Pink Trombone.

IMAGINARY, a non-profit organization for open and interactive mathematics, presents a nifty project:

Pink trombone is a model of the human vocal tract that synthesizes human voice from scratch, controllable with your fingers.

Your voice is the oldest and most likely the most complex musical instrument. By interacting with this model, you can discover how the human voice works.

The voice system consists of two components: sound production and sound articulation. The sound is produced with the vocal cords and the vocal folds, were we can control its pitch and loudness. The articulation is what makes our voice sound like a recognizable speech sound (vowels, consonants…). This happens in the vocal tract, a tube where the sound wave travels and bounces back and forth. Using the tongue, lips and nose, we can change the profile of the tube, affecting how the sound bounces on its interior. The final wave that comes out of the lips is the sound we hear. This program is based on a simplified model of the voice tract and a discrete solution to the wave equation (discrete d’Alembert solution).

Enjoy! (Thanks go to that fine poet and provider of links, Trevor Joyce.)


  1. “A self-confessed player of the pink oboe” [at 2:20] (The whole judge’s address is a laugh-out-loud take-down of the British establishment, even if you don’t know who ‘Mr. Norma St-John Scott’ is referencing.)

    The story goes Peter Cook got this line from Billy Connolly — the original from Glasgow argot is ‘pink trombone’.

    Is their naming a deliberate tribute?

  2. Excellent question — now that you’ve brought it up, one can’t help but wonder!

  3. It sounds interesting, but the “discrete d’Alembert solution” doesn’t match what they are describing. The d’Alembert solution is the general solution of the Cauchy initial value problem for the (nondispersive) wave equation in one space plus one time dimension. However, to describe the vocal tract properly would obviously require more space dimensions, or it could perhaps be approximated by a one-dimensional equation with dispersion.

  4. Speaking of trombones (the musical instrument, that is) this NYT story is highly amusing. The rendering of the William Tell overture is a hoot, or a toot.

  5. Ah, Kai Winding, whiter than white (Danish, that is). I was impressed in an interview with Miles Davis about Birth of the Cool that despite Davis’ ‘attitude’, a musician is a musician — even white men can play jazz.

  6. I think, they’ve meant equation given by d’Alembert operator (box).

  7. David Eddyshaw says

    a self-confessed player of the pink oboe

    Also my immediate first thought.

    The extraordinary thing is that Peter Cook’s truly inspired … thing … is not actually completely different from the actual judge’s summing-up.

    My children think it’s wonderful despite having absolutely no memory of the original trial, or indeed much knowledge about it. It’s such an extraordinary affair that they might be forgiven for imagining that Cook simply invented the whole thing.

  8. @AntC: Miles not infrequently at certain points in his career had a white guy or two in his band and was known to be scathing toward black-nationalist types who might criticize him for it — saying stuff like “well last spring when I needed a new saxophonist, if you personally had sent me a black dude to audition who actually played better than Dave Liebman [or whoever] I would have hired him, but you didn’t so Liebman got the gig and why are you whining about that now.” And this was when his music was arguably “blacker” in style than Birth of the Cool, which was de facto a collaboration with Gil Evans, who was personally so white as to literally be Canadian, and featured lots of other white sidemen (Gerry Mulligan, Lee Konitz, Gunther Schuller, Joe Shulman, and probably others).

  9. David Eddyshaw says

    who was personally so white as to literally be Canadian

    There are cool Canadians? Truly the world is a more wondrous place than I ever imagined.

  10. May I present to you: The Band.

  11. David Eddyshaw says


    (But I thought cool Canadians automatically became American?)

  12. There are cool Canadians?

    FFS Oscar Peterson is Canadian. Leonard Cohen. (I’ll grant you plenty of Canadian musicians don’t qualify as ‘cool’.)

  13. not actually completely different from the actual judge’s summing-up.

    Indeed. IIRC “A tissue of transparent lies” is quoted verbatim.

  14. David Eddyshaw says

    … William Shatner …

  15. absolutely no memory of the original trial

    Strangely — despite my struggling to remember what I ate for lunch yesterday, or even whether I ate lunch — I can remember huge amounts of detail from the episode. (The dog’s name was ‘Rinka’; the dog it was that died — was Stoppard channeling?)

    Private Eye magazine kept up the satire for months with barely-disguised preposterous allegations (most of which turned out to be absolutely on the money). I guess you could not make this stuff up.

  16. Robbie Robertson is Mohawk/Cayuga+Jewish. Cohen was Jewish. Oscar Peterson was black…

  17. Robbie Robertson, despite his interesting family tree, was obviously the least cool member of the Band. Levon was American; Danko was Ukrainian-Canadian; but Manuel and Garth were *normal* Anglo-Protestant Canadians as far as I can tell. While some might think it in questionable taste to bootleg a funeral (or post-funeral “memorial service” as the comments clarify), this is a pretty fascinating field recording of Danko singing (after saying he hadn’t planned in advance on doing it) at a memorial service for Manuel, backed only by semi-cheesy church organ.

  18. here’s my favorite living trombone virtuoso (as a player and also as a person – a genuine mentsh). the website through the link kinda underplays his range.

    and since both the Band and miles davis have come up, i think the Band’s acid-funk playing (most credit due to garth hudson and richard manuel, i think) behind dylan on Before the Flood has some eerie similarities to what miles’ bands were doing at the same time.

  19. ” the original from Glasgow argot is ‘pink trombone’” …

    And the alliterative and mocking version preferred by some is ‘playing the pink piccolo’.

  20. John Cowan says

    While I think the Cook sketch is Pretty Durn Phunny(TM), I couldn’t help wondering whether Cook’s (actual? put on?) rhotic-RP accent bore any resemblance whatsoever to our own dear DE’s ….

  21. David Eddyshaw says

    Not really: I am rhoticker than that; and, apart from the intermittent rhoticism, Cook is affecting a fairly marked sort of RP there (not erstwhile BBC-newsreader RP, but going somewhere in the general direction of Tim-Curry-Rocky-Horror-Picture-Show RP, though with more of the pompous and less of the louche.)

  22. John Cowan says

    Ahhh, good.

  23. I’m more familiar with the phrase “pink piccolo” so “pink trombone” had me rushing to google, so thank you all for that life-enhancing moment. There was an excellent series on BBC a couple of years ago called “A very English Scandal” about the Jeremy Thorpe affair with Norman Scott, and yes, some of my compatriots did actually speak like Peter Cook in the link. I know someone who still does and is considered today to be more than mildly eccentric.

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