Ric wrote: > so essentially the above two statements mean that > > (3/2)^12 = (3^12) / (2^12) > > which clearly cannot be. > > Please correct and then repost. Ric, (3/2)^12=1,5^12=129,746337890625 (3^12)/(2^12)=531441/4096=129,746337890625 so this is the same. The thing that was not correct is that the pythagorean comma must be "added" in mathematical form with a "multiplicator" placeholder like * >Otherwise... I just have to say my own rendering was much more seat of >the pants as it were. I simply noticed that we tune using very close >to perfect 12ths in the tenor/treble/diskant registers as a rule... so I >tried it out and used the previously mentioned procedure with Tune Lab >97 to help assure a truly P 12th interval everywhere, and to divide the <<temperament 12th>> into its associated curve. I wanted at the time to >see if the idea would sound good. It did, and viola... the P 12ths >tuning was <<born>> for me... which I related to others a couple years ago. my P12 history was very similar in the beginning and also not a theoretical approach.... i was some times impressed by the Cordier P5th tuning and after a while practicing P5ths i experimented with the "natural fifth" in the overtones.... the 12th (3rd harmonic)... i tried it out and was shocked about its justness, so at this point i began to search the theroetical base for it. kind regards, Bernhard
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