I have a music theory question. Not a trick question or anything, just wondering.
Most common chords in pop/jazz songs can be tied to the original key, so that they "make sense". For example, in the key of C, all the diatonic chords (Cmaj7,Dm7,Em7,Fmaj7,G7,Am7,Bm7b5) make sense in the key. And we can also add the chords for Cm (Cm7,Dm7b5,EbMaj7,Fm7,Gm7,AbMaj7,Bb7). Then we can add dominant 7 chords that "approach" chords that are a 4th above, adding these to the key of C... C7,D7,E7
Also, C#dim7 makes sense in that it is like an A7b9 without the root.
It helps to know how the chord fits in to the key. For example, if you can think of a C#Dim7 like an A7b9, it makes a progression like C6|C#dim7|Dm7|G7 in to a simpler one CMaj7|A7|Dm7|G7
But how about a chord like Cdim7 (or its similar cousins Ebdim7,F#dim7. They occur commonly in the key of C, but how are they related to the key of C?
For example, these are common chord progressions:
C | Cdim7 | Dm7 | G7
C | Ebdim7 | Dm7 | G7
F | F#dim7 | C/G | A7
Is the Cdim7 related to some other chords in the key of C in some way?