<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"> <html> <head> <meta content="text/html;charset=ISO-8859-1" http-equiv="Content-Type"> <title></title> </head> <body bgcolor="#ffffff" text="#000000"> Ric, The guy who put you into the trail to P12 you was André Oorebek from Amsterdam (you figured out in another post) and  "a rather small article i found about in the seventies" (your own words, you still have to find it) Both indicates and proofs that it was not yourself who pushed you up into the thing. In practice, the "other guy" already did so. Now for the theory: Arnold Duin from Amsterdam, a former companion of André Oorebek, told me at a Mensurix workshop i hold in Amsterdam a few years ago at their convention that they learned the major sixth-doubleoctavemajorthird test from their old teacher who was not firm with any theory about tuning, but a good tuner. They tried to convince him, that it is not correct to do so from tuning theory. Some years later, after my publication in euro-piano, they began to adapt  to the  P12. The article you mentioned was probably mine (the initial publication of the pure twelfth temperement or "Stopper-Tuning" in euro-piano 1988) So your finding was indirectly (via Andre) and probably directly (the article) initiated by my work about the matter. I really hate to offend other people, but you do so to me a little by continously claiming independent authorship on the theoretical matter in your posts. It was always my intention with the P12 temperament to get the tuning theory compatible with what the best aural tuners tend to do, while the standard 12th root of two tempermant theory is not so. Mathematically the 19th root of three temperament is on a first look only one approach between thousands of possibilities to split the pythagorean comma on either side of the fifths circle. More important (if not sensational, sorry for the self-praise) is my finding of the beat symmetries (or symmetric interfenrence phenomene) inherent in only this equal temperament four years ago, cancelling out the beats in octave and fifths combinations and thus turning a tempered tuning into pure tuning when playing chords. And this the proof why this tempermant is superior to any other. regards, Bernhard Stopper Richard Brekne schrieb: <blockquote cite="mid4680D220.3090903@pianostemmer.no" type="cite"> <meta content="text/html;charset=ISO-8859-1" http-equiv="Content-Type"> <title></title> Hi Jason.  To take your thought a step further, The guy who first put me on the trail of the P-12ths idea showed me a series of test intervals. A major third, major sixth, octave 10th and double octave 10th. For tuning C6 for example,  the relevant notes would be Ab3, C4, F4, C5, and C6, with the Ab3 being the control note the whole way.  The Third should be slowest, but just slightly slower then the 10th. The 6th should be fastest, again by a very slight amount, and the note you are tuning... the double 10th should be just inbetween the 6th and the other two. This makes the 12th below C6 just very slightly off pure. Just got me thinking back then that it would be easy to use Tunelab to do this directly David Anderson using the clean fourths this way moves in a very similar direction. Cheers RicB <blockquote> </blockquote> <blockquote>Yes. As I think about it, I recall that David Andersen puts great emphasis on the fourths, especially on the way down through the tenor. Now fourths do happen to have the coincident partial that is a P12 from the upper note. So in a manner of hearing, David is emphasizing P12 in his own way. Hmm. Jason</blockquote> </blockquote> </body> </html>