Reply To: Half Diminished
Just for some extra clarification, while German Sixth is close to the dominant seventh save function, since it goes to a cadential 6-4 instead of what would be a tonicized I chord, no "sixth" chord(German, french, or italian) emulates the Half Diminshed 7th chord.
I'm pretty sure that Italian is Flat 6, 1, and flat 3, French is the same but adding in 4, and German is same, but swapping 4 for flat 5.
So in C Major, the chords would be:
It6: Ab, C, Eb
Fr6: Ab, C, Eb, F
Ger6: Ab, C, Eb, Gb