Am 03.05.2009 um 02:14 schrieb Richard Brekne: > 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 Sorry Ric, but you are completely wrong here. The difference of my temperament compared with Gary´s over a telfth is 3:2.998688889 (whithout inharmonicity, so that equals to 0,75 cent. That is not at all an academic difference for me. Cheers, Bernhard Stopper
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