I'm not sure if I should post this question here in English Language and Usage or in one of the music-specific forums...
The word for (sometimes deliberate) "sour" notes or semitones is "dissonance." Some musicians use this technique to good effect, such as Orleans on their song "Still the One" and Me First and the Gimme Gimmes on many of their songs.
What about deliberately singing "off time" though (ahead of or behind the beat)?
A prime example of someone who uses this technique often is Willie Nelson. And it's an interesting juxtaposition to his almost overly-precise enunciation/phrasing.
What is the word for this hesitation/gun-jumping while vocalizing? Is there one? If not, I submit "dischronance." And a picture of Willie should appear in the dictionary at that entry.