The commonly-prescribed formula for transposing is to count how many half steps the new key is above or below the original key…
… then to add or subtract that many half-steps from each and every note in the piece.
This widely-socialized formula is mathematically accurate, but suffers from two fatal flaws:
- While it is easy to understand in theory, it is almost impossible to execute in practice unless you are a computer.
- It totally devoid of any musical understanding of the piece you are transposing.
And so, as musicians, our challenge is not to train ourselves in the herculean task of adding or subtracting some number of half-steps to/from each and every note, but to apply our functional understanding of scales, chords, and chord progressions (which is something we should be doing anyway for all the music we learn!).