Where are they?
In theory of music and sound an overtone is a musical tone which is a part of the harmonic series above a fundamental. This tone, the overtone, however, does not exist on its own. Per definition the overtone exists only because of the existence of a fundamental, and although it exists no one consciously cares if it is there or not. I can also argue that the Fundamental without the overtones is not really a Fundamental (a fundamental to what?). And, I also believe that the fundamental needs the overtones just about the same as the overtones need the Fundamental.
The Fundamental alone, without any overtones, is synthetic and often referred to as a pure tone. In the real world, you may hear a pure tone in the form of a busy signal when you call a friend or the sound of a dump truck reversing its course, but not as a sound that was produced naturally by an instrument, a human, an animal or as a result of some natural process or event.
The overtones are a natural harmonic sound derivation of a fundamental frequency’s acoustic excitation. In the case of a plucked tensioned string, the overtones are all those other frequencies present in the sound produced that shape its color and without them, the sound produced is monotonous, flat, a pure toned stimulus. If that tensioned string is on a guitar for example, the overtones carry more than just the fundamental frequency. They bring forth all the extra information needed by the listener to interpret it to its own liking like the type of wood, the build material of the string, the size of the neck, the stiffness of tuning machines, the strength of the pluck, the duration of the sustain, the hand’s attenuation, the varnish, even that crack on the front that has been there ever since the guitar was dropped.
Removing the majority of the harmonics from the recording of the lowest E note on an acoustics guitar leaves the intended Fundamental almost inaudible. What is interesting to me is that when separated and played along or against the fundamental, the sounds produced can be both consonant and dissonant. What humans perceive as sound is the summation of consonant and dissonant contributions from the overtones to a fundamental excitation.