Hi Bernard. I really don't want to get into making a case for who was first with what per sé. It is enough for me to recognize that others were before me when it comes to tuning with the idea of perfect 12ths as a priority and not octaves. I'm really unsure when it comes down to just plain listening to the end sound of a piano just how much different your Tunic software is with what Virgil ends up with, or what Gary would end up with or what I end up with. And, as I said it is here I find the most interesting path forward. I do think tho that in the case of Gary, myself, and you.... we are all clearly onto very similar ideas... tho to be sure there are significant differences. But lets not over state these. For example... and from a purely maths perspective to illustrate what I mean... you stated in your last that 3:1 is not the same as 6^(19/31). This is technically true. But the latter does work out to 2.998688889... (:1). Translated to real world mechanics with all the imperfections that implies.... we are not really talking about anything different. In a real piano... with real inharmonicity if you take for example D3 and tune its 3rd partial to 440, and then tune A4's fundemental to exactly 440 or just sooooo slightly less then what the above difference implies... you change really nothing in the resulting relationship between A4's fundemental and D3's fundamental. D3's fundamental is a result of tuning D3's 3rd partial to 440. So its already fixed. Tuning A4's fundemental to this same 440... or 440 minus the 0.00006297... difference 6^(19/31) implies is not even a promile of a cent then in relation to that resultant D3 fundemental. But all this is really academic for my part. I'd have to actually study Gary's article very closely a couple times to completely digest all his article intended to convey. But I am quite certain, and he himself says this outright in an email to me, that in practicalities he didn't listen to octaves at all when tuning. Rather he was listening and tuning for pure(ish) 12ths and 19ths. It is this general perspective that interested me when I first read it, and that was timed with my introduction to ETD's and nearly immediate observation that the available single partial ETD's of the time were seriously flawed... a stance I maintain today. They sample a few partials ladders of a few tones... predict an expected inharmonicity table for that entire piano and off one goes. All para inharmonicity (which is far more significant then we are led to believe) is simply disregarded. To be sure... this approach does yield better results then many tuners can get by ear... at least more consistent results. But it seemed to me at the time that we should be looking at several partials at the same time. And I said so... which was rebuked by many saying things would get too confusing. A comment one could expect from tuners who listen to coincidents at their frequencies I might add. In contrast... Virgil types would immediately find something that rhymed here with their thinking..... if first they were to equate their thinking into the realm of coincident partials instead of the more holistic sound they listen for. Vertituner came out... and it was a definite improvement at least on paper... tho I never did manage to get ahold of exactly what tuning priorities were applied in the weighting algorithms that dynamically evolve as the tuning progresses. So I imagined that since we use aural tests that actually emphasis the 12th as an octave check, which automatically take into consideration any inharmonicity and para inharmonicity as well in the case one listens holistically, given Gary's writting and a couple other tidbits I ran into at the time... that I could simply use Tunelab 97 to impose exacting 3:1 12ths on top of a pianos inharmonicity as I have described. And, as you have also found much earlier then I did. following a completely different entrance route, this actually does work quite well. My route was empirical trial and effort most of the way... with a minimum of theory involved. I had no need to look more closely at Gary's article at the time... I just read <<tune with 12ths instead of octaves>>. I did run into a very interesting bit about how octaves stretch is affected by doing this... something I was pointed towards by Jim Colemans review of my initial discussions about this. The area between C5 and F6 gets changed stretch wise, while the end stretch number of C8 is fairly low... at least by American standards. You end up with a stretch that is actually quite moderate....but in some regards seem the opposite. So I plotted this on an Excell spread sheet and posted that on a few occasions. I didn't get much response on those postings. So you see... none of my work threatens any authenticity issues you have. I really can not answer for what Gary's article means in that context as I haven't ever seen the need to draw the needed comparisons to form an authoritive opinion... due to the more pragmatic approach my own path has been on. To summarize.... I think it wisest to let you and whomever else is actually concerned address those issues if you (and they) feel a need. I was clearly last out with any of this and have never tried to claim anything else. But to be honest with you... I'm kind of pleased with myself over the whole affair. Seems my more simple minded approach is in line with the more theoretical based paths both you and Gary, each in your own way plotted out. Its kind of neat to know that I figured out something very cool all on my own... and that it actually worked. I otherwise have no need to take any credit for anything.... I'm not interested in such things myself. But this points to exactly where we can all bear this further in a constructive direction.... namely to forward the whole concept of 12ths priority tuning. And I think a first very important step to take at this point in that effort is to quantify in terms of actual resultant coincident partials spread how these aforementioned tuning methods compare. And again... I would encourage any of my American colleagues that have a few bucks and are interested enough to buy Tunic software. I'm quite sure it would be worth the purchase... despite the fact that it offers just one single type tuning... or one very specific stretch if you like. Cheers RicB
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