Off-key is a term often used to denote musical content that is not at the expected frequency or pitch period, either with respect to some absolute reference frequency, or in a ratiometric sense (i.e. through removal of exactly one degree of freedom, such as the frequency of a keynote), or pitch intervals not well-defined in the ratio of small whole numbers.
The term may also refer to a person or situation being out of step with what is considered normal or appropriate.
The opposite of off-key is on-key or in-key, which suggests that there is a well defined keynote, or reference pitch. This does not necessarily have to be an absolute pitch but rather one that is relative for at least the duration of a song. A song is usually in a certain key, which is usually the note that the song ends on, and is the base frequency around which it resolves to at the end.
The base-frequency is usually called the harmonic or key center. 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."