By which neuronal mechanisms does music make us happy or sad?
In a comprehensive review that included 140+ primary research papers, Juslin &amp; Laukka (2003) explain that there is a close relationship between vocal expression of emotions and the musical expression of emotions. Indeed, music and speech have similar characteristics and therefore can illicit similar emotions (table 1).


Table 1. Commonalities of speech and music in emotional expression. source: KTH Sweden 

Wikipedia states that emotion is indeed linked with tonality in both music and speech: 


  The tones in music seem like a characterization of the tones in human
  speech, which indicate emotional content. The vowels in the phonemes
  of a song are elongated for a dramatic effect, and it seems as though
  musical tones are simply exaggerations of the normal verbal tonality.


References
- Gramfors &amp; Johansson, thesis KTH Sweden
- Juslin &amp; Laukka, Psych Bullet (2003); 129(5): 770–814