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 steps from each and every note in the piece.
This widely socialize counting “half-step” formula sounds quite logical, and 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.
- The counting formula is devoid of any musical understanding of the piece you are transposing.
The solution is not to do the ridiculous mental gymnastics required to add or subtract some number of half-steps, but to apply the deep musical understanding gained by the functional study of scales, solfege, chords, and chord progressions.