what is the best temperament?

[Newton Hunt]

> what is the difference between 4-2 octave and 6-3 ???

As simple as this question is it has far ranging answers
because there are so many concepts embodied.

The human ear tends to want to hear octaves expanded more in
the bass and less in the treble.  The ear also latches upon
specific coincidental partials while listening to octaves in
the different regions of the scale.  Generally speaking the
bottom three octaves are tuned using the 6th partial of the
lower note and the 3rd partial of the upper note.  The next
two to three octaves are tuned listening to the 4th and 2nd
and the upper two to three octaves are tuned to the 2nd and
1st partial.  The switch over point varies from piano to
piano, tuner to tuner and sometimes I think from different
way a tuner feels from hour to hour.

Another governing factor is inharmonicity.  Think for a
moment and realize the the ends of the speaking lengths of
the notes are not hinged, they are followed through by
continuous lengths of string, no discontinuity except the
termination points.  The string then begins to flex a little
away from the terminal point.  Each successive partial has
less mass to work with so it begins to flex the wire further
and further from the termination point which shortens the
speaking length of the partial and makes it sharp.  When we
tune octaves we are matching the 6:3, 4:2 and 2:1 partials
which causes us to tune flat in the bass and sharp in the
treble.  Hence stretched octaves.

Those are the simple answers, the rest you will have to grow
up to understand. :)  Understanding comes with further
knowledge and a LOT of practicing.

Lots of luck.
-- 
		Newton Hunt
		Highland Park, NJ
		mailto:nhunt@jagat.com