Aural Pure 5ths Temperament Part III

[Richard Moody]

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

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> 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.
> >