Jan Swafford’s second recent article on Slate.com concerns the history of tuning and temperament, and it’s an excellent summary of the subject. It’s another enjoyable read–I particularly like the way he describes the impossibility of pure tuning as “the laughter of the gods” and continues the image throughout the article. And again he includes some great musical clips, including Peter Watchorn playing from Bach’s The Well-Tempered Clavier (which, Swafford says, was written “not only to show off this improved system but to help make well-temperament mandatory by writing irreplaceable pieces in every key”) and a side-by-side comparison of a Beethoven sonata movement in modern equal temperament and in a 19th century tuning called Prinz. Can you hear the difference? (Hint: I think it’s a little easier to hear listening to the Prinz first and then the equal temperament, rather than the other way around.)

“The Wolf at Our Heels: The centuries-old struggle to play in tune”



  1. Gravatar

    Hmm? on 04.30.2010

    “As Pythagoras also realized in mathematical terms, if you start with a C at the bottom of a piano keyboard and tune a series of 12 perfect 3:2 fifths up to the top, you discover that where you expect to have returned to a perfect high C, that C is overshot, intolerably out of tune.”

    It’s not a C, though. It’s 12 perfect fifths above the note you started on. To call it a “C” is to try to fit something natural onto something unnatural. It only makes sense if you start out from the perspective of 12-tone equal temperament.

    And what makes it “impossible”, to achieve a perfect tuning? Make a harp and tune it to the harmonic series. Done. There’s nothing impossible about it. The thing that’s impossible is trying to pick and choose frequencies so that they are roughly equally spaced from each other, yet also harmonious, when there’s nothing about harmony that would lend itself to such a spacing. Harmony is fractal, not regularly-spaced.

    “Equal temperament is the price we pay for all the marvelous modulations and exotic scales”

    Oh man. Modulation is so cheesy.

Leave a Comment