Inharmonicity

[Jim Coleman, Sr.]

Hi Richard:

When a partial is flatter than its theoretical harmonic, we know that 
something unusual is going on. Dean Reyburn invented the word 
para-inharmonicity to cover a multitude of these kind of sins. I suspect 
that it has something to do with soundboard movement.

Perhaps related to that is something I documented today on a pitch-raising
job. The FAC numbers I measured before pitch raising were: 15.3, 9.0, 7.0.
When I came back today to do the fine tuning, they were:   14.5, 8.0, 5.7.
The change is not due to the strings getting longer, but shorter if 
anything. The diameters did not change. The bends at the terminations 
may have changed slightly. I still think that it has something to do with
the soundboard loading.

For those who are not familiar with FAC numbers used with the SATs, the
first number represents the difference between the 4th and 8th partials of
the note F3. The second number represents the difference between the 2nd 
and 4th partials of A4. The third number represents the difference 
between the 1st and 2nd partials of C6.

Jim Coleman, Sr.

PS the amount of flatness observed for the second partial on some pianos
has usually been on the order of .5 cents. For pianos with the 1 inch over-
wrap at the bridge ends, it has been more extensive and it has affected 
more than just the second partials. I have also seen a few cases where the
3rd partial was flatter than the 2nd partial. Usually everything smooths out
by the time you get the 4th and 5th partials. This is my primary reason for
not tuning by 3rd partials in the tenor area.  JWC

On Fri, 21 Aug 1998, Richard Moody wrote:

> Hi Jim 
> 
> >>There are two
>  7' pianos in which the second partial of C5 is flatter than the
> fundamental.<<
> 
> 	The second partial of C5 is FLATTER that the fundamental?  You mean it is
> flatter from 2x the fundmental.??
> What pray tell could cause that?  It seems that in piano wire with
> stiffness being a factor of ih, all partials MUST be sharp.  
> How much flatter? 
> 
> Richard Moody 
> 
> ----------
> > From: Jim Coleman, Sr. <pianotoo@imap2.asu.edu>
> > To: Richard Moody <remoody@easnet.net>
> > Cc: pianotech@ptg.org
> > Subject: Re: Inharmonicity
> > Date: Thursday, August 20, 1998 12:52 AM
> > 
> > Hi Richard:
> > 
> > The variations of inharmonicity especially in the lower numbered
> partials
> > is something which can be seen even in plain wire strings. There are two
> > 7' pianos in which the second partial of C5 is flatter than the
> fundamental.
> > This is most unusual.
> > 
> > More variation is observed in wound strings in general. The most weird
> thing
> > is found when the copper wrap is over wrapped for about one inch at the
> > bridge end of the strings. This often causes more than just the second 
> > partial to be flatter than the fundamental and makes tuning by any means
> > utterly impossible. This phenomenon was witnessed on one of the most
> > prestigious 6' piano in the world.
> > 
> > Jim Coleman, Sr.
>