I always had problem in understanding the reason people call it sheet music. Isn't it a sheet (an object) that has an adjective of being related to music? We don't say things like sheet Excel, or sheet cheat. The correct syntax or grammar of English tells us that we should use the adjective before the noun. So, why don't we call it music sheet?
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In this case, 'music' is in fact the pluralization, and 'sheet' is an adjective describing the music.
So, rather than "A sheet of type: music," we're talking about "Music (pl.) in sheet form."
Sheet music is essentially synonymous with 'notation', as in "Do you have the notation for that song?" We would say "Do you have the sheet music for that song?" because "Do you have the music sheet for that song?" would be referring to a definite object that the asker supposedly already knows about. We could technically say "Do you have a music sheet for that song?" but that semantic construct is never used because it's a bit too broad in the interpretation of what the "correct sheet" would be.
"The sheet music" refers to "the correct notation for your part of the song we're playing," where "the music sheet" would be "a specific piece of paper I gave you earlier that has music on it."
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Actually you offer half of the answer already:
Now, imagining for a second that you don't know which term is an established term: sheet music or music sheet, you should admit that an equally relevant question is:
To me it seems rather obvious that the principal noun here is music and that the sheet only determines the context. We are firstly talking about music and therefore the music remains the noun.
It is similar to these constructs: piano music, elevator music, shopping music, chin music, etc..
As for the term music(al) sheet look at the results of the ngram search (you can explore the examples by clicking on the links in table below the graphs to see actual usage in books):
This shows that the actual terms music sheet and musical sheet are actually used sometimes, especially when referring to a single sheet of sheet music (or when the actual sheet is an object in the sentence). Still sheet music is appropriate when talking about the actual music written on the sheet and as such it is much more common (as a subject and consequently in the language).
As for etymology, etymonline only lists the date