With future perfect (F2) you jump to a point in the future, turn round and say some action is finished then. Actually a complicated thing and cumbersome and in most cases you can express the same idea much simpler without using F2. This tense existed in Latin and it was imitated by writers.
In current English usage, muse can refer in general to a person who inspires an artist, writer, or musician.
The Muses. The Muses were the Greek goddesses of inspiration in literature, science and the arts. They were the daughters of Zeus and Mnemosyne (the personification of memory), and they were also considered water nymphs. Some scholars believed that the Muses were primordial goddesses, daughters of the Titans Uranus and Gaea.