Key Transposition Calculator
Transposition shifts every note of a piece by the same interval, raising or lowering the key while keeping the music's shape unchanged. This calculator takes a starting key (as a chromatic number where C is 0) and the number of semitones to move, then returns the new key name, the frequency ratio of the shift, and the change in cents. Singers, accompanists, and arrangers use it to move a song into a comfortable range, and players of transposing instruments use the same arithmetic to convert between written and concert pitch. Positive semitones move up; negative semitones move down.
Transposition formula
New key = (starting key + semitones) modulo 12
Frequency ratio = 2^(semitones / 12)
Cents shift = 100 * semitones
Note name = lookup of new key in the chromatic scale
Keys are numbered C=0 up to B=11. The modulo 12 keeps the result inside one octave for naming, while the frequency ratio reflects the true pitch shift including octaves.
Transposition context
- Common intervals: whole tone 2, major third 4, perfect fourth 5, perfect fifth 7, octave 12 semitones.
- Transpose up to brighten and fit higher voices; down to suit lower voices.
- A B flat trumpet sounds two semitones below the written note, a constant transposition.
- Each semitone is 100 cents and a frequency ratio of about 1.0595.
- Negative semitone values transpose the key downward.
Key transposition: frequently asked questions
What does transposing a key mean?
Transposing moves every note of a piece up or down by the same interval, keeping the melody and harmony intact but shifting the overall pitch. A song in C transposed up two semitones becomes a song in D, sounding identical in shape but higher in pitch.
How many semitones are in common intervals?
A whole tone is two semitones, a minor third is three, a major third is four, a perfect fourth is five, a perfect fifth is seven, and an octave is twelve. Enter the semitone count for the interval you want and the calculator names the new key.
Why do singers ask to transpose?
A key that suits one voice may sit too high or too low for another. Transposing shifts the whole song into a more comfortable range without changing its character. Accompanists transpose on the fly or rewrite the chart in the new key.
Does transposing change the frequency ratio?
Yes. Each semitone multiplies frequency by the twelfth root of two. Transposing up n semitones multiplies every pitch by two raised to n over twelve, and the cents shift is one hundred times n. Transposing down uses negative semitones.
Do transposing instruments work the same way?
Transposing instruments such as the B flat trumpet sound a fixed interval away from the written note, which is a constant transposition. The same arithmetic applies: add the instrument's transposition in semitones to the written pitch to get the concert pitch.
Official sources
- UNSW School of Physics: Note names, MIDI numbers and frequencies.
- UNSW School of Physics: Music acoustics.
Reviewed by the CalculatorHub team, edited by James Graham, 17 June 2026. See our methodology.