Inharmonicity Judgments: was Tuning exam question(s)

[Jim Coleman, Sr.]

Hi Carl:

For many years I tuned using the Wm Braid White temperament. I finally
caught on to the fact that in the middle of his sequence he used the
contiguous M3rds to prove that he had not skewed the 4ths and 5ths in one
direction or another. So, I decided that if this is the real test of a
temperament, why not start there and still use the 4ths and 5ths as they
are interconnected with the 3rds.

The next thing I learned is that even getting the 3rds to balance out was
not sufficient, because it is possible to skew the contiguous 3rds within
one octave so that they increased too fast. This is where I discovered the
importance of extending beyond the octave to prove the correct rate of
increase as you play the contiguous M3rds. This was the beginning of the
Coleman A to A temperament. This became very helpful as I was soon to be
tuning a lot of Acrosonics when I worked for the Baldwin Piano factory.

Later the Baldassin Sanderson approach became another great step ahead in
letting the piano determine what the correct beat rates should be for
any particular piano. This is spread over the A2-A4 double octave range.

The only addition to this has been the suggestion of Michael Kimbell and 
much later from Fred Tremper concerning an easier way to nail the note
B3 which is in the middle of the F3-F4 octave. This procedure has been
written up on this list before. For any who did not receive it, I can
send it as regular email again even though it is in the archives.

Jim Coleman,

PS To answer your original question about how inharmonicity exhibits itself
   in aural tuning, When the 5ths in the lower Tenor have to be too fast
   in order to satisfy the octave relationships of the lower note, you know
   that the inharmonicity is higher than normal. My approach to this is to
   widen the octaves a little to keep the 5ths from becoming obnoxious. I
   have even been known to let the 5ths be on the wide side to accomplish 
   this in extreme cases.

On Wed, 24 Feb 1999, Carl Root wrote:

> JIMRPT@AOL.COM wrote:
> > <<Carl said:
> > > > "Describe how your tuning procedures measure the effects of
> > > > inharmonicity on the beat rates of your temperament sequence.">>
> > 
> > Carl;
> >  I have been thinking about this and the only answer I can come up with is
> > that my aural tuning procedures do not "measure" per se, inharmonicity. 
> 
> Instead of 'measure', maybe 'reveal' or 'account for' would be clearer.
> 
> > Since
> > the main thing I am interested in is a smooth, even, progression from partial
> > to partial, note to note, octave to octave, etc., inharmonicity is
> > automatically accounted for without being measured directly...isn't it?
> 
> If you have accomplished this, then, yes, you've accounted for
> inharmonicity, but some sequences -  a circle of fourths, for instance -
> don't do a very good job of providing you with sufficient information. 
> What specific tests tell the tuner that his first attempt at setting an
> F-A third at 7 beats per second, for example, need to be modified? 
> 
> Carl Root, RPT
> Rockville, MD
>