My understanding from the circle of 5ths is that there are 6 diatonic chords for each key, is that because the the 7th chord is diminished?
Diatonic chords are chords that are built of all chord tones (notes) that are in the key. These chords are built in thirds starting from each of the notes in the key.
If we take the key of C major for simplicity(notes: C, D, E, F, G, A, B) and talk about triads (not sevenths or extended chords, again for simplicity) we will have the following chords:
C Major (C, E, G)
D minor (D, F, A)
E minor (E, G, B)
F Major (F, A, C)
G Major (G, B, D)
A minor (A, C, E)
B Dininished° (B, D, F)
Note that these are built by literally taking the note names in thirds, and keeping the notes within the key. You can take any major key and always get Major, minor, minor, Major, Major, minor, Diminished° chords.
for example key of G Major: G Maj G, B, D)
A min (A, C, E)
B min (B, D, F#)
C Maj (C, E, G)
D Maj (D, F#, A)
E min (E, G, B)
F# Dim (F#, A, C)
The "flavor" of chord doesn't really dictate if the chord is diatonic, the only concern is that the notes are in the key.
You can do the same thing for 7th chords by added one more note a 3rd above the 5th and you will find that the "flavors" will be the same in every key.
Hope this helps.
There are seven diatonic chords. One can be built off of each scale degree. I think the confusion is if you start on the tonic of a major scale and go up 5ths in a major scale, you will be missing the 4th since the interval from scale degree 7 to scale 4 is a diminished 5th not a perfect 5th.
If you look at the Circle of 5ths in let's just say the key of C major, the F will be a 5th below not above the tonic. It's still in the circle, it's just you have to go down a 5th (or up a 4th) to get to it. The Lydian mode is the only mode diatonic mode where you can get all the notes of the scale just from going up Circle of 5ths
I think you're talking about the 6 most used chords from a key. As in 3 majors (I, IV, V) and 3 minors (ii, iii, vi). That leaves the diminished chord, which doesn't feature in many songs, compared to the other 6. But it can be thought of as an extension of the V chord, making V7 - a very commonly used chord, diatonically.
There are 7 diatonic TRIADS. This is only a vaguely interesting fact, and certainly not the basis of a set of 'rules' for constructing music. It could be argued that in 20th century popular music the most USED chords are I7, IV7, V7 - only one of them diatonic. (That's the basic blues chords.)
Don't work outward from theory. Try to derive your 'theory' from observation of real music. For instance, in today's music you'll rarely encounter a plain vii (dim) triad, even if it IS 'diatonic'. Much more likely to run across iv, bVII, II7, #1dim7 etc. etc. These are the 'chords of the key' in a very real sense, even if they're not diatonic.