Tone deafness was a hearing impairment regarding the lack of relative pitch – the ability to discriminate between musical notes. Being tone deaf was having difficulty in or being unable to correctly hear relative differences between notes; however, in common usage, it referred to a person's inability to reproduce them accurately with their voice. It was also known as "tin ear".
The fictional 19th century sailor Horatio Hornblower was tone deaf. (DS9: "The Visitor", "The Muse", "For the Cause")
By 2371, none of the Dax symbiont's hosts were known to have possessed any musical ability, prompting Jadzia Dax to comment, "You would think one of us would've been born without a tin ear." (DS9: "Equilibrium")
In 2373, Harry Kim recalled finding it odd that he loved music when his Human parents, John and Mary, were practically tone deaf. (VOY: "Favorite Son")
In 2375, when the genetically-engineered Humans Lauren, Jack and Sarina sang scales to help Sarina regain her normal speaking voice, Jack jokingly asked Sarina if she was tone deaf, to which Lauren replied that he was tone deaf. (DS9: "Chrysalis")
Jack's actor, Tim Ransom, is in fact tone deaf.
Soon after, a hologram of Dr. Crell Moset apologized to The Doctor for humming an opera along with him, saying his wife told him he was tone deaf. The Doctor disagreed, saying (at least in that case) that he was right on key. (VOY: "Nothing Human")