The “a-” prefix 1 intensifer is at work here, putting one intensely in the power of the muses.  OED notes that Shakespeare never used the word.  I find it notable that amusements end well before the capture in Mirkwood.

• 01.020 Very amusing for me,
• 04.013 and set dancing up by the roof to amuse them.
• 06.071 and they soon had a plan which seemed to them most amusing.

“amuse, v.” OED Online. Oxford University Press, March 2015. Web. 18 May 2015.