Interesting discussion...
Music is not math! But there is a huge correlation between the two, just like there is a correlation between math and pretty much anything else. Math is a language that describes phenomena. It is a human-made language and as such reflects the human experience. Math, most often, does not even explain things, it just describes them. Therefore, I don't see why so many people react hostile to the notion that math and music are "related". They almost think that as soon as one evokes math, all the human elements are being taken away. Childish.
Anyway, if math can be used to describe something, it can usually also be used to predict something. And thus it is not surprising that computer programs exist that create pieces that sound so much like Bach that it is not possible to distinguish between "real" and "synthesized" Bach.
Now, with respect to emotions: it is undeniably true that music has as much to do with emotions as motor oil. Emotions are reactions that relate to past experiences. If certain music is associated with certain experiences, then hearing this music again later will trigger emotions related to that experience. If there are no associations between emotions and a certain type of music, this music would be emotionally meaningless. For example, if somebody was brought up with hearing funeral music during carnival, then this person would always feel happy when hearing funeral music. The reason most people start to feel sad when hearing funeral music is because it is usually associated with funerals, which is a sad occasion. Not many Europeans would feel sad when hearing music during a funeral procession in Louisiana where happy Dixieland Jazz is being played by a marching band. On the other hand, if Cajuns hear this music in the streets of New Orleans, they know someone died.
Music is a language. As such, one can express ideas, but the idea that a performer attaches to a certain passage does not have to be the same as what a listener attaches to it. Therefore, there may be a huge discrepancy between what the perfomer intends and what the listener experiences. Only if everybody associates the same feelings and emotions with the same type of music is it possible to use it constructively as a language. This is the problem that many musicians have when they play music from different cultures. One often hears that Asians are not capable of playing Western music (don't start a flame war now, I am generalizing), because they don't associate the same emotional ideas as Westerners do. And the other way around. Likewise, one often hears that young musicans are not able to adequately display the emotional content of a piece, because they have not yet had certain life experiences that would allow them to attach certain emotions to certain music. And one can easily "hear" this.
So, in a nutshell: music is able to evoke emotions provided the listener has been conditioned to associate emotion with the music in the first hand. The same is true for visual, olfactory or any other kind of sensation.
My 2 Cents.