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This site is young and asking some questions and seeing how they end up received is a good way to judge what kind of coverage can be found here.

That said, questions entirely disconnected from a mainstream interpretation of what are "languages" or "linguistics", questions unlikely to be studied by too many "linguists" or at least tangentially occurring in university curricula of "general linguistics", perhaps aren't ideal for such testing, because to get a meaningful answer here, let alone a transparent consensus regarding the relative quality (popularity) of any submitted answers, then becomes a matter of luck.

All four definitions listed in the OP allude to there being not just a structured system, but also some "meaning" behind expressions constructed upon the structure studied. (All of the terms "symbol", "sign", "communication", "understanding" require that the language not just exists as a structure, but also that it carries a meaning that can be communicated through the language.)  The most general study of such systems, i.e., a system of signs with meanings, would be considered called "semiotics", of which "linguistics" would be just a subarea.  

"Music" does not seem to me to be primarily a method of communication.  A composer can have a meaning in mind, a performer another meaning, and a listener may thoroughly enjoy the performance without working through a conventional system of systems to find out what the meaning was.  We would hardly ever say that the listener enjoyed themselves but "that their perception was incorrect".  Music can be structurally and functionally very deep, be interwoven with sung or other scenic scenic language, and offer lots of excursions into semiotics, but that does not make all of musicology a subfield of semiotics, and much less of linguistics.

"Math" as I understand it seems to have the opposite deficiency preventing us calling it a language (or a language family).  It has a meaning independent of its expression.  There are languages capable of expressing mathematical ideas, one of them being English.  A mathematician might ask "what is the (current or original) meaning of \`given' in \`given an object x'" and that would be a linguistic question.  However it would be a valid question for this site because it's about English (as used by the community of mathematicians) and not primarily about math itself.  

Mathematics can also be expressed in a number of formalized languages, including languages whose syntax and expressivity is extremely limited, such as propositional logic.  Another example of languages with strictly limited expressivity are programming languages.  While these types of languages can arguably be understood to meet the definitions of a "language" as listed in the OP[^1], and indeed the study of formal languages has a certain level of resonance with mainstream linguistics, including some of the terminology used, it's still the case that the scientific field most successful at analyzing these formal languages tends to be [mathematics](https://en.wikipedia.org/wiki/Metamathematics) rather that traditional linguistics.

If an example will help, a question about Sanskrit or Esperanto would typically be on topic, a question about Fortran or the Zermelo-Fraenkel formalism would typically be off topic.  Why?  We think that humans have an inborn capacity for learning a language, which is crucial for individual human development. This site focuses on that particular device of human communication.  A native speaker of Sanskrit or Esperanto is at least in principle possible, while a native speaker of Fortran is not.

To conclude, "applying linguistic principles" to this or that matter is only on topic for this site if that subject matter _is_ part of a language or how language works.  A clearly formulated question might elucidate such a connection, or inquire about a specific connection, but the connection should perhaps not be taken for granted just because something is a "formally structured system" and "used by humans".

[^1]: Least of them the quoted Wikipedia one, unless a single sentence is left artificially extracted from an entire wiki page plus its corresponding disambiguation page which together can be interpreted as the "current Wikipedia consensus" of what a language _is_ with much more accuracy than a single short sentence can convey.