Although I alluded to the definition earlier, the term used truly is "sympathetic vibrations". The "harmonics" of a note are what (most often) are sympathetically vibrated by source sounds. An example of the difference in these terms can be demonstrated on a piano by slowly holding down the forte' pedal (the one on the right that allows the notes to sustain) and singing a note into its strings. The resulting sounds that comes from the strings is sympathetically generated. The resulting loudest tones are usually the harmonics or upper octaves and extensions of "Pythagorean proportions", and unless you yell or sing real loud, the fundamental or lowest occuring octave (ie. your voice note) resists sympathising.

"Is it live, or is it Ella Fitzgerald"?