Ever wondered why different instruments sound different even when they’re playing the same pitch? Worry no more young pupper. The answer lies in the timbre of the instrument (pronounced tam-ber). Basically, every pitch has harmonics. The pitch that dominates, the one your eyes and tuners hear, is called the fundamental frequency
This is easily visualized with string instruments. In the case of a guitar, the fundamental frequency is when the string is moving up and down like a jump rope. The two ends are anchored and the entire string moves up and down together. The second mode of frequency looks like an entire cycle of a sine wave, with the two ends anchored and the middle stationary as the first half and second half are moving up and down in opposition
This mode of vibration is one octave higher than the fundamental frequency. That is, if the fundamental is a C, the second harmonic is also a C but an octave higher
Each note technically has infinite harmonics. A “node” is a point that stays stationary. The fundamental has 2 nodes, for example. Here’s where it gets cool
Any time you hear an instrument play a note, you’re actually hearing the fundamental frequency as well as several other modes of vibrations or “undertones.” You can think of the sound you hear as a linear combination of those different modes of vibration. The timbre of an instrument is how much of each of those frequencies you hear
So while one instrument may have 80% fundamental frequency, 15% first harmonic, 5% other for a certain pitch, another instrument may only have 60% fundamental and higher percentages of the harmonics. This is also why human voices sound different, why a dog sounds different from a cat, etc.
BUT WAIT THERES MORE
Harmonics are used when playing guitar to make really cool sounds. If you pluck an open string, but gently restrict the middle of the string as you do so, you can force the first overtone to be strongly represented (because the fundamental frequency requires the middle of the string to move up and down). This also forces all odd numbered overtones and restricts all even numbered overtones.
If anyone has seen August rush or seen people slapping/tapping the strings instead of strumming, they are using harmonics. Here’s a sexy guitar solo filled with harmonics:
The gif below shows what this combination of frequencies can look like. The bottom is the magnitude of each harmonic and the top is the resultant wave.