The term may also refer to a person or situation being out of step with what is considered normal or appropriate.
A single note deliberately played or sung off-key can be called an "off-note".
[1] The opposite of off-key is on-key or in-key, which suggests that there is a well defined keynote, or reference pitch.
Being on-key presumes that there is a key center frequency around which some portion of notes have well defined intervals to.
Examples include the words "Thought He Was a Goner" in the song "And the Cat Came Back" and the words "Yum Yum" in the children's song "Five Green and Speckled Frogs".