I know a bit about tritones; I wrote the below in response to someone who was looking for clarification on "The Devil's Note."
Diabolus in Musica (Devil in Music)
Generally called a diminished 5th or a tritone. Enharmonic equivalent of an augmented 4th.
The intervallic relationship of a diminished 5th is six semi-tones, either up or down from the starting pitch.
On a keyboard:
C - C# D - D# E - F - F# G - G# A - A# - B - C
0 - 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10 - 11 - 12
Count up six steps starting from any note and you will arrive at that note's tritone. (C to F#/Gb is a tritone.)
Because western tonal music consists of 12 equal-tempered tones, the 6th tone splits the chromatic scale in half, thereby inverting the interval no matter what pitch is played.
A 5th (intervallic distance of seven semi-tones) is considered perfect. (C to G is a perfect 5th.)
Perfect has to do with the ratio of the two tones under consideration: 5:4, 3:2, 2:1.
Other intervals are considered imperfect (2nds, 3rds, 6ths, 7ths). These rations might be 18:32, 12:15, 30:36, etc.
The imperfect are more mathematically and harmonically complex whereas perfect intervals are more simple.
Another way to look at the diminished (to make smaller or reduced) 5th is to consider it as slightly "less than perfect," as the perfect 5th is the most stable harmonic interval, as well as providing the tonic-dominate relationship for western music, pre-atonalism.
Similar to spiritual understandings: we strive for perfection but fall short of the Ideal.
Another way again to look at it again is in terms of sound-resolution. It simultaneously offers the most discordant of sounds, while providing the most tense need of motion: it entices the ear while immediately necessitating moving onward and away from it.
Skilled composers know how to manipulate the tritone to cause radical shifts in the listener's consciousness.
The ancient church forbid the use of the tritone (hence the name diabolus in musica) precisely because of the effect it had on the consciousness of the day.
We in the modern world are so used to it that it does not cause the same effects it once did to our ancestors.
Regarding Paganini and the tritone, can you be more specific how an intervallic relationship relates to Musical Theurgy?