Klarinet Archive - Posting 000578.txt from 2002/03

From: "fred.sheim" <fred.sheim@-----.net>
Subj: Re: [kl] R-13 and intonation. . .good grief
Date: Wed, 20 Mar 2002 23:29:00 -0500

But shouldn't the tuner simply be calibrated at the frequencies that we
deem to be correct for each note, so that pegging the tuner WOULD mean we
are in tune at each note, WHATEVER the intervals are?

Fred

At 04:27 PM 3/20/02, you wrote:
>Fred, this conversation is going in many different directions. In
>order to avoid a flame war, someone needs to summarize a basic
>mathematical dilemma --- in order that the other conversations can focus
>on their appropriate points. My apologies to those who don't want to
>read this.
>
>In Western music, the human ear and brain are deemed to respond most
>strongly to multiples, not to additions. For example, "octave" means to
>double the frequency. If A = 440 cycles per second, then one octave
>higher is 440 x 2 @-----. But how about the next
>octave? Is it 880 + 440 = 1320? Or is it 880 x 2 = 1760?
>
>Your ear will tell you immediately that the answer is 1760. Thus it is
>multiplication, not addition that we care about.
>
>So far, so good.
>
>But how are we going to divide the space between 440 and 880 into seven
>intervals? Perhaps we should do the arithmetic of (880-440) / 7 =
>62.9. In order to simplify the typing, let's round it off to "63".
>Then 440 + "one note" would be 440 + 63 @-----.
>
>Doing the same with the next octave: 880 + "one note" @-----.
>
>OOOOPS !!!!! One octave above 503 would be 503 x 2 = 1006, but we just
>calculated that "one note" higher than the next octave is 943. What's
>going on here?
>
>It's obvious enough. The interval of one "note" becomes progressively
>larger as we move up the scale. But it's not practical to shift the
>positions of the holes in our clarinets as we move up the scale.
>(mental image of the golf cartoon where the golfer is using a hydraulic
>jack to move the hole)
>
>So somehow we need to make a compromise that is least offensive. But
>mathematically, your instrument can never be in 'perfect' tune. Your
>mouth and embouchure and so forth must make up the difference.
>
>Cheers,
> Bill
>
>
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