# Can a harmonic be louder than the fundamental frequency?

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1. Apr 13, 2015

### Jon.G

This is not a homework question per se, but rather something I have come across during a homework project. Using Audacity, I recorded a few different instruments playing the same notes (investigating timbre). I noticed that (using a steel string acoustic guitar) the first harmonic at 131 Hz (~C3) peaked at a decibel value of -34.5, whereas the second harmonic at 263 Hz peaked at -12.4 dB. I didn't see this happen for other instruments.
I was under the impression that the fundamental frequency would always be the most dominant component. Will it just be the string/body resonance that causes this? If so, could you try and help me understand it a bit better. and if not please help me understand why this occurs :)

Thanks :)

2. Apr 13, 2015

### BvU

My estimate is that it's more a matter of where the string is plucked: in the middle the fundamental frequency is favoured, more near the ends higher harmonics get a chance. Extreme case: pluck very close to the bridge and you'll get a high frequency.

3. Apr 13, 2015

### Jon.G

You're right, I didn't think of that :) I read this and quickly recorded the same note a few times but plucking at different points and it definitely has a noticeable effect on the relative intensities of the spectrum.
If I remember correctly, plucking at L/n should remove every nth harmonic (in an ideal environment, I'm sure this won't happen perfectly in practice for me :P )

4. Apr 13, 2015

### collinsmark

In nature, the higher harmonics certainly can be "louder" than the fundamental, and often are, depending on the instrument, and how the instrument is played. There is no rule which says the fundamental must be dominant.

As an experiment, you can isolate the higher harmonics by using this method: Pluck the strings as normal with one hand, but use your other hand to "mute" the strings at certain intervals such as L/2, L/3, L/4, L/5 or whatnot. You'll see what I mean. [Edit: to do this, very gently place your finger atop the string such that your finger barely touches it. Don't squeeze the string; that's not what I mean. Just hold your finger to the string in the right place, so that it barely touches. Immediately after plucking the string, remove your "muting" finger, and let the harmonic ring.]

This technique is often used in music . As an example it is used, in part, in the introduction to this song (Band: Yes, song: Roundabout)

Furthermore, there are instruments that rely completely on harmonics to differentiate pitch. One such instrument is the bugle. The bugle has no keys, no finger-holes, nothing to induce a particular note, besides the way the player blows into the thing. All tunes played on the bugle are simply formed from harmonics.

Using the method I described earlier of plucking a single string with one hand and muting the string with your other hand at L/2, L/3, L/4, L/5 and such, you should be able to play this tune on a single string, without even "fretting" the string:

Last edited: Apr 13, 2015
5. Apr 13, 2015

### collinsmark

By the way, this method of using harmonics is also a good way to tune up your guitar, at least to itself, to standard tuning, if you don't have an electronic tuner around.

Get a harmonic going by plucking and lightly touching (and immediately releasing) the first string, seventh fret (the 7th fret is L/3) and again with the second string at the fifth fret (the fifth fret is L/4). These should produce the same note. Listen for beats and adjust the tuning knob accordingly.

You can use this process all the way up the neck, to get all six strings in tune with each other, with the exception of the second and third string, where you will have to fret something.

This method is nice, because it once the harmonics are produced, it frees up both hands to adjust tuning knobs, except for that one string (when comparing the second and third string).

(Of course as mentioned, this method only works verbatim for standard guitar tuning.)

[Edit: and conceivably you could get around this limitation with the second and third string using the following technique. Get the first string and sixth string in tune by muting the sixth string at the 12th fret (L/2) and compare that to the first string, plucked, but not muted, near the twelfth fret. That should produce the same note (an E). Then tune up the second string using the previously method. Then, go backwards tuning up the 5th string, comparing it to the 6th string, using harmonics. Repeat for the 4th string comparing harmonics to the 5th string, and again to tune up the 3rd string.]

Last edited: Apr 13, 2015
6. Apr 17, 2015

### Jon.G

Wow, thanks a lot!
Some very interesting points there. I knew about "muting" the strings at the different intervals but never really make the connection :P

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