interesting inharmonicity information

[Ron Koval]

A few weeks ago, Ric B listed a link to his site to share an inharmonicity 
graph measured from a piano.  It displayed the first 8 partials for the 
C3-C5 range.  Very nice, multi-colored, showing increasing spacing between 
the partials with smooth curves.  The measurement unit is Hertz, so the 
range is from 0-5000.

I've been doing a bunch of measuring, getting ready for a chapter meeting, 
and found this graph, though informational on the macro level, doesn't 
reflect what goes on at the micro level.  If you just consider the scale 
from 0-5000, it's obvious that a few cents difference won't even make a bump 
in the graph.  So...... I started measuring in cents, the difference from a 
math-predicted calculation of the partials.  The numbers produced are 
something like:
0,2,5,8,13,19,26
for the first 7 partials at around A4.  Fine and dandy, I've got a scale to 
work with that will be from 0-60.  Small differences will show up.

So what?  Well this actually has a lot to do with both calculating a tuning, 
as well as measuring a tuning, say the EBVT.  What I've found is that when I 
tested a 7' Baldwin SF10, this new graph showed pretty much a smooth curve 
with some "constriction" of the partials in the area of the bridge/stringing 
break.  Still, it would seem that any of the sampling tuning gear could make 
pretty close assumptions to come up with a matching tuning.

But, when I tested an upright, things started to get interesting.  From 
about C4 and up, I still found an nice predictable pattern to the Ih data.  
Going down into the wound strings, it was if some drunken, inked spiders had 
stumbled across my page!  The single partial that the piano had been tuned 
to was fairly linear, but the other partials (this is the important 
part)ESPECIALLY the lower partials were all over the map.

What this means, is that anyone hoping to gather information about an 
aurally constructed alternate temperament would get the best results doing 
their measuring above C4.  Also comparing only the lower partial pairs from 
the tenor into the bass may lead to some inconsistancies.

Not all uprights share this tendency, I'm guessing this one is just a nasty 
example of why some instruments are a little tougher to get a good tuning in 
place. (subliminal message: try a Verituner)

Ron Koval

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