Interesting in that I added 1.95 cents to widen A(3) - A(4) which produced a pure A-E fifth. This was before the FAC stretch numbers, which not owning a SAT I don't really understand. Also I need to double check the formula for using cents. If I want to alter the Freq. of a note by adding cents I use (spreadsheat style) f*2^(cents/1200). So if A is 220 and you want to make it, say 3 cents flatter so as to widen the octave, then the formula would look like this. 220*2^(-3/1200), or 2^(-3/1200)*220. By hunt and peck -1.95 cents gives the A-E fifth a beat of .002. or as they say in South Dakota "pert'near. But that's if the formula if right. BTW the -1.95 cents gives a freq. of 219.752. That seems like very little "stretch" to get a pure fifth. Its only flat by one quarter of a cycle per second. Me thinks my formula needs tweaking. Any Math majors out there? And another question. Since Jim suggests the octave can be stretched, perhaps a formula could be worked out such as 2.19*2^1/12. For those interested in spread sheet analysis of tempered intervals. (gotta sound important) email me and we'll see how it gets sent. Its on MicroSoft Works. Other wise I can post the formulas, and you should be able to paste them into pret'near any spread sheet. Richard Moody ---------- > From: Jim <pianotoo@IMAP2.ASU.EDU> > To: Glenn <rockymtn@sprynet.com> > Cc: pianotech@byu.edu > Subject: Re: Aural Pure 5ths Temperament Part III > Date: Sunday, May 25, 1997 6:15 PM > > Hi Glenn: > > Yes, that's all there is to it. Well, almost. some pianos may require > 1.5 cents to be added to the A4 number. I can't guess the inharmonicity > curve of every piano, but if 1.0 does not make the 5ths pure enough, > try 1.2 etc. It has just amazed me how simple this really is. More and > more I'm beginning to appreciate the genius of Dr Sanderson and his > piano tuning formula. > > Jim Coleman, Sr. > > On Sun, 25 May 1997, Glenn wrote: > > > > > > > ---------- > > > From: Jim <pianotoo@IMAP2.ASU.EDU> > > > To: pianotech@byu.edu > > > Subject: Aural Pure 5ths Temperament Part III > > > Date: Saturday, May 24, 1997 11:21 PM > > > > > > > > > The original experiments were done on my Steinway L which had > > > FAC stretch numbers of 7.0, 8.5, 8.6. By adding 1.0 cents to > > > the A4 stretch number, the center octave was stretched enough > > > to make the 5ths come out pure in almost every case. Now this > > > was at the expense of making the 4ths faster as well as the single > > > octaves. The smooth curve ability of the SAT kept the 3rds and > > > 6ths well in line, but the 10ths were a little faster, but the > > > progression was smooth for all intervals. > > > > > > Jim Coleman, Sr. > > > > So is this all you have to do to tune pure fifths with the SAT II? Add 1.0 > > cents to the A4 FAC tuning and away I go? If there is more to it, please > > explain how to do it. > > > > Glenn. > >
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