Inharmonicity - causes

[Jim Coleman, Sr.]

Hi Richard and others:

Typically the cents deviation of partials can be plotted on graph paper by 
setting 
up cents on the vertical axis and the Partial numbers squared on the 
horizontal axis. The curve you get will be a straight line slanting upward.
Para-Inharmonicity is any deviation from that straight line. It usually 
manifests itself by showing the 2nd partial being sharper than the 3rd
partial or any other anomaly. My best guess is that this is caused by
board relationships. It is worse at the Tenor breaks on plain strings. I
do not have a clue as to how to correct this other than changing the mass
loading of the board or bridge.

Because of this erratic behavior of lower numbered partials it is my belief
that notes in this area should be tuned by higher partials which are 
more regular, not lower partials. I tuned a Janssen console today in which
it was best to use the 4-2 matching partials going down into the upper 
Bass area. 6-3 matching was too wide. It would have been alright to tune
by the 6th partials, but not 6-3 matching partials. With the new SAT III
one can tune smoothly across the Tenor break on small pianos by decreasing
the double octave stretch and still tune by the higher 6th partial. As one
goes lower into the Bass the matching can be made closer to the 6-3
matching relationship. All of this can be adjusted on the fly.

When tuning these kind of pianos strictly aurally, it is necessary to
continually make compromise adjustments to keep as many things nearly in
line as possible. There are trade-offs between keeping smooth 10ths, smooth
octaves and smooth 5ths going across the break. Another neat thing about the
SAT III is that one can change the stretch numbers on the fly without 
remeasuring in the normal way. Neat Huh? This facilitates tuning across
the wound string break in the Tenor section.

Jim Coleman, Sr.
PS Here is an example of plotting inharmonicity in cents versus partial num.
squared:

                                           x





C
                           x
E                            
                         
N                    
                  x
T               
             x    
S         x

          1  2    4        8                16
          Partial No.

If the Inharmonicity were plotted again partial number, the curve would
swoop up like the upper surface of a trumpet bell.  JWC




On Sat, 15 Aug 1998, Richard Moody wrote:

> 
>  
> ----------
> > From: Jim Coleman, Sr. <pianotoo@imap2.asu.edu>
> > 
> > As far as I know there is only a small effect on the inharmonicity
> caused
> > by the terminations, but perhaps a little more by the impedance
> matching,
> > or I should say mis-matching of the soundboard and bridge assembly.
> > Some call this para-inharmonicity. This can include the effects of
> voicing.
> > 
> > Jim Coleman, Sr.
> 
> Can anything be done to ameliorate the mis-matching of soundboard and
> bridge?  How can technicians identify such a mis-match in pianos.  It
> would be interesting to hear more about the effects of voicing on this
> para-inharmonicity. 
> 
> Richard Moody 
>