# Violin bow and strings in super slow motion

November 27, 2009 at 08:01 PM ·

I saw an episode of Discovery channel's show Time Warp where they filmed someone pulling the bow across two open strings-it was a quick stroke, only about 2 seconds, but they captured it with a super highspeed camera.  The result was a super slow motion video clip that allows you to examine what happens when in those two seconds are stretched over a minute.  Here's the link to the  video.  Unfortunately, I haven't found a clip of it in real-time so you can hear and see the original.

The slow motion allows us to actually see the physics of the classical ratio of a perfect fifth.  If you count the vibration cycles of the two strings, you'll notice that in the time it takes for the D string to  vibrate twice, the A string vibrates three times.  To do this, I set the video at the 0:20 mark and counted the "grab and release" cycles of the D string until I counted 10 cycles - the video was now at 0:27.  Next, I counted the cycles of the A string from 0:20 to 0:27 = 15 cycles.  This indicates that the violin was in tune as the 3:2 ratio in the movement of the strings vibration reflects the ratio a perfect fifth (A = 440 Hz D = 294 Hz,  440 / 294 = 1.5).

While doing this, I noticed that the "grab and release" action of the bow hair on the strings was not perfectly consistent.  Sometimes there wasn't a steady pulse in the vibration of the D or A strings.  I'm thinking that perhaps the bow was not equally on the two strings. Also, I'm wondering if this video illustrates what happens when the bow pressure and speed and distance from the bridge are not in the optimum balance (i.e., the sound point).  Even though the elapsed time is only a couple seconds, a number of things happen that introduces inconsistency and I'm thinking that these abberations create noise that detracts from the purity of the tone.  My theory is that when a violinist plays a note with good tone - the sound point is achieved, that the physics of the string motion under the bow would be perfectly consistent (or nearly so).  Some of the inconsistencies I noticed in the video were:

1. The vibration cycles do not hit their peaks like clockwork or in perfect synchronicity.  From the beginning of the video, if you count each "grab" of the bow on the D string, the first 3 grabs are pretty much in a steady cadence, but around the 0:05 second mark you see that the 4th grab is a little delayed and 5th grabs follows very soon after the 4th.
2. The bow moves closer to the fingerboard during the course of the stroke.
3. The bow stroke starts perpendicular to the strings, but begins to go crooked at the 0:25 second mark.
4. At the 0:35 second mark, a plume of rosin dust forms and builds up through to the end of the clip.  This may indicate a change in pressure (or hitting a more heavily rosined section of the bow).

I'm wondering what others notice from this clip.  Do you think there is any merit to the theory that the noise/abberations we see are a hinderance to producing a pure tone?

From what I remember from watching the original episode several months ago, the real-time duration of this clip is about 2 seconds and the woman playing the violin casually pulled the bow across the strings (i.e., there was no apparent attempt to produce a high quality sound).  It would be very interesting if this clip were duplicated wtih a violinist who could instantly hit the sound point.

John

FYI: HowStuffWorks wrote up a description of this video that outlined some of the basic physics involved.

## Replies (7)

November 27, 2009 at 10:07 PM ·

Hi, I agree it's very interesting!!!   One member here once post something in the same "idea". It was a PHD study and something called the science of good tone or soo. It much be archieved here.   I love to read those!

Anne-Marie

November 28, 2009 at 07:57 AM ·

Thanks for mentioning the thread on tone quality Anne Marie. I found the thread in the archive and the link to the paper is here. I am reading it with great interest. (I had to upgrade to Acrobat 9.2 and save the target file, but eventually I got the file open.)

The video referenced above so clearly demonstrates the “grab and release” action of the bow hair on the string that it made me realize that the bow must grab and release the A string 440 times each second.  Amazing!  Even more so that this grab/release cycle of 440 per second on the A string stays constant regardless of how fast the bow is moving. A faster and heavier bow will increase the deflection of the string (greater amplitude) but the vibration cycles remain constant at 440. Can someone tell me if I am understanding this right?

If so, then I must have been wrong in the first post when I said that the elapsed time of the bow stroke was two seconds. It was probably less than one second.  If you’re interested in the reasoning read on:

In the video it appears that the bow grabs and releases the A string about 25 times for each inch of travel. Another way of saying this is that, for this particular bow speed, the A string is vibrating at 25 cycles per inch.

If the bow stroke took about 2 seconds to draw the bow from the frog to the midpoint (about 12 inches), then the bow travelled 6 inches in 1 second. That means there were 25 grab/release cycles per inch.  This covered six inches in one second, for a total of 150 cycles per second. But that can’t be right because, according to the laws of physics, an in-tune A string vibrates at 440 cycles per second, not 150!

