# Why does a harmonic still sound even though you lift your finger?

I have been experimenting with harmonics lately on my cello and found that the harmonic still sounds when you release your finger. Why is that? I know how to not let it sound (by plucking it) but why does it sound?

• Leave harmonics out of if: When you pluck a string normally, it continues to sound after your pluck is finished. Why? Commented May 30 at 17:58
• Do you mean that you're using the bow, finger on the string for the harmonic, and then lift the finger off the string while continuing to bow, and the harmonic continues to sound? Commented May 30 at 18:52
• @Stinkfoot It seems clear Andy's asking why the freed string doesn't collapse to the fundamental. Commented May 31 at 21:29
• @MichaelCurtis - No, What I mean what is stated in '@'Edwards's answer: There is no reason why it should stop vibrating at the harmonic frequency with removal of the finger, since it was set it into motion to vibrate at that frequency, just as when you pluck a strong normally. Commented Jun 1 at 17:46
• @CarlWitthoft. it seems clear... Perhaps to you it seems clear, but your point is not at all alluded to in the question, nor does it make sense that it should then vibrate at the fundamental. It should simply continue to vibrate at the frequency it started at. See my comment above to Michael Curtis, and Edward's answer, which is quite correct and should be accepted, IMO. Commented Jun 1 at 17:53

I'll attempt some clumsy ms-paint illustrations.

When you play the string, it vibrates:

When you put your finger on the string as normal to stop it, only the part between your finger and the bridge vibrates.

When you play a harmonic, though, the part of the string "behind" your finger vibrates as well!

If you pluck a harmonic and then immediately remove your finger, the harmonic will keep ringing until the sound fades away, because you've set these two sections of string moving in waves, and their momentum will continue moving them like that. (In fact, you can often get a brighter and better-sounding pizzicato harmonic by removing your finger like this.) If you bow a harmonic, and then remove your finger while continuing to bow, then after a while the harmonic will turn back into the fundamental, because as you bow, the string is repeatedly "plucked" by the friction of the bow. The harmonic continues for a while because of momentum, but eventually the wave pattern as these new impulses act on the entire string, and you're back to the first diagram.

Disclaimer: not only are these drawings crude, but they're vastly simplified representations of the way the string really vibrates. At the risk of getting in over your head, see this question and its answers for a much more detailed look at the motion of the string.

• The harmonic doesn't necessarily "collapse"; it's present in the normal tone; it's just that the fundamental overwhelms it. Touching the string lightly at the center suppresses all the odd harmonics, including the fundamental, leaving the second harmonic as the dominant mode of oscillation. If you remove the finger as you bow the string, the odd harmonics return, but the even ones don't go anywhere. Commented May 30 at 0:48
• @phoog, the odd harmonics returning includes the fundamental? Commented May 30 at 18:54
• @MichaelCurtis yes, the fundamental is the first harmonic. Commented May 31 at 0:20
• @phoog might add that touching a higher harmonic node forces only those harmonics which "fit" into both parts of the string, e.g. 1/3 + 2/3 suppresses anything that isn't compatible with 1/3 string length. Commented May 31 at 21:31

Why should we expect it to stop ringing?

A natural harmonic is a mode of vibration of the string. Just like vibration in the fundamental mode and every other mode, the string will continue vibrating unless you do something to stop it. Removing your finger does not stop it because placing your finger there was never required to produce the vibration in the first place- it was required to prevent other unwanted modes of vibration.

Plucking the string does not actually stop the harmonic from ringing, except maybe briefly while your finger touches the string. After being plucked, the harmonic will sound again*, along with several other modes of vibration that were not present before.

You could probably learn a lot from the typical physics 101 string oscillator demonstration- which demonstrates several modes of vibration of a simple string oscillator by driving the string at certain frequencies. A cello string is approximately a simple string oscillator.

*Technically, if you pluck exactly at the right spot, you can avoid exciting a particular harmonic.

• "Why should we expect it to stop ringing?" - Because, intuitively, us humans build tools to do only do what we "tell" them to. If I push button A and B at the same time, and I release button A, I expect A to no longer perform its function. The fact that physics here offers additional functionality is not obvious until you understand the physics itself. Commented May 30 at 4:20
• @aggregate1166877 Have you ever had a car accident? A car is a tool for moving along a street, drive where you tell it, and stop when you tell it. But go into a curve too fast only once, and you'll experience that it does not drive where you tell it to go! Above all, a tool must be feasible to build and function with justifyable effort in order to even exist. Otherwise, we'd already have a space elevator... Commented May 30 at 13:52

Once the string (be it violin, cello, guitar, whatever) is touched on a node, the string will not vibrate at that point. So a harmonic is produced. Take the finger away, leave it there, it makes no difference at all. That point is where the string doesn't move, so why should there be any difference whether the finger is still there or removed?

A lot of guitar sites say take away that finger straight away, but there's really no point - there's no vibration there in any case, so even placing it back on the node will make no difference - the sound will continue!

• Btw the OP didn’t specify, but I’m guessing they’re thinking of “removing the finger while continuing to bow,” which is a different matter from a plucked string. Commented May 29 at 23:58
• Leaving the finger there wouldn't make any difference if the fingertip was a sharp point positioned exactly where the node is. However real fingers are soft, thick and imprecise so leaving the finger there longer than necessary will make the note die faster. If you continue bowing after lifting the finger, is the fundamental frequency somehow still muted?
– ojs
Commented May 30 at 16:09
• @ojs - I was considering from a guitar point of view, where the finger can be left, or returned to the spot with absolutely no problem at all. May be different on cello - may depend on which harmonic is in question - as the window gets smaller as we move up to higher harmonics. However, the same phenomenon occurs with sax, when a harmonic is sounded rather than the required note, going off subject somewhat.
– Tim
Commented May 30 at 16:38
• Yes; my point to this and Edward's "why should you expect it to stop" response is that if you continue bowing, you'll get the fundamental again within a couple of seconds. The OP, I think, is just surprised that it isn't instant. Commented May 30 at 18:33
• @AndyBonner interesting, it never occurred to me to try but it really happens
– ojs
Commented May 30 at 19:06