Notes 85-86-87-88

[Tim Keenan & Rebecca Counts]

In my reply to Frank, I forgot the punch line:

 > The idea that the ear likes sharper tones as pitch increases does not
> > jibe with experience.  The piano seems to decide what the ear will
> > like.  Why?
> >
> > Wondering - Frank Weston
>
> The amount of stretch that your ear likes is due, I believe, to the
> inharmonicity of the strings in the octave(s) below them:  you are tuning
> the higher octave to the (sharp) partials of the lower octave.  The
> amount that the harmonics of the lower octave are sharp with respect to
> the fundamental of that octave, in combination with the relative loudness
> of the various partials with respect to the fundamental, determine how
> sharp the upper note has to be in order to sound "in tune" with what your
> brain interprets as the "average" pitch of the lower octave.
>

The reason it differs widely among pianos is that anything which affects
the degree of inharmonicity and the relative dominance of the various
harmonics will affect the amount of stretch your ear demands--scaling and
voicing, for example.

Tim