It's not half diminished though, since there's no 7? I'm talking about just the diminished triad (min 3rd + min 3rd). It's been years since I read jazz notation (classical background), but I thought that was just written "dim"
Also, if you're seeing sevenths thrown in, it might be because in jazz chords are more for suggesting a scale than the actual pitches of the harmony. At least, that's how I understand it as a classical musician.
E.g., an example of a minor 3rd would be an A and the first C above that A? E.g., on violin could play the A the first A on the D string and the C the first C on A string?
- Diminished: Minor Third + Minor Third
- Minor: Minor 3rd + Major Third
- Major: Major 3rd + Minor Third
- Augmented: Major Third + Major Third
With the intervals being between the tonic and third, third and fifth. So for your example, that would be A, C, Eb as a diminished triad.