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Roger Mills wrote:
> Given a tritone, if you raise the top note 1/2 step and lower the
bottom tone 1/2 step, you resolve to a major chord; this is because, of
course, the tritone contains 2 of the 4 notes of a Dom7, which of course
resolves to Tonic.

And, of course, the chord of the diminished seventh, composed of two
interlocking tritones (e.g. C-Eb-F#-A), was a standard means of
modulation in the 18th-19thC for exactly that reason - drop any note by
a semitone and you have a complete dominant-seventh chord.

Other chords containing two tritones either form part of a whole-tone
scale (C-D-F#-G#) or contain scrunchy semitones (C-C#-F#-G). Debussy
used the first (Pelleas, act 3 scene 2-3 if memory serves), and I'm sure
somebody's used the second - Ligeti or Webern maybe?

Jonathan.