By which neuronal mechanisms does music make us happy or sad? There are brain regions (X) that show stronger activation for joyful music, regions (Y) that show stronger activation for sad music, and regions (Z) that show similar activation for both.

Assuming that joyful or sad music activates similar brain regions as other tasks designed to induce a joyful or sad mood, we know more specifically:


Both joyful and sad music produce similar activation of the amygdala-hippocampal area, with activation extending into the parahippocampal gyrus, as well as activation of the prefrontal, temporal, and anterior cingulate cortices and the precuneus (regions Z).
Joyful music produces stronger activation in the dorsolateral prefrontal cortex, the cingulate gyrus, the inferior temporal gyrus, the cerebellum, and in the vicinity of the ventral medial frontal cortex (regions X).


On the other side, it has repeatedly been found that happy music is characterized by fast tempo and major mode, whereas sad music is typically played in slow tempo and minor
mode. 

Bringing these findings together the question arises


  By which specific neuronal mechanisms does fast tempo and major mode
  music activate more strongly brain regions X than regions Y? And vice
  versa.


Is it by some kind of fine-tuned resonance (involving feedback) between the sensory input from the ears and the brain regions involved? 

Are there specific theoretical (computational) models, and have they been tested?

How can - by these mechanisms - the subtle difference between a major and a minor third become so significant, both neuronally and emotionally?



References:


A systematic review of the neural correlates of positive emotions
A Functional MRI Study of Happy and Sad Emotions in Music with and without Lyrics 
Brain correlates of music-evoked emotions
Music and Emotions. Research on the Theory of Musical Equilibration
The Cambridge Handbook of Human Affective Neuroscience
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