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I've separated out the explanation for how inverting the Tritone works, to keep the main article brief. Read on if you're curious about the theory concepts behind the Tritone.
Please finish reading the page on Interval Inversions before continuing here!
The first thing to understand is that the Tritone sounds so dissonant, so jarring compared to the root note, because it's as far as you can get from the root note on the note wheel.
For example, see the image of the note wheel here. If F is your root note, your Tritone will be B, 6 frets higher than the root.
But, notice that it could also be considered 6 frets lower.
The F and B notes are as far away from each other as it's possible for two notes to be, 6 frets either way around the note wheel.
This means that, practically speaking, it doesn't matter what you do to these two notes, octave-wise. It's always a Tritone, whether the root note is on the bottom, or inverted to be on the top.
And yet, in theory terms, there is a difference.
If you've read the page explaining intervals, then you know that the Tritone can also be called a "Diminished 5th".
"Diminished", essentially meaning the same thing as "flat", that it's one fret lower than normal.
Now, we need to learn the last rule of Interval Inversion.
Third, a diminished interval inverts to an augmented one, and vice versa.
So if we treat our Tritone as a "Diminished 5th", and apply the rules we know about interval inversion to invert it... what do we get?
We know the two intervals added up need to equal 9.
Since we're dealing with a 5th, it must then invert to a 4th.
Since it's diminished, it must invert to an augmented interval.
So our Diminished 5th has inverted to an Augmented 4th! Which is really the same thing. Music theory can be silly sometimes.
Use the image here if you are having trouble wrapping your head around this. Notice that the Tritones above and below the root have the same relationship to the root, while the 4th's and 5th's do not.
I hope now you can see theoretically how the inversion of a Tritone works. As always, I am much more interested in the reality of how things sound than the minutiae of theory. But if nothing else, perhaps you now have a better understanding of the Tritone!Â
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