#1
An augmented triad is a root, 3rd, and sharp 5th, creating a stack of two Major 3rd intervals.

Likewise, a Diminished triad is a root, flat 3rd, and fifth, which makes a stack of two Minor 3rd intervals.

With different voicings, would it be wrong to assume that E Aug is a possible voicing of C Aug? And that Eb Dim is a possible voicing of C Dim? The same applies for G# Aug (For C Aug) and F# Dim/A Dim?

If I were to make a massive chord that contains all notes of C Aug, and aother for C Dim, would they not contain all of the chords above?

And if I am correct so far, if a voicing of E Aug contains the notes E, G#, C, and E, (A triad with a possible octave), is it E, G# or C Aug?

Same applies for a voicing of C Dim that contains Eb, F#, A, and C Dim, (A triad with a possible octave), is it Eb, F#, A, or C Dim?

And the applicable question, if I see E Aug, can I play C Aug or G# Aug?
#3
A lot of chords share the same notes. In the context of a song it will usually draw more strongly to one interpretation of the notes than another.
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#4
as a resolution standpoint:
usually you can tell from the chord after it, which ever it resolves too

applying: yes if you play a E+ arpeggio over a C+chord then it would be fine



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#6
Just a quick thing to add:

The only time diminished chords will ever REALLY be inversions of each other would be in Xdim7 chords (C Eb Gb Bbb) because at that point... you're just a m3 away from the C again! It really IS just a stack of m3's. Though, if you do a m7b5 chord... then no. Cm7b5 =/= Edim or Gbdim.

tl;dr - Cdim7 = Ebdim7 = Gbdim7 = Bbbdim7
however, Cm7b5 =/= the above mentioned (unless you alter the chord names/functions).

Quick note: as mentioned the root changes with function and context, so Cdim7 might be more suitable in a song in D Minor while Gbdim7 would suit a song in Ab Minor.
#7
In practicality, there are only 4 augmented triads and 4 diminished triads. The rest are simply inversions of one another. However, in theory they will function differently and also to note is that if you see the notes CEG#, that's a C+ triad, because to be an E+ triad in first inversion it would have to be spelt B#EG#. They will both sound the same, though function differently. The same goes for diminished triads and FULLY diminished seventh chords.
#8
Quote by jazz_rock_feel
In practicality, there are only 4 augmented triads and 4 diminished triads. The rest are simply inversions of one another. However, in theory they will function differently and also to note is that if you see the notes CEG#, that's a C+ triad, because to be an E+ triad in first inversion it would have to be spelt B#EG#. They will both sound the same, though function differently. The same goes for diminished triads and FULLY diminished seventh chords.
Diminished triads don't have enharmonic equivalents. C diminished is not the same as Eb diminished. That's only the case for fully diminished seventh chords.
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#11
In the context of a minor ii7b5-V7b9-i7 the V7b9 can be treated as a diminished chord, and because diminished chords are symmetrical in their structure (being comprised of minor thirds), you can modulate to keys a minor third away.