David: Thanks for the response! I guess if I really want to understand the theory, I will have to do the math, which I am capable of. On Sat, Feb 7, 2009 at 7:20 AM, David Andersen <david at davidandersenpianos.com> wrote: > > On Feb 7, 2009, at 4:20 AM, Jeff Deutschle wrote: > > I would have to do additional math to understand this thoroughly, but > I can now see how 4ths and 5ths might be tuned so that they beat at > the same rate across the keyboard (or close enough to appear that way) > if the octave stretch is large enough. > > Not LARGE enough. PRECISE enough. In my tunings, all the fourths "seem" to > beat close to the same pacific, rolling beat, usually about 1.5 beats per > second, but it could be 1.0bps, or it could be 2.0bps. When all the fourths > beat like that, and all the fifths are slightly compressed, with no > discernible beat, you have a highly idealized equal temperament and a > precise, full-sounding, "automatically calculated" custom-to-every-piano > stretch down to the bottom and up to the top. All of the traditional equal > temperament checks---thirds, sixths, tenths, seventeenths, minor > thirds---conform and line up in an idealized fashion. All of the octaves > "sound" or "appear" beatless. > All I can say is I welcome anyone reading these words to look me up at the > California PTG Conference in Burbank, February 19-22. I'll be heading up the > big bad Steingraeber wing of the Hall of Pianos, therefore dead easy to > locate. I would be thrilled to show you exactly how this works. You can > watch me tune and ask questions. I'm going to drive a stake in the heart of > one of the oldest, most toxic illusions in the book: the beat rate of > fourths and fifths increase and decrease in speed like other intervals do in > equal temperament. THEY DO NOT. Not in the world I live in, which is the > world of my ears, which are connected to the trillion-dollar package, the > greatest tool of all. Please come by the booth; all skeptics welcome. I'll > have a private room with a piano in it, so we can get right to work. Come on > down. I'll prove it to you. > "Experience always---and I mean ALWAYS---replaces belief." > Shri David Andersen Ji > > > Hope this helps... > David Andersen > rainy (yay!) California -- Regards, Jeff Deutschle Please address replies to the List. Do not E-mail me privately. Thank You.
This PTG archive page provided courtesy of Moy Piano Service, LLC