A false relation (also known as cross-relation, non-harmonic relation) is the name of a type of dissonance that sometimes occurs in classical polyphonic music, most commonly in vocal music of the Renaissance. The term describes i) a "chromatic contradiction"  between two notes sounding simultaneously, (or in close proximity), in two different voices or parts or ii) in music written before 1600, the occurrence of a tritone between two notes of adjacent chords.
In the above example, a chromatic false relation occurs in two adjacent voices sounding at the same time (shown in red). The tenor voice sings G♯ while the bass sings G♮ momentarily beneath it, producing the clash of an augmented unison.
In this instance, the false relation is less pronounced: the contradicting E♭ (soprano voice) and E♮ (bass voice) (diminished octave) do not sound simultaneously. Here the false relation occurs because the top voice is descending in a minor key, and therefore takes the notes of the melodic minor scale descending (the diatonic sixth degree). The bass voice ascends and therefore makes use of the ascending melodic minor scale (the raised sixth degree).
False relation is in this case desirable since this chromatic alteration follows a melodic idea, the rising 'melodic minor'. In such cases false relations must occur between different voices, as it follows that they cannot be produced by the semitones that occur diatonically in a mode or scale of any kind. This horizontal approach to polyphonic writing reflects the practices of composers in the Renaissance and Tudor periods, particularly in vocal composition, but it is also seen, for example, in the hexachord fantasies of William Byrd (for keyboard). Indeed, vocal music from this era does not often have these accidentals notated in the manuscript (see Musica ficta);  experienced singers would have decided whether or not they were appropriate in a given musical context.
Many composers from the late 16th century onwards however began deliberately using the effect as an expressive device in their word setting. This practice continued well into the Romantic era, and can be heard in the music of Mozart and Chopin, for example.
- Dyson, George. "False relation", Grove Music Online, ed. L. Macy (accessed 16 February 2007), grovemusic.com (subscription access).
- Arnold Whittall (2002). "False Relation", The Oxford Companion to Music. Ed. Alison Latham. Oxford University Press. King's College London. Oxford Reference Online. Accessed 18 March 2007.
- Bent, Margaret. "Musica ficta, §1: Introduction", Grove Music Online, ed. L. Macy (accessed 16 February 2007), grovemusic.com (subscription access).
- Luís Henriques (Saturday, July 21, 2007). "William Byrd - Ave Verum Corpus", Atrium Musicologicum. Another description of the use of false relation in Byrd's Ave Verum Corpus.