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 are the inspirational goddesses of literature, science, and the arts in Greek mythology. They were considered the source of the knowledge embodied in the poetry, lyric songs, and myths that were related orally for centuries in these ancient cultures.