Bill Ballard wrote: > At 8:54 PM +0100 12/6/02, Richard Brekne wrote: > The desire for a perfect 5th gets like really in the way of any and all shemes for spliting it up when it comes down to it.... so why not split the distance between a perfect 12th up into 19 evenly spaced semitones instead ?, > > I seem to remember in the Fall of '97, Jim Coleman described a very similar tuning scheme in which he tuned the circle of 5th (alternating with 4ths to stay within one octave), whose resultant 2:1 octave he took as the general width of the octaves for the outside 6 octaves. Of course what we were listening to was the Comma of Pythagoras, which when I went through school , had the Mark of the Beast. > Yes, he wrote a couple times about that when I started talking about using 12ths in this fashion and thought at first it was the same kind of thing. But its really not as he concluded himself. Tuning pure 5ths and compensating with 4ths widths within an octave remains a scheme that divides up the octave itself, where as spliting an interval of the 12th into 19 (evenly spaced) semitones is something else. > But octave widths are a matter of taste, as is garlic and blue cheese. So once you agreed to octaves which beat twice as fast as you would normally allow a 4th to, you got to enjoy pure 5th and 4ths throughout. Of course how this played out on any given piano with its particular inharmonicity was another matter. But given that we were already swallowing rollicking and roiling octaves, this other stuff went down pretty easily. The stretch at the ends of the keyboard was near psychedelic. This kind of thing is exactly the point I think Bill Bremmer was making. ETD's today dont really have any way of accomplishing these kinds of stretch variations. You can force Tune Lab 97 to do the 12ths tuning, but I dont think you can get it done in TL Pro or Cyber Ear or SAT. And I dont think Colemans tuning would come out right on these either. > I seem to remember Ed Foote (or was it Jim Bryant) trying it in household with classical string players with an immediate and overwhelmingly positive response. > > While we're at it, I'd like to patent the "3:1 octave" (the P12th). I published it in 1993. <g> Well, then you were too late. There is reference to perfect 12ths in the 70's in a journal article, along with the formula for dividing it into 19 semitones (a simple variation of what we do with the octave / root of 2 ) > > Bill Ballard RPT > NH Chapter, P.T.G. -- Richard Brekne RPT, N.P.T.F. UiB, Bergen, Norway mailto:rbrekne@broadpark.no http://home.broadpark.no/~rbrekne/ricmain.html
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