One octave is 6 tones wide. So, if you split the octave in two , you get an interval of tritone. A tritone is 3 tones wide. https://commons.wikimedia.org/wiki/File:Tritone_in_the_chromatic_circle.png If you arrange the notes on the circle of fourths or fifths, and you pick for instance C, the interval of tritones gets you the F#. On the circle, F# and C are opposite. C and F# are said antipolar. It is also the case of D and Ab, B and F, etc... Let's unroll the C major scale and the F# major scale The C major scale is : C D E F G A B 1 -1 2 2'' -2 3'' -3 4 The F# major scale is : F# Ab Bb B C# Eb F F# 2' 3''' 3' 3 4' 4° -5 5° If you assemble the notes of each scale, you get the chromatic scale, that is, all the notes : the twelve notes C C# D Eb E F F# G Ab A Bb B Some musicians were interested in the properties of the tritone because of its symmetric properties. For instance, Nicolas Slonimsky used it as a mirror by which transposing ...