If you're referring to Classical Music (the period in European classical music from about 1750-1830) then yes. If it's classical music as in the generalised art music then no. If your referring to Classical Civilisation then yes.
The first and third are proper nouns as they refer to specific historical movement and eras respectively; the second is just a generalised term.
Also, Classicism would usuallly be capitalised it was a specific artistic movement in the Eighteenth Century.
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yes
the connection between analytical (classical) line and static compositions
no. manga is not a proper noun
A classical accompaniment style based on triads.
possibly classical