@Ryan, I read @HertzDevil 's post many, many times (@HertzDevil thank you for the information).
I think I finally understand how Supermodes are intended to work. But to make sure let me restate in my own words using a bit of a metaphor. If I’m missing relevant documentation let me know, all I’ve found on the topic is here: http://www.hooktheory.com/hookpad/docs#non-diatonic-chords
Let’s say for the purpose of discussion that the progression of a song is: C D7 F C E7 F
First, when you fire up Theorytab, you find yourself in the key of C Major. Two of the chords C & F are in that key, so no worries.
To find the D7, I could use the Applied Chord: D7, V of V; however, though this is the correct chord, it is not behaving as the V of V. Because this is the incorrect choice in this context (correct when D7 leads to G) I should look to borrow the chord from another mode.
To assist in this process I created the following visualization, consider a Mode Hotel, 7 floors, Lydian is staying in the Penthouse, Locrian, the Ground Floor. Keys are ordered in the cycle of fifths. Since I’m in Ionian/Major, I’m on the sixth floor.
7 - Lydian ------------- (G) - #
6 - Ionian/Major ------ ©
5 - Mixolydian --------- (F) - b
4 - Dorian ------------- (Bb) - bb
3 - Aeolian/Minor ---- (Eb) - bbb
2 - Phrygian ---------- (Ab) - bbbb
1 - Locrian ------------ (Db) - bbbbb
The chord I need is a D7: (D,F#,A,C). Since there are no #'s in the key of C, I know from the diagram that I need to call up to a floor with more sharps. I know F# is available in the key of G, so I call the Lydian Penthouse, 1 floor above, and sure enough I find a D7.
Similarly with E7 (E,G#,B,D) I could incorrectly use a V/vi (correct when E7 leads to A-) but to correctly analyze the song, I should look to borrow.
In this case, I need a G# for my chord, which (for one) is in the key of A. That’s 3 floors above C and there aren’t that many more floors in the hotel!
The solution is to go down several floors by changing the mode of the song. In this case I visit the Dorian floor, again I call the Lydian Penthouse, now 3 floors above and sure enough there is my E7. When I switch back to Major, the chord is an E7 labeled as a Major III, which is exactly what I wanted.
If the above is an accurate description, then a quick rule of thumb is: in Major, you are likely to find flatted borrowed chords by calling floors below, but, if you need sharp borrowed chords, you should visit a lower floor and call above.
As to why it’s called a Supermode, I imagine it’s because the next ‘imaginary’ floor in the Hotel would be the key of D, which contains a C#, rather than the tonic C.
Please let me know if I have missed anything regarding TheoryTab usage. If the above is correct, I may have some follow up questions which I’ll locate in separate topics. Thanks.