Vintage Synth Repair

> Isn't it a known fact that to get a musically useful tuning you cannot
> go by a perfect mathmatical tuning?  Seems to me I remember that if you
> tune "by the numbers" on a freq counter you will get odd harmonics and
> beating.  But if you tune "by ear" you will find that the numbers aren't
> exact on the freq counter, but it will be far more musically useful.
> 
> If anyone knows of a web page where this is documented fully, let us
> know.  I'd be interested in seeing the math.

It is a fact that the human ear isn't quite linear in this respect - the
perception of octaves gets closer together as you get higher. But this
only really starts to get noticeable really quite high up! You will find
that people like violinists just do this naturally when pitching very high
notes. I am not sure whether pianos and such get tuned like this or not.

As far as beat frequencies go, they're down to pure mathematical
relationship, just like Lissajous, they are also what make nice intervals
sound nice, simple ratios like 2:1, 3:2 and so on. The less simple the
ratio is, the more dissonant the interval, in general. Tuning by ear will
produce nasty beat frequencies the higher up you go, as you are deviating
from the clean ratios. So, I think the problem here lies in the accuracy
of the electronic tuner rather than the human ear effect.

Apologies if I'm teaching grandma to suck eggs here ;-)

Regards,
Matt Nolan.