Music and IQ

Dr.Matt fields at login.itd.umich.edu
Fri Sep 29 08:00:37 EST 2000


In article <d3t8ts46rfqqf09okhgv90uqit6ofs0jfc at 4ax.com>,
Hans-Georg Michna  <hans-georgNoEmailPlease at michna.com> wrote:
>"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

There is no mathematical concept of "small". The closest thing mathematics
provides is "finite".

>one below 20.

19 works.

> 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
>________________
>No mail, please.


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