The difference between the 12th root of 2, and the 19th root of 3 is 0.00006297038. That's not a difference I can aurally detect. dp David M. Porritt dporritt@smu.edu -----Original Message----- From: pianotech-bounces@ptg.org [mailto:pianotech-bounces@ptg.org] On Behalf Of Ric Brekne Sent: Thursday, April 14, 2005 6:43 PM To: pianotech Subject: Was OnlyPure not P12ths Tunings Hi Bernhard I dont think anyone is having any problem accepting the significance of your work on this matter. Your maths are impressive, and I am certainly looking forward to trying out your aural plan to see if there is any significant hearable differences between this and other approaches. My own method is fairly straightforward. Initially observing one can take the 19th root of 3 to equally divide a 12th into equal steps, and then having Robert Scotts tunelab 97 available in which a very handy little tuning curve editor made it very easy to construct such a division while taking into consideration the inharmoncity of the piano to be tuned. It amounts to tuning D3 to A4, then A3 to A4 as a pure 6:3 octave to the degree the beat rate of D3-A3 allows that. Then in similiar fashion setting D4 to D3 assuring an acceptable D4 to A4 beat rate. Once these 4 anchour points are made, Tunelab 97's numerical editor will do the rest very nicely. Robert was unhappy with his <<quadratic interpolater>> approach to constructing tuning curves, but I found that if used judiciously, it could create very nice curves indeed. One simply had to be a little <<inharmonicity aware>> as it were. Aurally, it is no real trick to come up with a bearing plan with these 4 anchour points. And they are easily enough set by ear or by machine. I found, and way before I even heard of you or your own work, that extending such a 12th to the entire tenor-treble range of the piano created a wonderful sounding piano with a kind of presence I dont get with traditional octave stretching schemes. Jim Coleman offered a few explainations and thoughts as to why the tuning had its own unique colour, and then you popped up. I've heard Bill Ballard talk about an article or column he wrote in the journal some 20 years back or so, and I've seen another column on the matter from the 70's I believe. Its an interesting idea, and another one of those things that gets thought up in various ways by different people about the globe without being aware of each other. Probably, if one digs enough one can find P 12ths in detail much further back in time I should think. But patenting this ??... Heck even Stanwood is having a hard time both justifying his methods as patent worthy and making enough money on the whole affair... and he has a whole methodology complete with tools and the lot. I just dont see this as patentable in the first place... to much loose priors around, nor do I think a patent will accomplish anything more then squelshing whatever method you end up getting. You might get a few bites... no doubt. Personally, I'd publish, make my little mark... and be happy to have contributed something positive... hoping all along that it may be of some real use. signed.... a confirmed open source development person RicB My own William, Ric, same people who giggledd and laughed about the P12 approach when i came up with it in 1988 say today "thatīs how i have done all the time..." very interesting that especially P12 tuners have such problems in accepting when there is an important discovery (the fractal symmetry of beat ratios to frequency ratios in the P12 ET allowing the new pure interval method) on their own subject. kind regards, Bernhard _______________________________________________ pianotech list info: https://www.moypiano.com/resources/#archives
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