Hi Richard, nice to see your hand and open mind back again too. More thoughts interspersed. Am 02.05.2009 um 20:31 schrieb Richard Brekne: > Hi Bernard... > > I suggest we take the prior art bit off list. I am not really > qualified to judge I feel qualified to judge it. Let me try to make more explanations: > one way or the other what qualifies as prior art you understand. I > think its pretty clear that a very similar tree is being barked up > between you and Gary Don´t agree. There is no doubt that Schulze is tuning in case of present inharmonicity pure twelfths at a 3/1 partial level. In his chart of the checks, he is using the standard 5/3 (sixth) and 5/1 (double octave +maj third) check for the 3/1 partial twelfth. Remember: In case of present inharmonicity, an octave is definitvely not aurally pure (in the sense of the whole tone) if it is pure at the 2/1 partial level. The same is true for the definition of an aurally pure duodecime (twelfth): if it is pure at a 3/1 partial level, it is not pure aurally (in wholetone sense). Schulze´s intention to tune the twelfth at a 3/1 partial level results in an equal tempered nineteenth when inharmonicity is present, what he is finally defining so. In case of abscence of inharmonicity, one can not tune twelfths at a 3/1 partial level with an equal tempered nineteenth, just because 3/1 does not equal 6^(19/31). Read the quote from Gary´s article carefully again: "Still more control can be gained by incorporating a different*, albeit compatible system of temperament: the equally tempered perfect nineteenth. Assuming that an ideal tuning is one which contains the most nearly coincidental partials, inharmonicity then becomes quite convenient." *He means different from standard ET. Another quote from his article, what i want to question is: "By so doing, it has been my experience that all octaves, double octaves, twelfths and nineteenths can be made to give the appearance of being “beatless” The intention of my tuning approach is to achieve aurally pure duodecimes (twelfths) and it is no question that Schulzes statement is defintively not true for the octaves and double octaves in my case: Already in the temperament there is a noticeable beat in the octave and in the higher treble the beats of the octaves are really prominent. > ... but again thats not for me to judge. My only concern here has > been to show where my direct influences came from in my own > development. > > What IS fun to talk about is just how all these different approaches > compare in the real world. And I am anxious to see someone start > doing some measuring of the sort Sanderson did in his article some > 30 years back. He measured the first 8 partials of a two octave > range in the middle of a piano (excepting the 7th partial) in an > analysis of how the stretch behaves when looked at from the > perspective of several intervals in the form of their coincident > partials. > > Measuring Tunic, Virgils approach, > and any other that might be interesting to compare, and looking at > the actual results in this same perspective would perhaps be very > enlightening. I am the first to admit and recognize that the world > of coincident partials and listening to these at their actual > frequencies has limited value. Misunderstand me correctly folks... > using coincidents can get you very very far down the road to a fine > piano tuning. But I am personally convinced that, as Kent, David > Andersen, Ed, Virgil himself, and others have said time and time > again each in their own way, the finest tuning is that one which in > the end is tweaked carefully by ear listening to the whole beating > effect or the "sum beat" that results from playing any of the > several intervals that we as tuners want to sound pure(-ish). > Still, coincidents allow us a vocabulary for communicating clearly > that no other description of beating allows us.... so I cant see > that we can really live without them either. > > Cheers, and delighted to see your outreached hand. > > RicB > > > -------------- next part -------------- An HTML attachment was scrubbed... URL: <http://ptg.org/pipermail/pianotech_ptg.org/attachments/20090502/4ecdd8e1/attachment.html>
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