Discovering the Universe of String Vibrations

April 1, 2020, 1:34 PM · I’m no physicist but I have an idea of how the strings and bow hairs interact, and it’s very different now than when I was 10. There is a correlation between what we do with our bows and the sounds we know and love, the warm, lush vibrations that float in the air and fill our hearts. What I know now is inspirational to me, gives me food for thought, and serves as a foundation for lots of experiment.


I look back at my first years as a violinist and saw myself in a rote fog. However, even with my tiny, elementary school mind, I detected there was a glimmer of light at the end of the tunnel, an awareness that something beautiful existed, and that there was a reason it existed. I’m talking about the rich, luscious sound on the G string. In spite of my scrapes and dry sound syndrome, moments of full vibration slipped through. One other thing that gave me hope was the elegant and warm vibrato that my teacher, Billye Cook, played with. I didn’t know what cause-and-effect was, but something inside of me was awakened: a deep frustration with not understanding the violin.

What I knew about the bow when I was 10 were vague notions that could fit in one long sentence: "Don’t use pressure, use 'weight,' know where the sounding points between the bridge and the fingerboard are, don’t run out of bow, relax my wrist, stay in the string, keep my bow straight."

Then the sentence got longer and cleverer when I was 18 and started experiencing various violin camps and colleges: "Use the whole bow all the time (scary theory but there were many true believers), get as close to the bridge as possible in order to fill a big hall, make a circle-eight with the arm and wrist."

When you’re 10, not knowing what you’re doing with the bow is unimportant because you’re barely thinking about it as it is. When you’re 18, the void of not knowing becomes a chasm; you need to think of things that make sense and make a difference. Whole bows and arm choreography were merely making me dread my bow changes and string changes more than ever.

Hope Springs Eternal

Try as I might, I couldn’t come close to getting the warm, spinning tones that my violin was capable of. Fortunately, I had a nagging notion that this process was easier than I was making it. I needed to know how the hairs and the strings interacted, but for many, many years I couldn’t even formulate the question. Studying the violin and music in general teaches us to be extremely patient while we’re searching for answers.

Every answer must be preceded by a question. What I finally asked myself was, "Which factors make the string vibrate fully?" I knew that using the whole bow wasn’t going to help.

Gorgeous tones come from a compound of one beautiful sound building on top of other beautiful sounds. Volume and texture came out of a pure vibration of the string, a simple effect that renews itself with every down-bow and up-bow out of necessity, because the string stops with every bow change. The way the vibrations start anew is called the "engagement." (I need just a moment of patience to wait for it to happen. Like a gentle touch or kiss, it’s microscopic and meaningful.)

My experience of trying to create with my playing what I heard in my inner ear was more challenging than a dog chasing its own tail. When I hear Szeryng, Perlman, Frang, and Ma, even nature has a hard time emulating such beauty. The warmth of a violin, exceeded only by instruments with thicker strings, is lovely to behold. When you add the musical flow of an exquisite phrase to a blossoming sound, it just keeps getting better and better. To have a goal of recreating beautiful tones on the violin makes us very lucky.

A Safe Environment for the Strings

We evolve in our thinking about how the strings and the hairs interact. What started as two hard surfaces traveling in tandem at 180 degrees becomes a large vibrating string in a union with a flat bed of horse hairs. At this point in the explanation of beautiful sound, the science of dry physics takes a back seat to verbal images and good old-fashioned trial and error. How do we explain the working of the hairs? How do our minds reconcile seemingly incompatible bedfellows?

The main job of the hair is to provide an environment in which the strings can vibrate fully. The idea of pressure from the bow onto the string contradicts what actually needs to happen. In lieu of a physics treatise on what is in reality taking place, my musical mind accepts the illustration that the hair acts as a vacuum cleaner. Absorbing strings of four different thicknesses makes us gauge and plan accordingly. This explains why playing the G string demands a lighter touch than playing the E string. Part of our trial-and-error exercises is to understand this concept: Pushing into the string is a losing battle, but absorbing it pays great dividends.

Three Sound Relationships

There’s a triangular relationship in my music studio, with the presence of a violin, a piano, and a very tonal chime made of black metal. I might add that sitting next to the violin case on the window seat is a viola. So it’s really not a pure triangle; the viola made it a geometrical figure as yet unidentified.

