I love music and am very passinate about Hindustani music. Mathematics is part of music. But it is not just that. Because music is mix of various things. It has the pattern of notes which signifies a raag and brings in a certain mood. This was evolved out of last hundreds of years out of nature (which includes our species). If you look at taal cycles in music it is of course mathematical. Aspects of octaves and harmonics is mathematics. But there is a big aspect of what is called the 'bhaav' in the rendition. Even when you have a set of notes in a pattern, the combinations, emphasis on various notes and how that changes in various octaves influences the mood. This cannot be mathematically framed because this happens out of the creativity and feel of the mood that the artist has.
When I started learning music I had a thought that music is various permutation and combinations of the 7 notes rendered in a specific taal cycle in various octaves. But I discovered that it is much more than that. One day I was in thenmusic class. I was learning early morning raag "Bhibhas". I had started learning this raag 3 weeks back and it was 4 th class. My guruji Shri. Keerthi Kumar Bhaswashiji asked me to sing alaap. Alaap is the first phase in a raag rendition when the raag is introduced to audience and the mood is created. I had practiced alaap and started singing. After 5 minutes my guruji asked me to stop and with a mild smile he told me that "You are technically right but there is no bhaav. When you sing this raag you should feel the rising sun because raag has essence of nature" Then he started signing and I could feel the 'rising sun'. That experience made me think. It is an emotion which cannot be mathematically modelled. It is not a tangible material but an intangible experience.
Look at the para below. This I took from http://www.itcsra.org/ You can go thru this site for more information on Hindustani raags.
It is an ocean there and it is some thing like computer science. But it has some dimensions which science does not have. That is the spiritual and emotional dimension.
"Two ragas may have identical notes and yet be very different ragas; for example, two ragas mentioned earlier, Shree and Puriya Dhanashri, have exactly the same notes, but are unmistakably different in structure and temperament. The first can be identified by its continual exploration of the relationship of the note Re to the note Paa; while the repetition of the phrase Ma Re Ga Re Ma Ga, a phrase that would be inadmissible in the first raga, is an enduring feature of the latter. Certain arrangements of notes, then, are opposite to particular ragas and taboo to all others. A simple and abstract knowledge, thus of the notes of a raga or the thaat on which it is based, is hardly enough to ensure a true familiarity or engagement with the raga, although it may serve as a convenient starting point.
Thaat familiarity can only come from a constant exposure to, and critical engagement, with raga's exposition. "
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