Is it possible to have beautiful tone and play out of tune?
Not on the violin, viola, cello or bass. And the physical proof lies not just in our ears, but in the science of acoustics.
John Burton, cellist and music professor at the University of Texas at Arlington, explained how the physics of sound relates to good tone in a lecture about "Resonance, Intonation, Tone: The Secret to Playing In Tune" at the 2015 ASTA conference in March. Introducing the subject, he asked how many in the audience of about 30 music teachers had ever taken a class in acoustics, and only three in the room raised their hands. (I was not among them!)
Though string players tend not to have formal education on the subject, the science of acoustics lies at the heart of what we do and how we do it.
"When you are playing the violin, viola, cello or bass, you're playing a complex standing wave," Burton said. "We have the ability to be very discriminant, when it comes to intonation."
Playing with good tone involves producing sound waves that resonate with the instrument and its strings -- it involves precision of pitch and just the right amount of force and motion with the bow.
What exactly happens, when a string player bows a string? In terms of physics: when the string is still, it is in equilibrium. The force of friction from the bow disrupts that equilibrium and makes the string move. Watching a down-bow in super-slow-motion: the bow moves the string a tiny bit to the right, then the "restoring forces" of the string make it break free of the bow and snap back to the left. These happens over and over, as the bow moves across the string, constantly grabbing and releasing it along the way.
The string resists the force of the bow; it wants to be in equilibrium. If you were to simply pluck a string once, it would vibrate but then return to equilibrium. The bow, by contrast, sets up a continuously oscillating system, whereby the string is "plucked" hundreds of tiny times and kept in vibration by applying that friction continuously from the bow.
The length of the string determines the pitch at which it vibrates. When we put down a finger to make a note, this in effect shortens the string to change the pitch.
The vibration from one string can set into motion other vibrations, and this is called "resonance." It happens on our instruments when, say, you play the note "G" -- third finger on the D string. When played perfectly in tune, the vibration of that "G" will also set the "G" string vibrating. In fact, it could also set anything in the room that is tuned to a G -- a string inside a piano, a string on the mandolin on the wall -- vibrating. If you hit a tuning fork, and another tuning fork set to the same pitch is sitting across the room, it will likely vibrate in sympathy, or "resonate."
"Anything tuned to that pitch should vibrate," Barton said.
But consider this: the "complex standing wave" that is a string produces many frequencies, not just that "G." The "G" is called the "fundamental frequency," and that's primarily what we hear. But because of all those vibrations, many other notes are present, and these are called "overtones," or the "harmonic series." The overtones are not quite as audible, but they can be magnified if they resonate well with another string or with the wood of the instrument (or even that pitchfork across the room).
Each note has its own set of overtones, and the overtones for any note follow a pattern, based on physics. The overtones of a vibrating string are 1/2, 1/3, 1/4, etc., of the string's "fundamental" wavelength. For us musicians, those fractions represent notes that are certain intervals above that "fundamental" note. They always follow a pattern (look at this chart from bottom to top):
So in this case, the G would be called the "fundamental" wavelength, and the overtones are portions of that wavelength and would produce the additional frequencies at higher octaves: G, D, G, B, D, F, G and it goes on.
What's remarkable, and what I did not know, is that you can see this phenomenon! With our instruments right under our chins and with the vibrations so high and small, we don't have as much opportunity to watch, but on a cello, the demonstration is a real revelation. So for the cello, let's talk about the note "C." Here is the "harmonic series," or the overtones, that are produced by the note "C", this time written as music:
"When I play a 'C,' those harmonics are present in the sound," Burton said. We mostly hear the fundamental (the C), but we also hear a lot of other vibrations: The "C" that is an octave above, the "G" a fifth above that, the next "C" a perfect fourth up, an "E" a third above that, and this continues for some 16 fractions of wavelengths and beyond. Those overtones can be magnified if they resonate with another string.
Barton showed that when he bows the "C" string on the cello, the overtones cause the "G" string to resonate, because G is an overtone (the "third partial") of C. Looking up close, one can see the "C" string vibrate, and also, one sees that the "G" vibrates. Interestingly, it vibrates in a way that looks a lot like the third example up on the wave chart: at two points of amplitude. Since I was sitting at the front of the class, I got to go up close and look at the string, vibrating in those two places. Physics in motion, check it out!
So not only can you make another string vibrate sympathetically with a specific note, but any of that note's overtones can also set a string vibrating.
This science demonstration has some implications for what we call "good tone" on our stringed instruments. Basically, "we're trying to create resonance on our instruments," Burton said. The best players make their instruments resonate as much as possible. And science shows us that our instruments resonate when we create pitch in a way that gets the overtones to ring.
"Resonance happens in two directions," Burton said. "If I play a fundamental, the notes that are predisposed to vibrate at that frequency will vibrate." On a cello, playing the note "D" on the C-string will cause both the D and A strings to vibrate, because those notes are overtones (the second and third partials) of that D.
It also happens in reverse: if you play a note that is an overtone, you can make the fundamental resonate. For example on the violin, a well-played "D" on the A-string might cause the G-string to resonate because that "D" is an overtone of "G."
Of course, this does not happen with every note on the instrument.
"All notes are good on cello, but some notes are gooder than others!" Burton joked. Not every pitch will have a harmonic series that relates to the instrument's strings.
Burton pointed out some really cool stuff on the cello, like: If you play a high G, then the G string will vibrate in four equal lengths, something you can feel better than you can see. Also, the vibrations on the G string have two points of amplitude, when you play the "G" that is one octave higher. You can also finger a note to make the string vibrate in sympathy with another note on another string.
Though these phenomenon are integral to the violin as well, they aren't as easy to demonstrate because "the shorter the string, the greater the tension, and the harder it is to see," Burton said.
Suffice it to say this: "intonation and tone are synonymous," Burton said. When you play a note that is even slightly out-of-tune, "it's dead, it has no ring," he said. An out-of-tune pitch will not set any of those resonances in motion. If one plays pitches, with no awareness or feeling for resonance, it's very hard to find the voice of the instrument. "The more I can drill the sound of this cello, associated with the resonance of these notes, the more I can teach pitch."
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