# What is 'harmonic likeness'?

While reading about sympathetic vibrations/resonance, I came across the term 'harmonic likeness'.

Sympathetic resonance or sympathetic vibration is a harmonic phenomenon wherein a formerly passive string or vibratory body responds to external vibrations to which it has a harmonic likeness.

What does it exactly mean?

For example, if you pluck the fifth string (bottom to top) of a guitar it vibrates in a superposition of numerous modes (harmonics). The frequency of the nth mode is $n\cdot 110$, where $110\, \mathrm{Hz}$ is the frequency of the fundamental mode. Then this will make the 6th string to vibrate as well. This string has a fundamental frequency of $82.4\, \mathrm{Hz}$ so its 4th mode will be in resonance with the 3th mode of the 5th string since both have approximately the same frequency, namely $330\, \mathrm{Hz}$. This is called harmonic likeness. The effect is a bit hard to notice in an acoustic guitar since those third and fourth harmonics have small amplitudes which means small volume. It is easier to hear if the sound is amplified such as in an electric guitar.