Why aren't all overtones integer multiples of the fundamental?

[cscott]

When plucking a string on an instrument, are all the overtones heard produced by the string itself (assuming all other strings are muted)? Would plucking the string without muting the others make a significant different? Another thing, why aren't all overtones integer multiples of the fundamental?

Thanks.

 

[Hurkyl]

Another thing, why aren't all overtones integer multiples of the fundamental?

Because real-world strings aren't idealized strings.

 

[brewnog]

When plucking a string on an instrument, are all the overtones heard produced by the string itself (assuming all other strings are muted)?

No. Not all are heard, and many of the overtones are produced by the instrument itself; this is one reason why a cello sounds different to a banjo, for instance.

Would plucking the string without muting the others make a significant different?

'Significant' here isn't really quantifiable. I can hear the difference between a plucked string with the others open, compared with a plucked string with the others muted, on a guitar. Some people might not be able to. It also depends which note is being plucked; if you pluck the bottom E on a guitar, it will cause the top E to resonate too. Same with a piano, except there are a lot more strings to set in motion.

 

[Rach3]

Another thing, why aren't all overtones integer multiples of the fundamental?

Just to be sure, you are aware that the usual scales are essentially exponential in frequency? I.e., the 2nd harmonic (at the 12th) is in fact an integer multiple - thrice the frequency of the fundamental, or 1/3 the wavelength. The pure harmonics are all at integer multiples of the fundamental frequency.

 

[rbj]

I.e., the 2nd harmonic (at the 12th) is in fact an integer multiple - thrice the frequency of the fundamental, or 1/3 the wavelength.

we would call that the "3^rd harmonic". some might called it the "2^nd overtone" or "partial". but it's a pretty solid convention that the "1^st harmonic" is the fundamental.

The pure harmonics are all at integer multiples of the fundamental frequency.

true, but not perfectly true. when we use the term "harmonic" we mean an overtone or partial with instantaneous frequency that is virtually an integer multiple of the fundamental frequency at the same instant of time. but in "quasi-periodic" tones, the phases of the harmonics (relative to the fundamental) might well be changing in time (as well as the amplitude) which will detune them slightly from their perfect harmonic frequency value.

"partial" means any sinusoidal component of a tone (including possible subharmonics) and "overtone" means a partial with frequency that is higher than the frequency perceived to be the pitch (which is usually the fundamental). "harmonic" means any sinusoidal component with instantaneous frequency that is virtually equal to an integer times the fundamental frequency.

you can look up "Additive synthesis" at wikipedia to get a little more.

 

[wywong]

Another thing, why aren't all overtones integer multiples of the fundamental?

The stiffness of the string causes overtones to be slightly sharper (higher frequency). Please see page 4 of

"[URL

That document is about piano but the same principle should apply to all string instruments.

Wai Wong

 

[rcgldr]

overtones heard produced by the string itself

for most stringed instruments, the string generates very little sound on it's on. It's purpose is to vibrate the instrument, like the sound board on a guitar or the frame of a piano. In the case of an electric guitar, the pickups sense the vibration of a string and this electronic waveform is amplified. In the case of a midi guitar, a pulse is sent through the string and back (at the pickup end), and is timed to determine the desired frequency, the actual string frequency is ignored in this case.

 

[cscott]

Wow, thanks a lot. That cleared up every freaking misconception I had :P

 

[string querry]

Guitarist Point of view

I'm an amateur with physics, but an expert on guitars. The main reason that a guitar string sounds different if the other strings are muted is simply that unmuted strings are resonating, which apart from possible mathemtaical models for estimating the results, is just a fancy way of saying that every action has an equal and opposite reaction. Vibrating molecules that bump the other strings will cause them in turn to vibrate, primarily at their own tuned note, thus they in turn create their own sound vibrations. Incidentally, some modern virtual instrument synthesizers, especially grand piano samplers, add the reasonant sounds of other strings to the note played in order to more accurately simulate the real instrument.