tin ear

from The American Heritage® Dictionary of the English Language, 5th Edition.

• noun An insensitivity to music or to sounds of a given kind.

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

• noun idiomatic Insensitivity to and inability to appreciate the elements of performed music or the rhythm, elegance, or nuances of language.
• noun idiomatic Insensitivity to the nuances of current situation or subtleties of a craft; indifference to somebody else's attitudes and moods.

from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.

• noun an inability to distinguish differences in pitch
• noun insensitivity to the appropriateness or subtlety of language