tuning narrow and wide

[Ron Koval]

Tony wrote:
In reality A4 fundimental of 440 should match the second harmonic of A3 at
440 and the fourth harmonic of A2 at 440. Likewise going up the second
harmonic of A4 should match the fundimental of A5 and the second harmonic of
A5 should match the fundimental of A6.
<snip>

That's one of those 'truisms' that sound right, but turn out not to be 
'quite' right.  In reality, the temperament octave usually turns out to be 
somewhere between a 4:2 and a 6:3 octave.  So instead of the fundimental of 
A4 matching the second partial of A3, what ends up getting done is comparing 
the 4th and 6th partial of A3 with the 2nd and 3rd partials of A4.  By ear, 
you just tune it till it sounds and checks right, but the machines use 
different paths to try and find that spot.

Dig a little deeper, and with each answer, more questions appear!

Ron Koval
Chicagoland

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