Now explain tritone substitutions.
Useful in a cycle of fifths as a kind of shortcut so that the cycle of fifths doesn't end up going through the entire circle of fifths. Basically, you get to use every diatonic chord in a particular key without modulating.
So for example in A minor, you begin on an A chord, the tonic (i), then to D minor (iv), to G major (VII), to C major (III) to F major (VI) ....... so far the progression is perfect fifths ..... but wait! What happens if we move a perfect fifth from F, downwards? We end up on B flat which is alien to the key of A. So this is where we substitute a tritone in order to land on a B diminished (ii), then we go to an E major (V) and Bob's our uncle! We can close with a perfect cadence.
Some argue that the tritone here isn't really a tritone because it's a diminished fifth rather than an augmented fourth. Personally I think they're splitting hairs.
And what if you have an extended dominant seventh chord, that contains both a third and a flatted third, Like C, E, G, Bb, C, Eb? (A very common voicing in jazz and rock.)
Holy fuck! That sounds really wild! Thank you!
I don't know what jazz and rock people do with that chord but approaching it from a more baroque angle you can resolve it to an F whilst leaving the Eb as a minor seventh in the F chord, turning the F into a dominant seventh which would no doubt resolve to a Bb.
Are there other uses that you know of?