What to play over this diminished chord
 

The song is in the key of C major.

Chord progression (one bar of each):

C
C diminished 7
D minor
C

I've read "There are two types of diminished scales: the whole-step/half-step (or auxiliary diminished) and the half-step/whole-step (or auxiliary diminished dominant)."

So which diminished scale do I play over the C dim7?

The standard advice is WH on dim7 chords, which is really only saying "the dim7 chord tones, plus 4 other notes a half-step below" I.e., Cdim7 and Bdim7 mashed together. The point being that you get a scale with approach notes to the chord tones, so it works for a dim7 wherever and however the dim7 is being used. You can ignore the context, IOW! :)

That gives you C D Eb F Gb G# A B. In this case, that suits the context pretty well. The chord tones are C Eb Gb A, and the added notes all come from C major, aside from G#.
I might be tempted to use a G natural instead, to tie it back to the C major key context. (Having tried it, I think I prefer the G. It gives it a kind of bluesy sound, C D Eb F Gb G A - forgetting the B.)

BTW this sequence is more common with the Dm(7) leading to G7, and two beats each, not four - that makes it an old jazz/R&B sequence from the 1930s/40s/50s. The Cdim7 would usually have an Eb bass, so you'd probably call it Ebdim7, but the scale would be the same. Then again, on only two beats you hardly need a whole scale, the arpeggio would be enough.

JonPR, thank you!

:)

You would not go wrong with what Jon says (as always).

But I would add that the Cdim7 is functioning in your progression as a F7b9, and you can play any kind of F7 arpeggio over it, or the F mixolydian scale.

Do you just want put a scale in there over the chords or do you want to create a melody line over the chords?

You're too kind... ;)
Based on what?
I mean, a common-tone diminished is what it actually is; that's its functional interpretation.
It has an affinity with F7b9 to be sure, but there's no real need to go there.
But F mixolydian won't take account of the b9. ;) (while the WH dim scale includes F as well as all the Cdim7 chord tones.)

(See, I said you were too kind. :))

Based on the common use of a dim7 in the second bar of a blues where a change to the IV7 in that bar is also common, with the dim7's root being the same as that of the first chord. And also that a dim7 chord more often than not is used harmonically as a 7b9 with root omitted in American popular music.

I was going to add to my first post that you would soon appear to disagree with me. Nice to see you, as always.

Yes, but this isn't a blues. That's what I meant. You're basing it on an unfounded assumption. ;) (Yes I'm nit-picking now)

I agree that you can argue that the F7 in a C blues is a kind of diminished version of the tonic.

But the OP's sequence - following the Cdim7 with Dm - is more like that old jazz sequence where Cdim7 would usually be interpreted as Ebdim7 (although only because the root is different). It's not really like F7 when it's going to Dm instead of returning to C.

I mean, I think the difference - while arguably subtle - is worth distinguishing.
Changing a single note in a chord by a semitone (or adding one) might produce a different version of the same chord - or help reveal the function of the chord - but just as often it produces a different chord with a different function.

It walks like a duck and quacks like a duck... but there are many different kinds of duck. :D
You too. :)