Transposing key signatures - how to do so quickly?

Question

I've been attempting to pick up my music theory after a 1 month hiatus, and I've stumbled across transposing key signatures - is there a quick method of figuring out the new key signature? Because right now I'm transposing every note of the key signature to find out the new key signature - but I feel like there's a much quicker method to do so. Right now I can't be completely certain of a new key signature if a couple of newly transposed note fit it - because I don't know whether there will be 2 notes that might not do so. Help will be appreciated, thanks!

EDIT: If you don't understand - what I mean by transposing key signatures is by transposing each note of it up or down by an interval such as a major 2nd - such as how if you transpose C major up by a major 2nd it becomes D major. To clarify - I am not struggling with the transposition of key signatures - I am struggling to do it quickly. An example would be where I transpose E minor up by a minor 3rd to find the new key signature - it would take me at least 10 minutes to do so.

Answer 1

The closest thing to a formula is the circle of fifths; key signatures operate in conjunction with the circle.

→ → → Add sharps/Remove flats → → →

                  Total sharps                Total flats
           -------------------------  --------------------------
           0   1   2   3   4   5   6 /6    5    4    3    2    1   (0)

Major key: C   G   D   A   E   B   F#/Gb   Db   Ab   Eb   Bb   F   (C)
Minor key: A   E   B   F#  C#  G#  D#/Eb   Bb   F    C    G    D   (A)
New Sharp:     F#  C#  G#  D#  A#  E#/
                                     /Cb   Gb   Db   Ab   Eb   Bb      :New Flat

                                             ← ← ← Add flats/Remove sharps ← ← ←

Note that the sharps and flats, respectively, are added in circle-of-fifths order as well. (First sharp = F#; second is C#; third is G#; etc.)

---

Notice that the columns in the above chart give two patterns: one for sharp keys; one for flat keys.

• Sharp keys: The columns comprise three notes ascending stepwise when ordered Minor Key - New Sharp - Major Key.
• Flat keys: The columns comprise root position major triads when ordered New Flat - Minor Key - Major Key.

Answer 2

Here's how musicians do this quickly.

Your prerequisites are going to be:

1. Memorize all 12 major and minor key signatures.

2. Memorize the order of the notes on the keyboard

3. Memorize the size of every interval you might have to transpose by

This might sound like a lot, but every* professional musician has already done this. (drummers included? I don't know). Doing it fast just requires applying prior knowledge.

Want to transpose from A up a whole step? If you know how big a whole step is and you know where the notes are, you can quickly find that your destination is B. And we know from memory that B has 5 sharps- F, C, G, D, A.