Posted by: laurie689 | November 22, 2017

Overtones, Sympathetic Vibration, and Resonant Frequency

Recently there was a discussion on one of the music list-serves regarding overtones. There seems to be some confusion about what they are. Many were confusing them with sympathetic vibration, when in fact they are not the same. Here’s what the difference is: sympathetic vibration is when a vibrating object causes other objects to vibrate, whether or not they are touching. Hence, in the case of something such as a plucked string, other strings sound because they pick up the vibration. Or some unrelated object vibrates in response to a musical tone. Some people call this “resonant frequency” – certain objects will vibrate at the same frequency because their density or materials are “sympathetic” to that specific frequency.

Musicians certified to play in therapeutic/medical settings often use the concept of resonant frequency, noticing what notes seem to feel best to a patient and then using those notes predominantly in the music they offer to that person. In that case the science is not exact, as there is no way to measure how or why each individual responds physically or emotionally to certain tones. We do know that it often works very well; patients usually report a feeling of well-being, or we see improvements in vital signs among patients who are seriously ill. (That is not, by the way, the only skill therapeutic musicians are taught  –  it’s just one of many.)

Sympathetic vibrations are transmitted through the air or through matter. In fact, the vibration of a soundboard on an acoustic stringed instrument could be called sympathetic because the vibration is transferred through the material of which the instrument is made  –  the string is attached to the soundboard in some way, depending on the instrument, and that material responds, its vibration transmits the sound of the string into the air chamber of the soundbox, inside which it increases, thereby making the soundboard vibrate even more. This amplifies the sound (a plucked string is not nearly as loud as one attached to a soundbox). But usually the term ”sympathetic vibration” refers to another string or another object vibrating in response to a tone.

Sympathetic vibration can be annoying if something in the room is vibrating, or when something on the instrument itself is buzzing when you pluck a string. Identifying the offending part or object can be challenging.

On the other hand, some of the pleasant uses of sympathetic vibration are those such as sympathetic strings on a nyckelharpa or a Hardanger fiddle. Their resonance makes these instruments sound like they are being played in a cathedral. (Some of their richness is from sympathetic vibration; some is from hearing overtones and undertones.)

Not to be confused with sympathetic vibration or vice versa, overtones are the spectrum of sound one plucked string makes on its own – including above, below, and within the range of human hearing. We subconsciously train our brains to be aware of just the fundamental tone, and we usually don’t notice the overtones because we are listening for the fundamental. But you can tell the difference between an instrument that has a “rich” sound (lots of overtones) and one that does not. The richness or lack of richness of an instrument may or may not be due to how well it’s made, but some are purposely made to emphasize just the fundamental note. Some people prefer them; others prefer richness.

You can listen closely to a plucked string – probably in the mid-range is easiest – and see if you detect more than one note. The overtones will be very subtle. You can prove, however, that they do exist by making harmonics. Most string players know how to create an octave harmonic by gently touching a string in its exact enter and plucking it at the same time; if you do it just right you get a note an octave higher than the note the string is tuned to. Fewer realize that you can also easily get fifths and thirds or octaves plus fifths and thirds by touching the string in various other spots. Experimenting with this is fun. The tones will “mirror-image” on both sides of center. What you are hearing are the overtones that are present whenever a string is plucked. The reason you can hear them now as the main note is because you have stopped the fundamental note from sounding, so they are no longer disguised by its relative volume.

Pythagoras said that all notes are contained within a single plucked string. He experimented with a one-stringed instrument to find and document that all chords come from harmonic mathematics, and the diatonic and chromatic scales do as well, because ideally (though not usually in actuality because it’s impossible to make a perfect string or soundbox) one plucked string produces all notes.

That brings up the subject of undertones. These are lower than the fundamental note, but occur for the same reason that overtones occur. There is argument about whether undertones exist. They do; they are just much harder to produce audibly.

For more detailed info see my book “Singing the Universe Awake” on the
books page of my website at www.laurieriley.com


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