Inharmonicity

[Michael Jorgensen]

Gary Isaac wrote:
> 
> >From time to time I read about inharmonicity of piano strings on this
> list.  I would be grateful if someone would clarify for me exactly what
> inharmonicity is and how it affects piano tuning.

Hi Gary,
    Inharmonicity is distrortion of the harmonic series present in piano
strings i.e., the harmonic series is warped sharp instead of exactly
2:1, 3:2 etc.  This means that each partial is alittle sharper than it
should be according to theory as you ascend the harmonic series.  When a
piano is tuned the octaves must also to be stretched so that the
partials of lower notes match the fundamentals and partials of higher
notes.  If the octaves were all tuned to fundamental frequencies of
exactly 2:1 ratios, the top of the piano would sound outrageously flat
and the the bass drastically sharp compared to the mid range.  Amount of
inharmonicity varies with each unison, at every partial level, and with
each individual piano.  Tunings must therefore be customized to match
the instrument. 
-Mike Jorgensen RPT