Derek Lane-Smith wrote:
>
> There is an implied assumption in the prior discussion that 'just'
> intonation, with small number ratios of the frequencies, is in tune, while
> other ratios, such as equal temperament, are slightly out of tune.
I think it's dangerous to use the phrase "in tune" in this context. It
seem to me that this discussion clearly demonstrates that perfect
intonation is neither possible nor desireable.
The entire discussion was sparked by a request for the "correct"
frequencies. I deliberately posted two alternative tables to show that
such an universal mathematically and musically correct system simply
doesn't exist. There are (at least) three basic mathematical models for
calculating the frequencies - all of them relatively simple and all of
them unsatisfactory in a real life musical context.
Another aspect is that no matter how rigid our basic system is, sound is
still a mechanical process, and slight "imperfections" will cause subtle
(and not-so-subtle) modifications that even an untrained ear will
perceive, even though the finest tuned measuring equipment misses it.
We can use all kinds of maths and physics and link up all computers in
the world to to the calculations, but in the end the most precise sound
monitor is the human ear, and the most advanced sound processor is the
human brain.
I don't know about the rest of you, but *I* feel good about that :-)
Frank Nordberg
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