Could someone please play a middle c on their violin and tell me if there is any sympathetic resonance on the e string?
I don't think the E string rings while playing a middle C.
Not necessarily a resonance as such, but my violin likes to give me a shrill afterglow which retreats when I mute the e
Warning! some maths here!
Very interesting, Trevor!
There is a characteristic resonance whenever a perfect 4th above an open string is played, including the C. While it doesn't ring with an octave below, it still has it's own ring. I don't know what the partials involved are, but they're there.
Trevor: "The viola C string would have to be tuned from 130Hz up to 132Hz to get the effect, and the cello C up from 87Hz to 88Hz."
Trevor - I'm not sure the reason for "close 5th's" tuning by string quartets is to achieve extra resonance. I'm no expert but I understand that if you tune by ear in perfect fifths starting with the top two strings, the bottom string and its harmonics will simply sound flat as compared with the top. Even in orchestral playing is it only me who often finds, when required to to play open G for the first time, that it has "gone flat"? So maybe everyone should do it as a matter of course, although it only seems to be taught in the context of string quartets.
I get a harmonic one octave above the open e on the e-string. That's two octaves and a third above middle c which is a natural overtone. @Trevor: This also works on a piano. If you silently press e' on a piano and play the middle c, the e will ring sympathetically. I guess, even though the e is not exactly on the overtone, it's still close enough. I can also move the c up and down a bit on the violin and still get the harmonic on the e-string, so there's some slack there too.
Cello C string is 65 Hz (give or take depending on the tuning system).
@Han, @Andrew. Many thanks for drawing my inadvertent wrong calculation (cello F instead of C) to my attention. I've amended my original post accordingly.
There is a major resonance around middle C on a violin which shakes the top and the bridge rather severely, so all of the other strings can be excited to some extent.
I dimly recall from string quartet courses that after tuning our instruments in close fifths, the check was to make sure the cellist's open C makes a sweet major 17th (!) with the violinists' open E. Does that answer the question?
All unmuted open strings will vibrate at one or more harmonics of the note being played. How loudly they vibrate depends on how close one of the harmonics of the played note is to one of the harmonics the open string is tuned to.
Trevor, I think your theory isn't correct. I have to admit it got me thinking, and digging....I found this chart which plots the "Reaction". There is a rollooff as the input frequency increases and nothing occur when the input frequency is 2X or 3x, etc....
Try https://en.wikipedia.org/wiki/String_vibration instead.
I don't get what relation you see between the frequency response of a single, strongly damped oscillator (single mass-spring-damper system) and that of a string, which behaves as a series of weakly coupled, weakly damped oscillators.
It has probably been obvious to everyone but me (until the last few months) that when one string is excited by the bow, that the frequency is transmitted through the bridge into the other three strings.
Just to muddy the waters a little, middle C on my Rippen piano is 256Hz.
Thanks Trevor! In my weekly tuning of about sixty violins in the student orchestras that I assist, sometimes I get a "C" registering on my chromatic tuner (no, I don't have perfect pitch and tuning all those instruments in a noisy room...).
Arnie Cohen write:
If you tap the side of a bridge, all the strings will sound. It can be a single tap, and doesn't need to be at any particular frequency.
Thanks all for the informative discussion. I have been reading attentively. Thank you