I'm trying to get better at reading and writing standard notation. I was wondering how to transpose a piece from one key to another on sheet music, so I wrote a 2-bar phrase and tried to do it myself. The first bar is just natural notes, the 2nd bar contains alterations. I quickly realised that, if there are no alterations, it is actually pretty easy. The problem seems to be that of transposing the sharps and flats.
In this first picture you can see the 2-bar phrase that I wrote, followed by the same phrase transposed through the circle of fifths (c major/g major/d major/a major/e major). In this 1st picture the transpositions were done automatically by the software, and as you can see, the software accomplished this by adding lots of natural signs. I can see why that is correct, but if I were to do this by myself, it would take a long time since I'd always have to remember which sharps are in the key signatures, recognise them on the score and calculate the intervals in the piece, etc.
So when I tried to do it myself on paper, I came up with what you can see in picture 2. All I did was to move the phrase up or down the staff until it was in the right key. This worked really well for the keys of G and D, but when I got to the keys of A and E (and I didn't notice this at first), I realised that I have to make those notes double sharp in order for the phrase to be correct.
I play guitar, and on most stringed instruments you could just move the passage up and down the fingerboard, and it would be automatically transposed.
Isn't there a simple way to do this on sheet music as well? It seems that you can move the passage up and down the stave just fine, but the sharp/flats and key signature accidentals really make this more complicated than it should be.
Am I missing something obvious here?