musicomania

from The Century Dictionary.

• noun In pathology, a variety of monomania, in which the intellectual faculties are deranged by an absorbing passion for music. Dunglison. Also called musomania.

from the GNU version of the Collaborative International Dictionary of English.

• noun (Med.) A kind of monomania in which the passion for music becomes so strong as to derange the intellectual faculties.

from Wiktionary, Creative Commons Attribution/Share-Alike License.

• noun A form of monomania involving an unnatural obsession with music