Overtone

One of the harmonics faintly heard with and above a tone as it dies away, produced by some aliquot portion of the vibrating sting or column of air which yields the fundamental tone; one of the natural harmonic scale of tones, as the octave, twelfth, fifteenth, etc.; an aliquot or "partial" tone; a harmonic. See Harmonic, and Tone.

(usually plural) an ulterior implicit meaning or quality; "overtones of despair"