Q:

Difference between “undertone” and “overtone”

Is there any meaningful difference between the terms undertone and overtone with regard to an utterance in the sense of an implicit meaning? 

A:

As per dictionary.com

un·der·tone   
  [uhn-der-tohn]  Show IPA
  –noun

a low or subdued tone: to speak in undertones. 
an unobtrusive or background sound: an undertone of static from the receiver. 

3.  an underlying quality or element; undercurrent: There was an undertone of regret in his refusal. 

and

o·ver·tone   
  [oh-ver-tohn]  Show IPA
  –noun

Music .  an acoustical frequency that is higher in frequency than the fundamental. 

2.  an additional, usually subsidiary and implicit meaning or quality: an aesthetic theory with definite political overtones. 

So it would seem that undertone is more about the vocal implicit meaning of saying something and overtone is about the way something is phrased. 
edited to clarify which meanings I was referring to

A:

An undertone typically refers to an implicit meaning conveyed by the manner of the utterance, that is, a literal sound in the voice that conveys the meaning.  So words that are growled, hissed, or said "with an edge in the voice" carry an undertone such as anger, frustration, or sarcasm. 
An overtone typically refers to an implicit meaning detected by "reading between the lines".  For example, describing the consequences of certain actions in a perfectly neutral tone could still convey a threatening overtone. 
So, undertone is conveyed literally by the sound of the words, while overtone is conveyed figuratively by the words themselves.