Why are melodies/harmonies perceived as pleasurable by humans?
There are strong connections between the auditory cortex and the limbic system, which includes such structures as the hippocampus and the amygdala.

A recent paper [1] builds on earlier notions of emotional "significance" of music without any lyrics.  It adds in lyrics, so giving a perspective of which portions of the brain are reacting to which component of the music.


  Additionally, contrasts between sad music with versus without lyrics recruited the parahippocampal gyrus, the amygdala, the claustrum, the putamen, the precentral gyrus, the medial and inferior frontal gyri (including Broca’s area), and the auditory cortex, while the reverse contrast produced no activations. Happy music without lyrics activated structures of the limbic system and the right pars opercularis of the inferior frontal gyrus, whereas auditory regions alone responded to happy music with lyrics.


One of the limitations of this particular study is that the subjects self-selected their own pieces, which may limit the reliability of the results.  Of course, defining "happy" or "sad" for every individual is slightly subjective and difficult.  They cited an earlier "pioneering" study which standardized the musical selection between subjects.  Without consideration of the lyrics:


  The first pioneer study using functional magnetic resonance imaging (fMRI) by Khalfa et al. (2005) chose a controlled manipulation of two musical features (tempo and mode) to vary the happy or sad emotional connotations of 34 instrumental pieces of classical music, lasting 10s each. Sad pieces in minor-mode contrasted with happy pieces in major mode produced activations in the left medial frontal gyrus (BA 10) and the adjacent superior frontal gyrus (BA 9). These regions have been associated with emotional experiences, introspection, and self-referential evaluation (Jacobsen et al., 2006; Kornysheva et al., 2010).


As an aside to answer your final thought, in cases like this I think trying to jam everything under an umbrella of one "neurotransmitter system" or another can make things overly simplistic to the point where you lose focus of the diversity of receptors expressed.  You can say a system is driven by Dopamine, but D1 and D2 receptors have exactly the opposite effects on the neuron.


  [1] Brattico, E., Alluri, V., et al (2011) A functional MRI study of happy and sad emotions in music with and without lyrics.  Frontiers in Psychology, 2: 308.  doi: 10.3389/fpsyg.2011.00308 (free pdf)


(see also, http://www.sciencedirect.com/science/article/pii/S0028393206003083 and related)