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OT: (long) Re: angry reply :-) Buzz Feiten tuning system.

It's a good thing this list doesn't seem to have any hardcore
advocates of just intonation or other tuning schemes. Note that
I'm not being critical of any tuning system whatsoever--I just
want to point out that this topic can be as explosive as the
computer platform debate (and let's *really* stay away from that

And yes, tuning systems are pretty far off-topic for L-D. But...
I can't resist chiming in with a couple points, myself. (Okay,
you can spank me, but no leather!)

People are correct who say that there is no single standard
for tuning. This is obvious if you consider the vast range
of tuning systems used throughout the world.

However, what we know as the major scale was originally based
on the naturally occurring overtone series. Overtones of a
fundamental frequency create an ascending pattern as follows:
(fundamental), octave, 5th, 4th, M3, m3, etc.

When composers such as Bach wanted to write music that freely
modulated from one key, or tonal center, to another, they felt
that the pitches corresponding to the natural overtone series
sounded "out of tune" at times. They realized that it is not
possible, in theory or in practice, to adjust the pitches of
our 12-note chromatic scale so that no matter on which note
you build a major scale, the pitches conform to the natural
overtone series.

Eventually, a compromise was reached in which all major scales
would be slightly out of tune with respect to the overtone
series, but modulation to all keys would be possible--none
would sound "worse" than any other. This tuning system is
essentially the one that we have inherited in the West, except
that most *acoustic* instruments I know of diverge slightly
in idiosyncratic ways from the "ideal".

As brass and woodwind players know, their horns are not "in
tune" on every note. In fact, many different fingerings have
been developed that allow good players to play more or less
"in tune", depending on the sound they're going for, and the
context in which they're playing.

It has been noted that guitars are "out of tune" with themselves.
Apparently the Buzz Feiten tuning system can remedy that to some
extent. However, for theoretical reasons, no guitar will ever be
completely in tune with itself. Again, it's because of the
cumulative effect of stacking "in tune" intervals on top of one
another. If you tune a guitar so that the A string is exactly
the same pitch as the A produced on the low E string, and the D
string is exactly the pitch produced on the A string, and so on,
your high E string will not be "in tune" with the low E string.

Concerning pianos tuning, there is an interesting aspect which
is often overlooked: even the octaves on an expertly tuned piano
are "out of tune" with each other. This is because we tend to
hear very high pitches somewhat flatter than they "really" are,
and very low pitches somewhat sharper than the "really" are. To
compensate, the highest notes on a piano are tuned sharp and the
lowest notes are tuned flat. This is called "stretching".

Well, I've rambled enough. My main point is that although there
are lots of physical, psychological, historical and cultural
factors involved, as musicians we should just use our ears and
realize we can choose a tuning system that sounds right to us for
whatever we want to do.