What is a tritone and why should it be avoided when writing harmony in the style of Bach?

A tritone is an interval between two notes in a diatonic scale that is exactly half an octave. It's characterised by the interval of a diminished fifth, or augmented fourth. As an example of a tritone, take the interval of a perfect fifth between the notes of C and G above it- this is generally considered a clear, pure sounding interval. A tritone 'compresses' this interval down by a semitone, so here the G slips to an F# and the sound changes. In diatonic music the sound of tritone is not generally considered a pleasant sound on the ears.

In the early days of music, this interval was disliked so much by the leading musical powers of the age that it was considered the 'Diabolicus in Musica'- the Devil's interval. It was even banned in Church music, as it was considered 'unholy'. Bach did not characteristically use this interval in his work as a result, so when students write Bach chorales, including this interval in parallel parts in a work is one particular way a candidate can lose marks, as it breaks one of Bach's rules of harmony. They can be quite hard to spot, so always check your work thoroughly to make sure that you haven't accidentally included parts that move in intervals of a diminished 5th/augmented 4th.