two strings flatter than one,

[Roger Jolly]

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At 10:55 AM 16/01/00 -0700, you wrote:
>Is it  possible that the impedence from the first string is going to
>interfere with the frequency of two or more strings vibrating together.
>Maybe there is an area of air movement created around the moving string
>that will affect the motion of the subsequent strings.  Or maybe the
>impedence of the sound moving through the bridge or the board could do the
>same thing.  
>

Hi Chris,
             An early theory on string coupling:
With 3 individual strings tuned perfectly, (if there is such a possibility?)
With a fixed amount of energy applied to the key, string #1 will the board to
move a set amount.
Adding the second string in a perfect world, will double the energy trying to
move the board, and hence making it travel further, this will have a slight
damping effect and lower the pitch.
Adding the 3rd string increases the energy yet again, but proportionately
less.
This is in line with the measurements that I have made.

Now the variables, that effect the amount of change.
1. Sound board impedence.
2. Back scale length.
3. Down bearing angle, ( bearing pressure) quite noticable on Baldwin with a
long back scale length, and lower down bearing pressures.
4. Bridge height and width. (bridge mass)
5. Velocity of blow, a fff blow tends to go VERY slightly flat. 
6. The coupling effect seems to more pronounced when the hammers are very
hard,
so the real time inharmonicity enters the picture.

To really investigate the subject, one would need a lab and good sized budget
for test equipment and a lot of man hours.

The man hours that I have spent making the 'Jolly Thumper'. A triggered device
that has controlled,
variable speed and mass, to strike the keys to make reproducable measurements.
Makes me believe that I'm slowly going nuts.

Just some ramblings on the subject, to fuel the flames.

Roger

Roger Jolly
Saskatoon, Canada.
306-665-0213
Fax 652-0505 
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