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 -------------- next part -------------- An HTML attachment was scrubbed... URL: <http://ptg.org/pipermail/pianotech_ptg.org/attachments/20090207/674bfa9c/attachment.html>
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