Work out transpose key instantly with clear inputs, formula shown and shareable results.
Transposition adds the semitone shift to the key's position in the twelve-note chromatic circle, wrapping around, and the frequency ratio is two to the power of semitones over twelve. Since an octave is twelve semitones, moving up three semitones raises every frequency by about 19%, which is exactly what makes a capo work.
New key
new position = (original position + semitones) mod 12
Frequency ratio
ratio = 2 ^ (semitones / 12)
new position = (original position + semitones) mod 12. Transposition adds the semitone shift to the key's position in the twelve-note chromatic circle, wrapping around, and the frequency ratio is two to the power of semitones over twelve.
Since an octave is twelve semitones, moving up three semitones raises every frequency by about 19%, which is exactly what makes a capo work.
Enter original key, semitones to move. The defaults shown are a realistic worked example — swap in your own figures to get a result you can use.