Hi Bernard... I suggest we take the prior art bit off list. I am not really qualified to judge one way or the other what qualifies as prior art you understand. I think its pretty clear that a very similar tree is being barked up between you and Gary... but again thats not for me to judge. My only concern here has been to show where my direct influences came from in my own development. What IS fun to talk about is just how all these different approaches compare in the real world. And I am anxious to see someone start doing some measuring of the sort Sanderson did in his article some 30 years back. He measured the first 8 partials of a two octave range in the middle of a piano (excepting the 7th partial) in an analysis of how the stretch behaves when looked at from the perspective of several intervals in the form of their coincident partials. Measuring Tunic, Virgils approach, and any other that might be interesting to compare, and looking at the actual results in this same perspective would perhaps be very enlightening. I am the first to admit and recognize that the world of coincident partials and listening to these at their actual frequencies has limited value. Misunderstand me correctly folks... using coincidents can get you very very far down the road to a fine piano tuning. But I am personally convinced that, as Kent, David Andersen, Ed, Virgil himself, and others have said time and time again each in their own way, the finest tuning is that one which in the end is tweaked carefully by ear listening to the whole beating effect or the "sum beat" that results from playing any of the several intervals that we as tuners want to sound pure(-ish). Still, coincidents allow us a vocabulary for communicating clearly that no other description of beating allows us.... so I cant see that we can really live without them either. Cheers, and delighted to see your outreached hand. RicB
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