Inharmonicity and Stretch

[Jim]

Dear Robert:

I read your article this morning with interest.  BTW, you are only the
second person to make reference to my series on Altering the Stretch.
I don't know if people out there are quite awake yet.

You are making some elegant analyses.  And, as you know, things do get
more complicated in real life.

Steve Fairchild has done the definitive study in this area.  He went
so far as to measure the string parameters of each note on the piano
and then to let his formula project the ideal tuning location for each
note.  This is all done in a spreadsheet program which he has written
in Macro language in Super Calc. At my urging, he has revised the
program several times to allow more controls for personal preferences.
I don't see how one can take it any farther than this.  The next step
is to simplify it for practicality sake.  Dr. Sanderson has taken simpli-
fication to the nth degree, first with his one step inharmonicity
measurement of F4 and now with the FAC facility.

What I am trying to do in my recent articles is to build a foundation for
practical alterations for the general curve and then specific alterations
for the weird jumps.  I have put most of this to practical use for some
time.

Since I have had so little response, I am thinking that perhaps I am
making it look more complicated than it really is. You may experience
the same thing.  Don't be discouraged.

Are you using your prototype device on a regular basis yet?

Jim Coleman, Sr.

PS BTW, Steve Fairchild also had his program running using measured
        partials, but withdrew that feature when it was discovered that
        there was infringement on the claims in the Sanderson Patent.
        There are some advantages in measuring the actual partials rather
        than arriving at them hypothetically thru string measurements.