Look at this chart of all the notes on a piano keyboard, along with their frequencies. Hopefully this will help you visualize how note names repeat.
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Iāve been mulling this over for a couple of days and think that I have got it.
On the basis that Justin is using E, G and Bb as an example with E as the lowest the scale would be, as noted:
Similarly if he had used G as the lowest note the scale would be (as shown by Shane):
and if he had used Bb as the lowest note then the scale would be:
On this basis the notes would be using 1, 3 and 5:
- E major scale - E, G, B and is E diminished.
- G major scale - G, B, D and is a major chord.
- Bb major scale - Bb, D, F and is a major chord.
Hopefully all the above is correct.
As this is about triads what is the fingering for the notes shown above?
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Would be Em.
E G Bb would be Ddim
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Stuart, you have correctly written three major scales and state that you will take the 1, 3 and 5 from each.
By definition that gives you three major triads, the tonic triad built from the root note of each scale respectively.
Major triads = 1, 3, 5.
That is already covered.
As for grips, there are many. There are three possible grips on each set of three adjacent strings. Justin has taught some major triad grips on the G, B and E strings so start there.
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Writing down the four triad types for all notes as suggested in the lesson text is a great exercise. I really like it. It has been almost ten months since I completed PMT module 3, so I always also make a point of recalling the major scales for each key with the major scale formula.
I started with C, and everything went just fine. Enter D# major. Andā¦ D# major isā¦ weird 
I can build the different triad types ( D# major = D# Fx A# ; D# minor = D# F# A#; D# augm. = D# F x B; D# dim = D# F# A).
I also understand that Fx is actually G (but may not be called G since G# is the 4th of the D# scale).
Given that the scale includes yet another doublesharp, I started googling whether there are any songs explicitly written in D# major. Interestingly I found statements claiming that the D# major scale only exist theory and that there are no key signatures with doublesharpsā¦ D# major is weird 
While this implies that all D# major key sounding songs are written in the key of Eb major, I have trouble believing that there are really no songs explicitly written in - or with passages of - D# major at all. For example, if a song written mainly in C# major were to include a passage sounding like D# major, this passage would be written in D# rather than in Eb major? Perhaps there are also some composers, who explicitly want to have a certain piece understood as D# major?
As your instinct tells you ā¦ anybody wanting to use those pitches created by pressing those keys or plucking those fretted strings would notate in the key of Eb ā¦ or be a sadist who deliberately wanted to make life difficult for people reading the music and playing the piece. 
Besides - the key of Eb is extremely common ā¦ ask any brass player.
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Thanks 
So, would it be safe to say that irregardless of major or minor keys, keys with doublesharps or doubleflats are mostly theroretical or conceptional only and that instead 99% of the time the enharmonically equivalent key without doublesharps and doubleflats is used?
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Thatās a good summary, yes.
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Stuart,
Almost! Here is a correction/further detail:
- E major scale - E, G, B is an E minor chord (Minor Chord formula is: 1, flat 3, 5).
- G major scale - G, B, D is a G major chord (Major Chord formula is: 1, 3, 5).
- Bb major scale - Bb, D, F is a Bb major chord (Major Chord formula is: 1, 3, 5).
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