At 7:13 PM -0400 10/16/03, BobDavis88@aol.com wrote: >Hi Michael, > >An "octave" can be many things ! > >Tuners, aural or visual, don't tune a 2:1 octave anywhere in the >piano. Here's why: Because piano wire does not vibrate harmonically, >the partials become progressively sharper, and only one set can >match at a time. This is different from an organ, the partials of >which are harmonic. Mathematically it's because the production of beat rates is a subtraction operation, and the deviation of partial frequencies from the mathematically pure harmonic series is a multiplication operation. There exist an inharmonicity factor for each note, which when multiplied by the partial number times the 1st partial frequency, will predict the frequency of the partial in question. And in our world it's a simple linear function. If you have a chance you could look in the PTG Journal's archives for a series on inharmonicity by Dan Levitan. But don't worry about the math. If you're already being guided by your ears, your interval series smoothing is probably producing a very even tuning. A good aural tuner might not be able to write a masters thesis on the complexity of tempering scales, but s/he has no trouble cleaning up a tuning, to begin with, his own. Were s/he an visual tuner with good aural background, s/he would be cleaning up the machine's tuning. I did ask Dave Carpenter at the NEECCSO in Boston this Spring whether the model of the temperament was a 3-D spreadsheet. It seemed to excel at interval series tuning, because a large number of partials were having their frequencies crunched (or as marketing would have it, smoothed). He replied, matrix algebra. By the way (BTW), welcome again, to the list. There is always alot to be learned about tempering. Bill Ballard RPT NH Chapter, P.T.G. "Baa, Ram Ewe....Baa, Ram Ewe, To your breed, To your fleece, To your clan be true Sheep be true.......Baa, Ram, Ewe" ...........Conversation starter in uncertain social situations +++++++++++++++++++++
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