I'm guessing that my error was that I over-estimated the time elapsed during the bow stroke. Perhaps the pull of the bow lasted a mere 2/3rds of a second (0.66667). If so, then the math works. My reasoning is that if it takes 0.66667 seconds to pull the bow 12 inches, then over the course of a full second the bow would travel 18 inches. At 25 cycles per inch, there would be 450 grab/release cycles per second (18 inches x 25 cycles per inch = 450) – much closer to the 440 Hz for an in-tune “A” string.

I see from Dr. Collin's dissertation that there's a whole lot more going on in the motion of the string and the prodution of pure tone (e.g., Helmholtz motion). Fascinating stuff. Wish I’d paid more attention in science class.

John

November 28, 2009 at 11:14 AM ·

Fortunately, using the bow to produce the desired sound (within limits imposed by the instrument and other equipment) is something which can be learned experientially, or from a good teacher, and it's not necessary to understand the physics in order to produce the result. In fact, scientific understanding at this point does a better job of explaining what musicians can already do, than of providing guidance to players.

In the paper, Collins draws some conclusions from the literature which might not be what the writers intended. For example,

"These five modes are the same on all violins, whether it is a hand made Cremona violin or a factory-made instrument. "

This appears to be a conclusion derived from something Bissinger wrote, and I doubt very much that Bissinger would agree with it. Not all violins have the same number of modes in that region; they don't occur at the same frequencies; the relative strength of these modes varies.

Confounding this further is that while researchers once believed that these lower "signature" modes defined the sound of a violin, more recent research has shown this is far from the full picture.

Bow/string interaction is interesting stuff though. Slow motion studies which go into more detail show slip-stick action other than (in addition to) the motion at the fundamental frequency. This is likely because there are vibrational inputs other than the string. One of these could be motion of the violin body itself, which feeds back through the bridge to the string. Another could be resonances and vibrations  inherent in the bow itself. It should also be considered that even basic isolated string motion (not coupled with a violin or a bow) is a little more complex than this video reveals, with multiple motions at numerous frequencies occurring at the same time.

I think one basic premise of the paper is sound though.... that what's going on at the bow hair/string interface has a major impact on sound, and that a good bit of this can be under the control of the player.

November 28, 2009 at 03:56 PM ·

Thanks John, that's very interesting.  I find it especially surprising how near the d string comes to the g when vibrating at "full" amplitude (i.e. about 40 seconds in).

I don't agree that the violin is necessarily in tune though: "This indicates that the violin was in tune as the 3:2 ratio in the movement of the strings vibration reflects the ratio a perfect fifth (A = 440 Hz D = 294 Hz,  440 / 294 = 1.5)."  I think you're right about the fifth, but I don't think you can infer from this that the strings are tuned to the right pitch, and hence that the violin is "in tune".

Cheers,

Russ.

November 28, 2009 at 04:20 PM ·

David - I spent several hours this morning reading the dissertation carefully and, although I've read many of those terms and concepts over the years, each time I introduce them to my brain more of it sticks.

With that paper logged into my brain now, I get your point that there are many more components that go into tone generation and that several of the author's points can lead to erroneous inferences.  I'm just a sponge and with every new level of understanding, it is good to get a reminder that there's always more to the story yet to be learned or discovered.

I agree that it is fortunate that students of stringed instruments don't need to understand the science behind the sound, but such facts help feed that curious voice in the back of my head that keeps a running commentary as I'm practicing.  I haven't found earplugs that will silence that voice, but lots of reading and listening and thinking about the techniques and science of playing does help keep the inner voice quieter.  I find that I can practice with greater concentration when that voice is contentedly digesting facts.

Russ - Good point. The observation of the 3:2 ratio in the string movement does not confirm that the D and A strings were in tune (i.e., 240Hz and 440Hz), but it does indicate that they were in tune with each other, i.e., an interval of a perfect fifth between them.  Given the amount of distance travelled by the strings, I wonder if they were tuned down an octave to make for better video.

John

November 29, 2009 at 01:20 AM ·

John, - I did some very close observation of the string vibration envelope when we were designing setup gauges for our overseas suppliers. A Dominant violin D string tuned up to pitch will definitely have enough lateral excursion to just about slap the adjacent strings if bowed for maximum volume.  The vertical excursion is much less, maybe 1/4 to 1/3.

November 29, 2009 at 08:55 AM ·

Thank you for this blog.  Very interesting.

Mike Felzien

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