# Music and IQ

David Webber dave at musical.demon.co.uk
Fri Sep 29 03:00:50 EST 2000

```Hans-Georg Michna <hans-georgNoEmailPlease at michna.com> wrote in message
news:o997tsou3iqebcu25ks8mcqdhplvm03rjd at 4ax.com...

> no, you haven't quite hit the point. Let me try to explain in
> more detail.

I have the point exactly.

> When you try to construct a tone ladder with equidistant tones
> whose steps multiply up to exactly 2 and where some intermediate
> tones happen to hit 3/2 and 4/3, there is no other solution with
> small numbers except if you use 12 steps.

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.

> I hope I use the right words. English is not my mother language,
> so I may not always hit the proper word.

You're doing fine :-)

Gruessen aus England.

Dave
--
Dave Webber
Author of MOZART the Music Processor for Windows - http://www.mozart.co.uk
Member of the North Cheshire Concert Band http://www.northcheshire.org.uk

```