Even the F# is a resonant tone!
Learning the physics of violin playing.
When I started playing violin in December 2020, I felt like an explorer getting into a rocket ship. I was alone with my cat, isolating for 2 weeks in the hope of safely driving home to Portland for the holidays. As I fumbled around with the screeching sounds of my new instrument, wondering how I was ever going to play in tune, I noticed something:
The violin itself teaches you how to play in tune.
For anyone curious, I’ll try to explain. The physics concepts you’ll need to understand are 1) sympathetic resonance and 2) the harmonic overtone series.
Sympathetic resonance is what happens when you sing the right note and break a wine glass. It’s the tendency of a passive string or chamber to vibrate if the correct frequency is vibrating in the air around it.
So if there’s a loud enough “G” in the air around the G string on a violin, the string will begin vibrating on its own.
What this means for the violinist: any fingered note on the violin that matches an open string (G, D, A or E) can be tuned to the open string. You can tell it’s in tune if the open string is vibrating freely, even when you’re playing on a different string.
There in my studio apartment in the middle of Covid, I put my 3rd finger down on the A string, bowed the resulting “D”, and wiggled my finger in search of the correct pitch. When I got it in tune suddenly the whole instrument lit up. The adjacent open D string started vibrating almost as loud as the note I had bowed, even though I hadn’t touched it. The sensation is like a glow surrounding the note - you hear the note you’re playing, and then you hear this extra, pure cloud of sound coming from the instrument.
If you’re a hair sharp or flat, the open string does not ring sympathetically. Nature doesn’t care how close you are to in-tune - there’s no “good try!” The vibrations match, or they don’t.
You don’t need perfect pitch to play that note in tune. You need sensitivity to find the sympathetic resonance - and then of course, a lifetime of practice to put your finger down in the right place on the first try.
Dr. Suzuki called these notes “ringing tones” and they’re a huge part of the magic of acoustic string instruments. When you play in tune, it’s like the whole instrument agrees with you and sings along.
And the “ringing” doesn’t just apply to G, D, A, and E.
The harmonic overtone series is a sequence of pitches produced by a freely vibrating string. When we hear a “G” on a vibrating string, we’re actually hearing a bunch of different frequencies contained within that note. We hear G: the fundamental frequency, whose wavelength is the full length of the string. We also hear a series of higher pitches whose wavelengths are perfect fractions of the string. G one octave higher; D; G two octaves higher; and so on, until you get notes like B, and an F that doesn’t quite match the F on the piano. (See diagram above.)
This series comes up all the time in music. It matters here because it’s not just G, D, A and E that ring on the violin. All these other harmonic notes will also ring sympathetically on the open strings - sometimes very faintly, like little ghostly voices.
It came up in my lesson this past week. Ms. Shimizu asked me to question my F#5, first finger on the E string. It sounded a little sharp to her.
My ear has developed around piano playing: all you need is to distinguish between two keys on the piano. That distance can be described as 100 cents. Meanwhile the distance between in-tune and out-of-tune on the violin is about 2 cents. So I’m gradually learning to listen more sensitively. It turns out, I tend to play F# a little too high when I rely purely on my internal sense of pitch. But Margaret pointed out a certain “ringing” sound the instrument makes when the note is in tune.
Why? We both asked. That’s not a resonant tone!
Or is it?
After some experimentation we found that the D string - more than two octaves below the note in question - was ringing sympathetically when the F# was in tune. All we heard was a ghostly echo coming from the body of the instrument. But it was, in fact, the 5th harmonic of that open D. A little voice from the instrument confirming, “yes, your F# matches mine!”
So now I have a new tool when I practice intonation: when I play F#5, I can listen for that faint, shiny sound of resonance with the instrument. The violin itself will train my ear and my fingers to play in tune.
Of course, this is all ignoring the fact that there’s more than one F#5. But that’s a topic for another newsletter.
Until next time,
Ted