Classification of Math, Logic, and Music as Language

Would you classify mathematics, logic and music as languages? Justify your answer, considering the extent to which they resemble or differ from natural language and the role they play in the acquisition of knowledge.

Language is best defined as something that is intended, creative and open-ended, and structured. Mathematics, logic, and music all fairly represent each of the requirements of language. Math, logic and music are all intended, creative, and open-ended. If spoken and written languages were considered to be “natural languages,” then it would be fair to consider these three to be “unnatural languages” due to their different nature. While they may not resemble natural languages externally, these unnatural languages are actually very similar when discussed further. For example, many college students majoring in the field of engineering and mathematics often describe their computer programming classes as nearly identical to a foreign language class, not only in the way it is taught, but also because learning to communicate with a computer is similar to learning a hard, new language. A large debate about language is whether it is innate or not. While it must be taught some, language must also be somewhat innate in order for children to have the ability to speak using grammar without having had formal instruction.
However, it could be argued that not all of these have an inherent structure, nor are they able to actually convey any knowledge, which would deny that they are indeed languages. Contrarily, math clearly has a structure, whether it is on metric conversions to long division to trigonometry to calculus. Every part of math has a basic structure to it, like using formulas. It is used everyday to discover new mathematical findings. Music also has a bit of a structure due to the necessity of actually being able to read sheet music in order to create sound. Music is often used to convey meaning and emotions as well, which gives it a form of