My background is in mathematics and physics, so this article holds some interest for me. While it may be very technical, the key points are fascinating, especially as regards the vertical and horizontal motion of the string, and the pin bridge distance effect. While the first aspect is well known, not many people have looked into the latter experimentally.
https://www.johnsankey.ca/string.html
This post was inspired by the current topic on spinet buzz.
Hi Andrew,
Thanks allot for this article!
This is a subject that has always been of great interest to me.
Tom
Interesting! I am also a mathematician, but my scarce knowledge of physics makes it difficult for me to follow the formulae. What is interesting is this conclusion:
“The monocord sound with no pin and the close pin are almost indistinguishable, both being full with a distinct pop at the beginning. The pin-bridge separation of 0.25 cm still sounds full, but has a more even decay of sound than the first two. At 0.70 cm separation, the sound is very close to that at 0.25 cm but slightly more nasal, …”
Good to know about these experimental results!
My Hubbard double has a pin-bridge separation of about 0.2 cm throughout, so I am fine in this respect.
[I am not surprised that up to 0.7 the sound is still good: bearing in mind the angle around the pin, it is obvious that the string moves vertically, and the distance from the bridge is only important if it is so large that it can audibly vibrate separately.]
Active research in piano technology using ultra-high speed videos produces a slow motion video in which you can see the individual higher partials reflecting of the bridge pin and (due to inharmonicity) racing ahead of the main impulse like porpoises riding the bow wave of a ship.
It is also possible to see a tiny wiggle of the string behind the bridge pin as the impulse is reflected.
In the piano, the originally vertical string displacement begins to rotate as the waveform progresses, and it is thought that this works as a sort of reserve to assist sustain, since the lateral movements are not transduced into sound by the movement of the soundboard and bridge
The Piano Technicians Guild Foundation is funding some of this research. The cost of the rental equipment is horrific, but maybe the technology will be available on iPhones before too long.
The technician doing the current research has announced his intention to make all results public domain. I’ll ask him to video a harpsichord string and jack if there is any extra time in the rental…just hoping.
Stephen Birkett and I did a great deal of this type of research some years ago before we both had to concentrate on other things for a while. I would hope the PTG technician has done a search for scientific papers on the topic? Anyway, yes, strings do move up and down on bridge pins, surprisingly much, and strings roll, though the theory of “a sort of reserve to assist sustain” is an unsubstantiated subjective concept. Getting meaningful results from such research requires very careful controls to ensure observations are not affected in unintended ways (such as vibration from air condition, even slight movement from the piano or model, etc.). I would be surprised as well, if Kawai doesn’t have a body of work already in existence. I know they were doing high speed video work over 10 years ago.
Re vertical and horizontal string movement, see this short excerpt from Weinreich: Gabriel Weinreich: The coupled motion of piano strings
Indeed, a now-classical set of five lectures I avidly read when it was published over 30 years ago.