in that great, ancient Greek way of theirs, the ancient Greeks started entire schools of philosophy and science built around dissecting every single aspect of music then known.
Could you please explain underlined parts to me?
: the Platonic school of philosophy . jaleh then known. = known at that time
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jalehin that great, ancient Greek way of theirs
= as the ancient Greeks were good at doing
jalehentire schools
= complete schools
school: the body of pupils or followers of a master, system, method, etc.:
the Platonic school of philosophy.
jaleh then known.