Electronic pianos and inharmonicity

[Robert Scott]

Diane Hofstetter wrote:

>A digital piano has only a fraction of the mix of 
>harmonics that an acoustic piano does. The samples are relatively short in 
>duration (frequently only a few seconds) and then the sample is looped over 
>and over for greater sustain so you hear only the harmonics from the first 
>attack of the key.

This business of the sound being "looped over and over" raises some
difficulties with respect to inharmonicity.  You can't have both in a
sampled electronic instrument.  If the sampled sound is repeated, even
once, then the phase of all the partials would have to be the same at the
beginning and at the end of one sample period.  If not, then the
discontinuity would be clearly heard as a "click" at the transition
point.  Therefore I have to conclude that electronic pianos either do
not model inharmonicity or else they do not recycle samples.

I am certain that the low-cost keyboards have zero inharmonicity.  
But I don't have access to any of the really expensive models.
If there is anyone who has access to a really fancy electronic 
piano and who also has an SAT or RCT or TuneLab, then simply
measure the inharmonicity (or get the FAC numbers) from such
an instrument.  I would like to hear about any such instrument
with non-zero inharmonicity.

-Robert Scott
 Ann Arbor, Michigan