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The tritone is one of the most dissonant intervals in music. It is also known as the "Augmented 4th" or the "Diminished 5th", and it is composed of three adjacent whole tones:

• Augmented 4th: F-B for example, F-G, G-A, A-B


• Diminished 5th: B-F for example, B-C♯, C♯-D♯, D♯-F

The tritone was banned in early Catholic music due to its dissonance. Is it still banned today?

I don't know that there is any evidence that the tritone was ever formally banned by the Catholic Church, although that story does get passed around a lot. An actual Church document that discusses this and puts the claim in context is needed.

I see no mention of tritones or intervals of any type in Musicam Sacram of 1967. The Sacrosanctum Concilium of 1963, one of the Church documents cited by the Musicam Sacram, similarly makes no mention of tritones. In "Chapter VI Sacred Music" of this document can be found:

116. 
     

     The Church acknowledges Gregorian chant as specially suited to the Roman liturgy: therefore, other things being equal, it should be given pride of place in liturgical services.

     
     
     

     But other kinds of sacred music, especially polyphony, are by no means excluded from liturgical celebrations, so long as they accord with the spirit of the liturgical action, as laid down in Art. 30.

     
     

Later, this seems to indicate an openness to other musical traditions, with no exception stated for tritones or other musical devices:

119. 
     

     In certain parts of the world, especially mission lands, there are peoples who have their own musical traditions, and these play a great part in their religious and social life. For this reason due importance is to be attached to their music, and a suitable place is to be given to it, not only in forming their attitude toward religion, but also in adapting worship to their native genius, as indicated in Art. 39 and 40.

     
     
     

     Therefore, when missionaries are being given training in music, every effort should be made to see that they become competent in promoting the traditional music of these peoples, both in schools and in sacred services, as far as may be practicable.

     
     

Finally there is this advice for composers:

121. 
     

     Composers, filled with the Christian spirit, should feel that their vocation is to cultivate sacred music and increase its store of treasures.

     
     
     

     Let them produce compositions which have the qualities proper to genuine sacred music, not confining themselves to works which can be sung only by large choirs, but providing also for the needs of small choirs and for the active participation of the entire assembly of the faithful.

     
     

From this, it would appear that the Catholic Church gives a special place to Gregorian chant, but is accepting of the music of other cultures, while encouraging composers to realize the best quality sacred music. None of this seems to support the idea that tritones have been banned by the Church, at least since the early 1960s.

Tritones have been used since Gregorian Chant days. There are several common patterns that outline a tritone and a few instances where a direct tritone is used. The term "Devil's Interval" seems to refer to the difficulty of resolving the interval rather than in forbidding its use. One amusing (if true) use was the direct F to B (I think downward) interval for a chant section outlining the presentation of the vinegar and the same longer pattern with Bb being used in a similar suggestion of drinking wine.

The is an acoustic difficulty in non-equal-temperament tunings in representation of the interval. A tritone would be 729/512 if using three C-D intervals. This is pretty far from the Square Root of two which would divide an octave in half.

It certainly isn't banned now! And the whole historical mythology of banning the 'Devil's interval' though a nice idea, is rather dubious.

As well as being the engine of a dominant 7th chord, resolving to a major 3rd (or its inversion, a major 6th) it's almost achieved consonance status when used as a b5 by jazz players.