I am confused with what I've read in various sources concerning chord notations. Is there a standard notation for chord inversions? As far as I understand, a chord inversion is determined from the bass or a chord : for instance, the 4-sound chord "Low C - EGC" (the latter three being in closed position) is in root position, as the intervals between the lower note and the others are 3rd, 5th and 8ve.
I was taking this for granted until I read some books/websites naming this a first inversion of C, as they look for the triad only.
Some sources also note the previous chord Ib (if C is the tonal center) Ia being the root position and Ic the second inversion. I guess this notation only considers the triad, but I'd like to be sure of its correct uses, specially in a context like Bach chorales where the "bass+upper triad" separation is, I think, not always relevant.