This is one of those funny, if offensive, mnemonic devices that are used by students everywhere to memorize seemingly random series. This one, like All Cows Eat Grass and Every Good Boy Deserves Fudge comes from music theory.
Fat Chicks Go Down After Every Bagel
The pattern F-C-G-D-A-E-B is the order in which sharps appear in the standard key signature. If a key has two sharps, the two notes that are sharped are F and C. Five sharps gives us F, C, G, D, and A. The sharps are displayed in the key signature in this same order.
In order to determine the name of major key, we can remember that the last sharp is the leading tone or "ti" of the key. In other words, take the last sharp (the furthest along in the sequence), and go to the note that is up 1/2 step from that sharp. This is the tonic, or root note of the scale.
So, for the following sets of sharps, here are the associated major keys:
- F#: Key of G
- F#, C#: Key of D
- F#, C#, G#: Key of A
- F#, C#, G#, D#: Key of E
- F#, C#, G#, D#, A#: Key of B
- F#, C#, G#, D#, A#, E#: Key of F#
- F#, C#, G#, D#, A#, E#, B#: Key of C#
It should also be noted that the order of flats is B-E-A-D-G-C-F, which is the reverse of the order of sharps. Rather than remember a little phrase, and reversing it, most students and musicians just recognize the word BEAD, and tack on the G-C-F.
If my terminology or usage of musical terms is off or inaccurate, please /msg me with corrections. My formal training is considerably lacking in the subject.
Thanks to Ouroboros for tip on referring to the leading tone. That is much simpler.