Michael G. re: 8ves

[Bill Ballard]

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.

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