The secret behind this bit of deft Fielding prestidigitation is simple:

Take any seventh chord(just grabbing one out of the air, lets say, A7: A-C#-E-G) and raise the fundamental (A, in this case) and you have a diminished chord: A#-C#-E-G--

The backward trick is even more amazing:

Lower any note in a diminished chord by one half step, and you have a major seventh chord of the same name:

A-C#-E-G is A7
A#(Bb)-C-E-G is C7
A#(Bb)-C#(Db)-Eb-G is Eb7th
A#-C#-E-Gb(F#) is Gb7 and F#7