(usually plural) an ulterior implicit meaning or quality
<noun.communication> overtones of despair
a harmonic with a frequency that is a multiple of the fundamental frequency
<noun.cognition>
Overtone \O"ver*tone`\, n. [A translation of G. oberton. See {Over}, {Tone}.] (Mus.) One of the harmonics faintly heard with and at a higher frequency than a fundamental 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}. --Tyndall.
But the letter also had an overtone of exasperation.