It finally occurred to me how similar the relationship of the violin’s hair and strings is to the felt on a piano hammer and the piano’s strings. The more that the felt can absorb the string, the more beautiful the sound. When the felt gets old, dry, and hard, a technician can put pins in it to spread the felt and bring it closer to its original condition.

What can I say about a hard chime emitting warm tones when it is struck? To the human eye, there’s no felt, no strings, and no flesh involved, like in plucking harp strings. However, something is being "absorbed" and vibrated. (I guess.) Even though I can’t say what physics underlies it, I still learn a lot about the violin by thinking about the chimes. The spontaneity factor also applies to both instruments. Violinists need a healthy dose of the decisive, on-the-beat attitude that percussionists have.

So how does the viola figure in this "triangle" of musical instruments.? It serves as a reminder that beauty lies in abundance. The thicker the string the richer the possibilities. What we must never forget, however, is that the slimness of the E strings can be gently manipulated to produce shimmering results.

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April 2, 2020 at 12:33 PM · Thanks for writing this, Paul. It was a delightful and interesting read.

April 2, 2020 at 12:52 PM · Beautiful article! You wrote, "Absorbing strings of four different thicknesses makes us gauge and plan accordingly. This explains why playing the G string demands a lighter touch than playing the E string." This may change my life! I have been doing exactly the opposite. I can't wait to practice today and try what you've discussed.

April 2, 2020 at 01:46 PM · There is always a balance between letting it happen and making it happen. (One reason, among many, why pianists who take up a stringed instrument later in life find it surprisingly difficult. On the piano, everything is pretty much "making it happen.") On the viola, the balance is shifted even more toward letting it happen, I find, which has implications for all aspects of bowing: sound point, pressure ("weight") and bow speed. I would say anyone who is struggling with tone on the violin's G string just needs to try the viola for a month.

April 2, 2020 at 04:38 PM · Thank you, Jane! Diana, Have a good practice today. I’ll be trying out something my teacher Broadus Erle recommended. Start with a focused, thin sound, then build it gradually but steadily until it’s full and vibrant. Paul, the balance you talk about reminds me of the importance of listening. A sound is only as good as it relates to the sounds of the other musicians. Unfortunately, some of the most gorgeous sounds are in their own universe. Working on tonalization gives us the ability to blend and to be the solo voice when necessary.

April 4, 2020 at 06:09 PM · Thanks Paul. Physics experiments show that for the bowed string, it doesn't do what we see; flop sideways, but, makes a kink in the string that travels length-wise out and back. So my mental trick of guiding the bow through an imaginary groove in the string is not so far-fetched. The cheapest thing in the case actually produces the sound; the rosin! Rosin is the glue that grabs the string. If you get a bow rehair back without any rosin you find out that without rosin the bow produces little sound. I try to get the maximum amount of the fundamental out of note, and let the equipment, the violin and strings take care of the overtone spectrum. I think of the violin as an instrument that needs balance; it is too easy to crush the sound. My Viola I call a recalcitrant donkey. I can keep pushing it and never hit bottom. But then, I have never owned a quality Violin or Viola.

April 5, 2020 at 03:02 AM · Joel, I resonate (so to speak) with your idea of guiding the bow through an imaginary groove in the string. That’s exactly what it feels like, but it’s hard to explain that to someone who is coarsely chopping his way through the string. I paraphrase what Carl Flesch said about the rosin and the hair: The rosin makes tiny particles stick out from the hair at 90 degrees. Hence, if the bow is gliding perfectly horizontally, thousands of little guitar picks will pluck the string. He said that in the 1920s. I never heard that from anyone since. It makes so much sense.

Can you please explain what “flopping sideways, but makes a kink in the string...” means?

April 5, 2020 at 04:51 PM · continued,-- In illustrations we see the string vibration as a shallow arc on each side of where the string is, when at rest. But what actually happens is that the bow forces the string into a kink, like a shallow sawtooth, this displacement travels out to the nut, bounces back to the bridge, once for each cycle; 440 times/ second for the open A. Hope that make sense. Is the hair just a carrier for the rosin, or does the rosin make the hair work better ? I'm not sure about that. I have some cheap bows that are not worth re-hairing, so after years of use, I just use sticky cello-grade rosin.

April 5, 2020 at 09:46 PM · It does make sense, Joel. All in all, I find the hairs and string to be one of the most efficient forms of energy.

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