One way to look at transposing. Let's take a simple chord progression in the key of A major: /A/D/Bm-E7/. First, let's look at this as numbers rather than letters. According to musical convention we use Roman numerals to express chords. Since this is the key of A major we designate the first chord, A, as I. Also we need to know a little scale theory. Remember back to those old piano lessons and the key signatures (for those that don't know their key signatures I try to explain that further down). We know that the key of A major has 3 sharps F#, C#, G#. Sticking those into our scale we find that the major scale in A is A,B,C#,D,E,F#,G#. To find the number for the D chord we count up the scale. A,B,C#,D making D the IV (4) chord. Counting up to the the ii (2) chord A,B gives us Bm as the ii chord. Notice the Roman numeral for the ii chord in this case is lower case. The lower case signifies that it is a minor chord. When we count up the scale to the E7 chord (A,B,C,D,E) we see that it is the V7 chord. Notice here the Roman numeral is upper case with a 7 signifying that it is a dominant 7 chord. So now expressed in Roman numerals our progression becomes /I/IV/ii-V7/.
What if we want to play this same chord progression in D? No problem, the key signature for D major has 2 sharps, F# and C# giving us D,E,F#,G,A,B,C# as our D major scale. So, now D is our I. Our next chord is the IV so we count up from D. D,E,F#,G so our IV chord is G. Counting up for the ii chord D,E and remembering that the lower case signifies minor our ii chord is Em. V7 chord? D,E,F#,G,A gives us our V7 as A7. Final result gives us /D/G/Em-A7/.
So what if we never learned key signatures? Well, here are 2 ways to figure out your scale. First, if you know the major scale pattern on your uke just start on the note that you want to know the major scale for and starting at 1 count as you play each note. When you hit the number you're looking for figure out what that note is a you got it. But what if you don't know your major scale pattern? Well, first off you probably got confused and didn't read this far anyway but if you persevered let me try and help a bit. You're going to need to know the circle of fifths. The circle of 5ths you're concerned with here is (F),C,G,D,A,E,B,F#,C#,G#,D#,A#,E#(F). Notice if we take the key of C, and count up the alphabet to the next key, G, (C,D,E,F,G) it is 5 thus the circle of fifths. Notice also that the it starts at C and goes all the way to E#, better known as F (they're the same note aka enharmonic) which are the 12 different notes that comprise the chromatic scale. Hence it circles all the way around all 12 keys. Now for the number of sharps in each key. The key of C major has no sharps or flats (C,D,E,F,G,A,B). Proceeding around the circle of 5ths the key of G major has 1 sharp. The way to know which is the 1 sharp in the key of G major is to return to our circle of 5ths and see that it begins with F. F# is the 1 sharp in the key of G major (G,A,B,C,D,E,F#). Continuing around the circle of 5ths is the key of D major. D major has 2 sharps, F# and the next note on the circle of 5ths, C#. So our D major scale is D,E,F#,G,A,B,C#. How many sharps are in the key of A major? Correct, 3 sharps, F#, C#, G# (G being the note after C in the circle of 5ths). So the scale of G major is A,B,C#,D,E,F#,G#. This continues adding one more sharp for each step around the circle of 5ths. Key of E major E,F#,G#,A,B,C#,D#. And so on. Oh, I know your next question. What about the key of F and Ab, Bb, etc? Well for that we spin the circle the opposite way and call it the circle of 4ths: (C),F,Bb,Eb,Ab,Db,Gb,Cb(B). Each note is a 4th away from the previous. Again, the key of C major has no accidentals (aka sharps and flats). The next key on the circle of 4ths is F major. F major has 1 *flat* which is Bb. The F major scale is F,G,A,Bb,C,D,E. The next key after F on the circle of 4ths is Bb. Since F had 1 flat Bb obviously must have 2 flats Bb and the next note after Bb on the circle of 4ths, Eb. So the scale of Bb major is Bb,C,D,Eb,F,G,A. Eb major has 3 flats, Bb, Eb, Ab and the Eb major scale is Eb,F,G,Ab,Bb,C,D. We continue around adding our flat notes to the next key until we get to Cb which is the same as B (remember enharmonic?). Since we already covered the key of B in the section on the sharp keys we don't need to go further. So now we have all the keys covered plus the commonly used enharmonic keys.
I know this is a little complicated. It's also not the only way to explain these concepts. Like many aspects of music theory there are more than one way to look at things. It can actually be kind of fun to see how it all links together. But never let the study of theory take you from what is really important which is this: HAVE FUN PLAYING MUSIC.
