FW: Partial relationships was Verituner spinner

[Alan Forsyth]

Hi,

Further to Ron N's query and my previous reply, I have fished out the 
data I
originally had on this and have decided that I must amend my previous
statement. This should now be; The gaps between the partials decrease 
as the
tension of the strings is raised, as well as the partials frequencies
increasing BUT it is the rate of change that is crucial; the rate of
acceleration actually DECREASES. When the data is plotted on a graph, 
the
curve starts to flatten out as the tension of the strings is raised.

I have attached the following;

Graph 1 which shows the gap between the partials decreasing as the pitch
increases. In other words their spacing tends to converge.

Graph 2 which shows the rate of increase in partial deviation ( or
inharmonicity - hate that word -) slowing down and this is quite 
dramatic as
the tension is raised to almost breaking point. The +2 semitone line 
(the
black dotted one) goes completely wild compared with the others.

Table 1 which contains the raw data from which the above graphs were
eventually compiled with a lot of intermediate calculations and 
analysis.

This unfortunately was all done before I became computerised, hence the
jpegs and not spreadsheets.

Hope this is of interest.

Regards
Alan Forsyth.

Graphics at:

https://www.moypiano.com/ptg/files/attachments/24/22/ac/05/Graph1.jpg

https://www.moypiano.com/ptg/files/attachments/97/98/98/92/Graph2.jpg

https://www.moypiano.com/ptg/files/attachments/2a/18/c4/78/Table1.jpg

Alternate URLs

http://tinyurl.com/r8zn

http://tinyurl.com/r8zt

http://tinyurl.com/r8zp


----------------Original message-------------

Ron N asked;

"Does anyone know, do the proportional relationships of the partials to 
the
fundamental, and to each other, remain relatively constant as string 
tension
is changed?"

I had to do some research on this in my college days as I was trying to 
find
out why some pianos sound "Tinny" and others sounded great. After taking
readings with an FFT analyser, the results actually confounded my
expectations. The gaps between the partials increase as the tension of 
the
strings is raised, as well as the partials frequencies increasing BUT 
it is
the rate of change that is crucial; the rate of acceleration actually
DECREASES. When the data is plotted on a graph, the curve starts to 
flatten
out as the tension of the strings is raised. This led me to the 
conclusion
that the higher the tension of the strings, the lower was the 
proportional
inharmonicity. This also gave me the impression that the curve on the 
graph
would  be a straight line just at the breaking point of the string. I 
shall
try and dig out the data from my archives.

Alan Forsyth

PS. Never did find out why some pianos sound so crap!