Bernhard I did not comment on the difference between your temperament and Garys. I only pointed out that your statement that 3/1 was not 6^(19//31) was a bit overstated.... which seems easy enough to defend since 3/1 is... well 3 and 6^(19/31) is well... 2.99868889. I haven't even bothered to decipher either your's or his temperament as such. Nor does this matter to me. 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 Again Bernhard, Gary suggests using a P-12ths priority, I picked up on that in my own way... put it together with a few other bits and dabs that came along at pretty much the same time and started off from there. You want to argue about who is first, who did exactly what, whose temperament is this that or the other... and I don't give a hoot about all that. Thats the second time you took me completely out of context. I'm not going to do this with you Bernhard. If I want to dissect yours and Gary's papers and compare them I am most certainly capable. But frankly... that side of things does not interest me in the slightest. Cheers, RicB
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