Electronic pianos and inharmonicity

[Kent Swafford]

Robert Scott wrote:

>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.

Sample-accurate wave editors are standard fare in preparing samples for 
use in sample playback musical instruments. One can put the wave form of 
a sample on screen and custom choose the loop points at similar positions 
of the wave cycle to be completely quiet. Choosing the loop points is 
straight forward enough that the process can even be automated.

>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.

Yamaha P-200 FAC numbers measured 11-8-99.

F  5.2
A  5.5
C  4.5

My experience with less expensive digital pianos is that they surely have 
inharmonicity, but are "tuned" as if they did not. So in other words, 
they are tuned to the mathematical model of equal temperament; a piano 
tuner would say such instruments have _negative_ stretch.


>Subject:     Re: Digital pianos and inharmonicity
>Date:        8/26/98 1:12 PM
>To:          pianotech list, pianotech@ptg.org
>
>Robert Scott wrote:
>
>>Do any of you know if there are any digital pianos that are
>>designed to have inharmonicity?  It seems to me a difficult thing
>>to put in to a synthesized sound, so I doubt if anyone would bother
>>to do it since no one would appreciate the effort, but I could be
>>wrong.  Has anyone tried to read FAC numbers from such a "piano"?
>>
>>Bob Scott
>>Ann Arbor, Michigan
>
>Digital pianos are specialized "sample-playback synthesizers," and their 
>sound is that of a recorded real piano. Therefore digital pianos tend to 
>have the same inharmonicity as the recorded piano did during the recording 
>session.
>
>I am familiar with the tuning of the Yamaha P-200 which is a very fine 
>digital piano. Its tuning can be said to exhibit only natural stretch 
>without any "artificial" stretch. To duplicate the tuning of the P-200, 
>easily done with RCT's Custom Equalizer, one would put 0.1 bps stretch 
>into the 4:2 A3-A4, O.0 bps into the 6:3 octaves at A2, A1, and A0, 0.1 
>bps stretch into the 4:1 double octaves at A5 and A6, and 0.0 bps into the 
>2:1 octave at A7.
>
>Kent Swafford