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 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.
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. She replied that he was. (DS9: "Chrysalis")
In 2375, 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")