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A bit like how I might pop down to a town in the south, but would pop up to a town in the north
Eb major: E♭, F, G, A♭, B♭, C, and D - has 3 flats.
D# major: D#, E#, F##, G#, A#, B#, and C## - is all sharps with two double sharps.
I know which one I would rather try to sight read- only a sadist and an asshole would give other musicians songs in D# major.
Yes, Ab is the 4th scale degree of Eb major.
But you can use whatever term you want.
What doesn't tend to happen is the mixing of sharps and flats when relating to musical key.
There are no standard diatonic musical keys that have a sharp and a flat within them.
So you wouldn't tend to have E♭, F, G, G#, B♭, C, and D, for example.
It is confusing to do so and it isn't the convention.
The other rule this sort of breaks is having two G's and no A. so E♭, F, G, Ab, B♭, C, and D would be considered 'correct'.
When we read music you denote the key signature so that you don't have to write down every sharp or flat on the stave.
But you do have accidentals- ie within a piece of music you might have a sharp note in a song that is in a flat key and vice versa.
(There are also some synthetic scales that have a mixture.)
If you know your circle of 5ths you will know that the first few flat keys: F Bb, Eb, Ab have relatively few flats in them and that the first few sharp keys (G, D, A, E) have relatively few sharps (as you go around the circle of 5th's/4ths you add one more sharp or flat each time).
For this reason it is much easier to read or even think about the musical key of Bb than it is A#.
You denote the musical key on the stave.
If you see this:
then you know you are in Eb major.
So when notes are written on the stave on the lines for E, A & B
This has been the convention for hundreds of years.
If you had to put in every sharp or flat it would make reading it very confusing.
Are you actually going to think of that as Eb dim rather than D# dim?
The reason these rules (actually conventions) exist is to make life easier, not harder.
But of course people can do as they please- I'm just pointing out that it makes things more confusing to mix things up in that way.
But it's not really very complicated, and working in the standard manner means you won't hit surprises or find that your habit causes you issues later.
In the olden days they started playing in C major or A Aeolian, with only the natural notes, but then the other modes and hypermodes came into being, starting with lydian and mixolydian. When C major was mixolydianised (not a word), they needed to flatten the B, so they wrote B with a small b; then they started to enjoy the sound of Lydian and tended to play it in F, but when they needed to ionianise that, they again needed to flatten the B. So the "b" sign was specifically designed to signify Bb, and B natural would be written capitalised. Then the b sign was repurposed for all flattenings; and the more pointy way of writing a little b, which was the natural sign, was then used to unflatten the B, but then also repurposed for all naturalisations, and then an even more pointy way of writing a b was created for sharpening a note, because in some keys when you went from, say, mixolydian to ionian, you actually needed to raise one of the natural notes.
I'm not actually tuning down, I just used that as an example.
I wanted to understand why sometimes chords are Ab rather than G#. This has been at the back of my mind for a few years. But watching a Jack Ruch video he was playing in C Major and then borrowed some elements and chords from Cm. He said you could consider it Cm or Eb Major - I understand this as that's the relative major. No problem there. He also used Ab Major and Bb Major within that scale. Again I understand the theory of those chords, but not why they were Ab not G# and Bb not A#.
Now I think I understand.
I only play at home, for me, so I don't need to adopt correct music notation, but it is useful to know the nest practice or convention.
I suppose that's 'mechanics' (tunings, capos, voicings) more than theory.