Music and IQ
Hans-Georg Michna
hans-georgNoEmailPlease at michna.com
Fri Sep 29 06:21:16 EST 2000
"David Webber" <dave at musical.demon.co.uk> wrote:
>The point is that if you use fewer than 12 steps you get less close
>agreement, if you use more (as people have done from time to time) then you
>can get better agreement. 12 is not unique in any precisely quntifyable
>mathematical sense - it just turns out to be a compromise which has what
>many people accept as *sufficiently close* agreement (not everyone likes it)
>with what many people think is *sufficiently few* notes in the octave.
>Choosing 12 is a matter of artistic judgement influenced by the accuracy of
>our aural pitch recognition and the number of fingers we have to play a
>musical instrument.
>
>12 neither "hits" these pitches nor is it a "small" number in any precisely
>mathematical sense: it is a compromise which gets "close enough" for most
>people and produces a "small enough" number of notes to be managable by most
>people. It is quite possible to conceive of martians who have developed
>exactly the same mathematics as we have, but who have better tuned ears and
>100 fingers on each hand. They'd be playing on a 53 note (was it?)
>chromatic scale and find our music unbearably out of tune.
>
>2^(31/53)=1.4999
>2^(22/53)=1.3334
>2^(14/53)=1.2009
>
>But of course my saxophone would need more buttons than I have fingers - so
>I have to put up with 12 and lip it. It's the poor keyboard players who
>are out of tune with a miserly 12 notes <g>.
>
>That's all I meant by saying that it was a bit more complicated.
David,
hehe, the example of 53 is neat! I see what you mean.
But 53 is no longer a small number in this context. Try to find
one below 20. I haven't tried it, but I wouldn't be surprised if
12 yielded the closest hit at 3/2 and 4/3 by far.
12 is also a kind-of-beautiful number. What a pity that we don't
have 12 fingers! <grin>
Hans-Georg
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