Karli
Your post aroused my interest so I have quickly outlined my response.
Let us start with the observation that everything in the universe vibrates: atoms, sub-atomic particles, molecules, etc. Our own body vibrates, ranging from circadian rhythms to the vibration of our DNA molecules.
Music is vibration. There are set mathematical ratios between the different intervals of the scale. If we consider a vibrating string the strong vibrates at the whole length of the string (the fundamental); at the half length (the octave), at the third length (the fifth), and so forth. After the octave the fifth is the most prominent harmonic. Thus, the cycle of fifths is following a mathematic progression and this mathematic progression is echoing states within our body, mind, and spirit.
Although I am not particularly religious I note the opening words of the Gospel according to St John "In the beginning was the word and the word was God." If we translate "word" as "vibration" then this quotation seems to make more sense. In our own body there are many, many vibration going on at the same time. Some of these are in harmony with each other, and some conflict. Could it be that when most of the body vibrations are in harmony that we feel healthy, happy, and content and when there is a lot of conflicting vibrations (disharmony) then we feel angry, frustrated and generally negative?
The notion of vibration is so fundamental that we use it without thinking: "S/he has good vibes."; "We are on the same wavelength". When two people are in love then it is probable that their respective energy fields are in harmony to a considerable extent with each other. (Lest any of my critics think that this is some kind of 'new age speak' please remember that energy is vibration and that all vibration is energy!)
We know that music is a very powerful tool for arousing various emotions. Military music is a good example. It is no accident that a march has a tempo of 104 - 108. This is the natural rhythm of a brisk walking pace. If music has the power to arouse or change our emotions then it reasonable to assume that our emotional state will influence how we produce music. Have you noticed that when you are calm and serene then you play more gently and with a more musical tone than when you are angry or in a bad mood? The listener does not need to be a musician in order to sense the music. S/he will be aware of tonal production, harmonic changes and general form even if s/he is unable to describe what is going on. I believe that it was the musicologist Stuart Mc Pherson that said the first level of appreciation is at the physical level - response to rhythm, and form. The second level of appreciation is at the intellectual level where we begin to understand the grammar and structure of the music, and the third level is at the spiritual plane where the first two elements come together and we are momentarily transported to a transcendental plane. As a listener I am able to appreciate your performance on the first two levels, and hopefully if you are really at one with the music, at the third level. The performer is, knowingly or unknowingly, taking on the responsibility of shifting the energy level of the listener and hopefully leaving the audience in a state where they feel moved.
In the context of the Biblical quotation given above, mathematics may be language of the universe but music is perhaps the language of the gods.