Final answer:
Harmonics are integer multiples of the fundamental frequency, with the first harmonic being the fundamental. Overtones are frequencies above the fundamental, with the first overtone being the second harmonic. Not all overtones are harmonics as the term 'overtone' includes all resonances above the fundamental.
Step-by-step explanation:
The difference between harmonics and overtones lies in how they relate to the fundamental frequency of a sound. Harmonics are all integer multiples of the fundamental frequency. The first harmonic is the fundamental itself, the second harmonic is twice the frequency of the fundamental, and so on.
Overtones, on the other hand, are all the frequencies above the fundamental. The first overtone is the second harmonic, the second overtone is the third harmonic, and this sequence continues accordingly.
Therefore, while all harmonics (aside from the fundamental) are overtones, not all overtones are necessarily harmonics, as the term 'overtone' is used generally for any resonance frequency above the fundamental.
To clarify, let's consider musical instruments. When a note is played on any instrument, it produces a complex sound consisting of the fundamental frequency and a series of overtones.
These overtones contribute to the timbre or tonal color of the note, making each instrument sound unique. It's the specific combination of overtones that give instruments like the trumpet and clarinet their distinctive sounds even when playing the same fundamental note.