para-inharmonicity and tuning curves

[Roger Jolly]

Hi Richard,
             I thought I would share some thoughts with you, Young's
formula is not quite accurate in an absolute sense but good enough for most
practical uses.
Test that I have conducted in the areas of inharmonicity and string
coupling, has more to do with the dwell time of the hammer on the string
than with the basic property of a given piano wire.
A well voiced hammer will rebound from the string quicker than an over hard
hammer, therefore there is an increase in sustain and power for the upper
partials, and a significant shift of inharmonicity readings. 
Needling various zones of the hammer effects the efficientcy of energy
transfer, and hence the partial build up from the string.
Taking a single wire on A440. The difference in inharmonicity reading at
ppp-mf-fff is quite dramatic, this futher reinforces my theory that dwell
time is the critical element.  I have further played around with the jack
height/position, and have noticed and heard a wide variety of changes in
this area.
The only way that I can figure possible, to get a true mathmatical picture
would be to integrate time, mass and energy into the formula. Unfortunately
it's been too long for me to take a run at it.
No answers just more questions.
Regards Roger

At 02:20 PM 5/17/99 +0200, you wrote:
>
>Hi Tom.
>
>Thanks for your input to my queries. I wonder if I might trouble you for a
>couple other tidbits of information. I am drawing up an essay you see, mostly
>to sort out my own understanding of some things about tuning that have
bothered
>me for some time. If you want to take a look at what I have so far then check
>out the page address below. Be advised tho that there are still present some
>akward wordings, and some statements that are directly wrong. When I get
it all
>right, well then I will have gained the knowledge I am after at this stage.
>
>In that regard I'm trying to hunt down the formula for the String Stiffness,
>and how that relates to String Frequency. I seem to remember some years ago
>somebody wrote in an attempt to describe inharmonicity, that knowing the
string
>stiffness of any given string would allow one to figure the frequencies of
all
>partials just by reducing the lenght of the string by the appropriate
amount in
>a formula that translated stiffness and lenght into frequencies.
>
>Now I know now that this notion of figureing partial frequencies does not
hold
>true. Yet it was a neatly packed in "theoretical" notion that I need for my
>essay.
>
>http://home.c2i.net/ric/octbehavior.html
>
>Thanks for your help, it is greatly appreciated.
>
>Richard Brekne
>
>
>Attachment Converted: "c:\eudora\attach\Repara-i.htm"
>
Roger Jolly
Balwin Yamaha Piano Centres.
Saskatoon/Regina.
Canada.