Understanding the Fundamentals of Music (2006), by Robert Greenberg, B.A. in music (magna cum laude) from Princeton, Ph.D. in music composition from the University of California, Berkeley. p. 54 of the Lecture Transcript.
Any given major key contains only one tritone. It's the interval between the fourth and seventh scale-degrees. In the key of C major, for example, the tritone occurs between an F (the fourth scale-degree) and a B (the seventh scale-degree). Now, because there are 12 different major keys and only six different tritones, the tritones are doubled up: the same tritone will serve two different major keys. So, what major key does C major share a tritone with? The answer: the key of F# major, the major key farthest away from C major, the major key a tritone away from C major! My friends, keys a tritone apart will share the same tritone! (For our information, in F# major, the tritone occurs between B, which is the fourth degree of F# major, and E#, which is enharmonic with F, which is the seventh degree of F# major.) Dang, don't we just love the chromatic collection! The metaphors it presents us with are endless: The end is the beginning, the beginning is the end; opposites unite into singularities and singularities become opposites; all points are connected within the continuum. It's a fantastic system!
Why can a given major key contain only 1 tritone?
I don't understand why the "only one tritone" must be "the interval between the fourth and seventh scale-degrees"?
I added to Greenberg's figures. In the left figure, why can't C-F# be another tritone for C maj? In the right, why can't F#-C be another tritone for F# maj?