Hi Richard again: After seeing Dr Sanderson's notes on the subject, you should by now see the futility in extending this study further because in general, the higher partials have less and less effect on the tuning because of their inherent weakness. This is why you do not find more fulfilling studies of this nature. If you read the Baldassin book "On Pitch", you will see why we listen to certain partials rather than other partials primarily. It's a matter of practicality and prominence during the tuning process. I know this may not be intellectually satisfying, but you certainly have my permission to knock yourself out doing further study along this line. It is tough enough just trying to consider up to 12 partials (which can never be all satisfied at once when tuning pianos). When you add to this the un- reliablility of the lowest partials and their often erratic behaviour, you may more fully realize the impractibility of considering much higher partials. To my knowledge there is no more extensive study of the nature you are looking for, so, buy yourself a Sanderson AccuTuner and do your own studies. It is the most accurate and dependable machine on the market and you can tune pianos any way you like with it now. Yes, there are some concerns about very high partials of Bass tones which are prominent. Sometimes these stick out like a sore thumb. Mostly this is in conjunction with the longitudinal mode of vibration, and there is very little you can do about that on an existing piano anyway. There are patents on controlling this, and there are people working on it now, but until as the late Percy Gatz stated back in 1949, until we are willing to have gold plated density controlled Bass strings, we will not solve that conundrum. Sure, lots of things can yet be done, but what is the practicality? Jim Coleman, Sr.
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