Hello @elephant welcome to the Community.
The potential list of major scales is much larger as you suggest.
Justin has chosen the list to avoid any major scales that would create the need to use a double sharps or double flats. Because there is always an enharmonic equivalent to those which would be more sensible and more commonly used. Keeping it simple.
Hope that helps.
Cheers 
| Richard_close2u | Community Moderator, Official Guide, JustinGuitar Approved Teacher
A little footnote: I found this book, written by two Hungarian pianists, a few weeks ago at a musical bookstore, though didn’t buy it as it seems way out of my musical scope.
The descriptions says, “The purpose of this book is the description, interpretation, categorization and analysis of all mathematically possible scales in the twelve-tone equal temperament system. The book consists of three units: the 1st and biggest part presents the 2048 scales; the 2nd part is a summary of the scales and their variations in the form of a table of modes; the 3rd part presents the possible occurrences of each chord in each key/tonal system.”
So yeah, there are a huge number of scales, 2048 feels incomprehensible to me, but I’m sure the authors know what they are talking about.
Holy cow.
Nobody has time in their life for that many scales.
Preposterous.
But possible!
Much as love theory, no way Jose. Not going that Mariana Trench of a Rabbit Hole. 
hello sir I have doubts kindly clear it
1- F# = G#, A#, B. C#, D#, E# { what this E# ? Why its written here } it should be F .
2- C# = D#, E# {again E# why? it should be F here }, F#, G#, A#, B# {Why its written here ?it } it should be C here
3- Gb = Ab, Bb, Cb {why it written here} it should be B here,
4- Also there is no Cb scale. though it mention in worksheet
kindly explain these 3 above issue in major scale worksheet I was Practising and matching it
i guess its written by mistake then
just want to clear doubt .
Hello @Inolas07 and welcome to the community.
No letter can be used more than once in any scale.
There are seven letters only which can be used, running from A to G inclusive.
Where a note within a scale would ordinarily take one name, if that letter has already been used, then it needs to be renamed using an enharmonic equivalent and flats / sharps.
The E# must be used.
E# is the same as F but the letter F has already been used.
You can not use the same letter more than once.
You must use all seven letters once each.
f E# was named as F, then it was followed by F#, the letter F is used twice and the ltter E is not used at all.
That breaches the rule above.
Cb is an enharmonic equivalent to B but the letter B has already been used. The same as above.
Cb major = Cb, Db, Eb, Fb, Gb, Ab, Bb
I hope that helps
Cheers
| Richard_close2u | JustinGuitar Official Guide, Approved Teacher & Moderator
Such a great exercise! I’ve had a few a-ha moments connecting what I’ve heard in years past to “So THAT’S why!?”. I appreciate the teaching style. In years past, I would create a spreadsheet and have it all laid out, etc. Now with the insights that Justin is giving, I will KNOW what and why, instead of 100% memorization.
I’ve worked out the chart a couple of times, but i know that I will mostly use the key of C and the sharp” keys G, D, A and E, unless I play in a jazz band or transpose songs from non-guitar songbooks.
Justin mentioned in one of his lessons that it is easy to visualize the C major scale by thinking about the white and black keys on a piano keyboard. If you haven’t had any piano lessons as a child or adult as I have (just 3 months as a child and 3 month class as adult), then that may go over your head. My suggestion is to check out Justin’s short discussion of Play Piano in 15 minutes in the Explore: Playground: “Food for Thought” section.
Justin says:
“One of the cool things about theory applied to the piano is that it’s a lot more obvious than guitar”
If you are interested in any supplementary info beyond that, I would suggest an updated version of the piano book I used in the adult piano class I took. The title is:
You can easily find on Amazon and I like the Kindle version on my IPad because it is one of the few music books that shows the unaltered book formatted view of the page. The major scale theory is discussed on page 100 halfway through book 1.
I’ve bought all 3 books, but only used book 1 so far, but it has a lot of printable worksheet pages for naming notes in scales and chords that might be a useful supplement to this course. Also, there are some tips on warming up your hands and fingers without playing and hand and finger anatomy that would also be useful to guitarists, which you can read in pages 4-5 and 10-11 in the Look Inside feature on the Amazon page.
Also, I’ve discovered that all the songs from the book are demonstrated in YouTube.
This just blew my mind. 
I’ve always wondered about and assumed there was a good explanation as to how and why music, i.e. certain sound frequencies “work” together and others don’t.
Now my follow up question to all of this, is why do we humans have ears that find certain frequency combinations pleasing?
Thank you, I had the same question.
So how can you play a E# when it doesn’t exist?
It does exist. Play fret 1 on either of your two E strings.
Play fret 8 on the A string.
Play fret 3 on the D string.
Play fret 11 on the G string.
Play fret 6 on the B string.
We ordinarily call these notes F but not if the context you are naming them from has shifted and the necessity of using the enharmonic name E# kicks in.
I hope that helps.
Cheers
| Richard_close2u | JustinGuitar Official Guide, Approved Teacher & Moderator
Is this a chicken and egg question? Which came first, the ears attuned to the notes or the notes that please the ears?
And we also feel these frequencies with our bodies, not just hear them with our ears.
so to clarify for you both, you are correct in the sense that according to this theory E# and B# would exist. They in fact do exist, it’s just a case of them actually being the F and C note and it’s just a lot less confusing to stick with C and F in a general context. In the CONTEXT of figuring out the keys in the major scale, they do ‘exist’ but yes you are correct that they are simply just the C and F notes.
P.S so by context I mean if you were playing to sheet music in a band in this key, the sheet music wouldn’t say a completely new note (C or F) but simply say your previous note (B or E) but the sharpened version. In terms of sight reading and playing along, this is fine, you would simply move up a half step to sharpen the note, which would land on C or F, but in the CONTEXT of playing to that key, that is where the B# and E# “Exist”. It’s once again in the typical habit of humans, just a way to be a bit lazy and make things slightly easier to write/read rather than having to put in a brand new note, just saying “yeah that one again but up a bit” lol
Interesting take on this. I understand it, yet it almost reminds me of how our government works.
A bit screwy
I am working with this on various levels now and am used to it.
thanks for the input
Paul Miller
if i wish to learn the major scales (to figure out stuff faster), do i learn them with the double sharps and flats?? because justin’s answer sheet has them.
( eg: e#, though this should be f)
There is a difference between ‘learn’ and figure them out’.
You are not expecetd to learn / memorise all major scales.
You are expected to learn the formula and the means for figuring out the notes of any major scale using the methods.
Justin encourages you to figure them out in this exercise - but not to memorise them.
Cheers
Richard
Hi,
I have a question which you might be able to help me. I was taking the Grade 3 exam and there is question where E# is mentioned (please see attached).
I am bit confused by this because i thought between B and C AND E and F, there were no accidentals. And if that is the case, why is there E# mentioned in the question?
Any clarification would be very much appreciated.
Regards
Bivek
@bivek123 Hello and welcome to the community.
The question comes up often.
See posts above in the topic.
Justin does give a full answer and explanation in the lesson:
I hope that helps.
Cheers | Richard | JustinGuitar Approved Teacher, Official Guide & Moderator
Hi Bivek,
In scales, each “letter” has to be used only once, hence B# and E#. Also, revise enharmonic equivalents if necessary.
