There is a way to get rid of this limiting factor of only 7 letters. We could make it possible to encode almost the entire alphabet, and therefore any message, in song form, by adding accidentals, extra musical symbols, to the basic 7 notes. The two most common accidentals are sharps ("#") and flats ("b").
So the first 7 notes, A B C D E F G, could represent the respective letters A B C D E F and G. Then, A# B# C# D# E# F# G# could represent H I J K L M and N. And so on: Ab Bb Cb Db Eb Fb Gb could represent O P Q R S T U. And if you really wanted to finish it off, you could use a double sharp ("x"), a less common accidental, for the last five letters. So Ax Bx Cx Dx Ex would be V W X Y Z.
Here's the complete new alphabet:
A=A
B=B
C=C
D=D
E=E
F=F
G=G
A#=H
B#=I
C#=J
D#=K
E#=L
F#=M
G#=N
Ab=O
Bb=P
Cb=Q
Db=R
Eb=S
Fb=T
Gb=U
Ax=V
Bx=W
Cx=X
Dx=Y
Ex=Z
This does complicate things, though, and creates a much more atonal(read: out of key) piece of music. For example, for the musically inclined out there, try playing this series of notes on your piano or keyboard. Yes, peel yourself off the computer seat. Heck, you can even use GarageBand or Cakewalk for the intrinsically lazy:
C# Ab A# A G# G# Eb E B A Eb Fb B# A G# B A C A#
Doesn't sound too musical, does it? I don't think even Bach himself would work that into a composition for self flattery. This gives us a much broader vocabulary, though. It would make a good code as long as it was only used in the written form.