Continuing the discussion from Making Major Chord Grips Into Minors:
Am I going mad, or is E aug I guess played as 2nd inversion 5th ,root, 3rd,5th and root the same chord as C
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Eaug ( EG#B#) and Caug (CEG#) share the same notes, different intervals.
Similarly with, Faug and Aaug, and with Baug and Gaug.
From what I understand, its just a quirk of interval movement.
@Richard_close2u will likely be able to provide some context here.
Cheers, Shane
It’s simple maths, really.
Augmented chords contain two stacked major third intervals. This means augmented chords have a combined interval of 8 semitones, which spans 2/3 of the note circle.
If you move the root note up by a major third (= 4 semitones), you’ll end up with another augmented chord. It has the same three notes (or their enharmonic equivalents), but a different root note.
Can you see what happens if we visualize it with a note circle?
Moving an augmented chord (combined interval of 8 semitones) up by a major third (4 semitones) takes us one full trip around the note circle. So now the augmented 5th of the new augmented chord is the same as the root of the previous chord.
C E G# = C aug
— up a major third —
E G# B# (= E G# C) = E aug
— up a major third —
G# B# D## (= G# C E) = G# aug
— up a major third —
C E G# = C aug
The same principle applies to full diminished chords, that stack three minor thirds, or 12 semitones. This means that each full dimished chord could be called different things, depending on the context, or which note is considered to be the root note.
C Eb Gb A = C°
Eb Gb A C = Eb°
Gb A C Eb = Gb°
A C Eb Gb = A°
Disclaimer - in theory some of the above chords should say Bbb, Dbb and/or Fbb - but that’s not very practical. I’ve consistently used A, C and Eb to keep it more or less simple. 
@Richard_close2u — we might need better visuals and explanations to demonstrate this stunning principle. 
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Hello @MASTERPIECE and welcome to the Community.
The short answer is no, you have made a mistake in the notes.
Shane gives the correct notes.
B# = C
This is spot on.
From any given start note, an augmented triad involves two equal jumps of four notes.
One additional note would arrive back at the start note on the 12-note note circle. Which creates the possibility of seeing a looping continuum if any of the notes within an augmented are used as the start point. And the rules of theory governing several aspects: stacking thirds for chord construction; using notes in strict alphabetical order for diatonic chord construction in harmonising the major scale; naming enharmonic equivalents according to whether the notes need to take a # or a B symbol all adds up the the possibility of any three notes on the Note Circle giving rise to many different (but equivalent) augmented chords.
E Augmented: E → G# → B# equivalent to
Fb Augmented Fb → Ab → C equivalent to
G# Augmented: G# → B# → D## equivalent to
Ab Augmented Ab → C → E equivalent to
B# Augmented: B# → D## → F### equivalent to
C Augmented C → E → G# equivalent to
D## Augmented D## → F### → A###
etc. etc. etc.
This is a point at which theory departs company with practical application and real-life usage.
Yours are all fine and dandy Jeff.
Whoops.
There is an error in my diagram. A## should be A###.
I will correct asap.
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I really dig these diagrams!! Just makes visualizing aug or dim chords so easy!!
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