also, the piano sound worked fine for me.

    KG replies: Yes! Yes! I love the increased intensity of the resolutions when tones shift slightly to fall consonantly into the next tonality, especially in the passage just before the end where I use all the higher overtones over a long E-flat drone in the bass. Thanks for noticing.

  8. Juhani Nuorvala says

    The microtonal voice leading makes it instantly recognizable as your
    music and the atmosphere is erotic and mellow. Beautiful!
    Can I ask a technical question? How do you tune your pianoteq? Do
    you write the .scl and .kbm file pairs by hand in a text editor or do you
    export them from a microtonal application such as CSE? Or do you use the real-time pitch
    bend tuning option that works especially well in pianoteq with LMSO or CSE (as multiple
    instances of pianoteq are not necessary)?

    KG replies: My kind of question. LMSO makes the .scl file for me (save as Logic file). I make the .kbm myself according to a template Aron Kallay gave me. Took me quite a few times to get it right the first time. I’ll send you the template if you need it. I haven’t tried pitch bend with Pianoteq yet, but I should.

  9. says

    Its so beautiful Kyle!

    Would love to host you playing microtonal music like this in my avant garde concert series in downtown new york city.

    For Sept. 9, are you available? With other microtonalist, Johnny Reinhard on the bill that night.

    Its the third season opening concert of a NewIdeas MusicSeries, with past artists Phill Niblock, David First, Elliott Sharp, Elizabeth Hoffman, and many more.

    Feel free to contact me if your interested.

    and thanks again for sharing your beautiful work!