Dominant 7th flat 9 - Diminish

The diminished chord is closely related to the 7b9 chord. Consider the C#dim chord containing: C# E G Bb. Any of these 4 notes can be the root for that diminished chord. Also, these same 4 notes are contained in 4 different 7b9 chords. Examine these four 7b9 chords:

C7b9 (C E G Bb Db)
Eb7b9(Eb G Bb Db E)
Gb7b9(Gb Bb Db E G)
A7b9(A C# E G Bb)

If the roots are removed from each of the above four 7b9 chords what 4 notes are left? The 4 notes left are those notes of the diminished chords named by any of those 4 notes: C#dim, Edim, Gdim, and Bbdim. By extending this comparison it will be seen that since there are only 3 diminished chords (each chord with 4 roots times 3 chords equals 12 roots in all.) Three diminished chords therefore, are common to 12 different 7b9 chords.(rd)