Comments on: Slate Magazine on “The centuries-old struggle to play in tune” http://www.thelisteningblog.com/2010/04/slate-magazine-on-the-centuries-old-struggle-to-play-in-tune/ “Listen all the time, and remind yourself when you’re not listening, or else the mike and the tape recorder will get the best of you.” – Pauline Oliveros Wed, 04 Jan 2012 01:08:30 +0000 hourly 1 http://wordpress.org/?v=3.3.1 By: Hmm? http://www.thelisteningblog.com/2010/04/slate-magazine-on-the-centuries-old-struggle-to-play-in-tune/comment-page-1/#comment-80546 Hmm? Sat, 01 May 2010 01:28:46 +0000 http://www.thelisteningblog.com/?p=527#comment-80546 "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. “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.

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