Cents & Transpose Calculator
Convert between cents and frequency ratios, and transpose a reference frequency by a number of semitones or cents. Includes a reference table comparing equal temperament and just intonation cent values, useful for describing tuning offsets.
12-Tone Equal Temperament Intervals in Cents (with Just Intonation Comparison)
Equal-tempered values are derived from the definition that one semitone equals 100 cents and one octave equals 1200 cents. For the perfect fifth, perfect fourth, major third and minor third, the table also shows the long-known just intonation ratios for comparison (e.g. a just perfect fifth is a 3:2 ratio).
| Interval | Semitones | Equal Temperament (cents) | Just Intonation (cents) |
|---|---|---|---|
| Unison | 0 | 0 | 0.00 |
| Minor 2nd | 1 | 100 | — |
| Major 2nd | 2 | 200 | — |
| Minor 3rd | 3 | 300 | 315.64 |
| Major 3rd | 4 | 400 | 386.31 |
| Perfect 4th | 5 | 500 | 498.04 |
| Tritone | 6 | 600 | — |
| Perfect 5th | 7 | 700 | 701.96 |
| Minor 6th | 8 | 800 | — |
| Major 6th | 9 | 900 | — |
| Minor 7th | 10 | 1,000 | — |
| Major 7th | 11 | 1,100 | — |
| Octave | 12 | 1,200 | 1,200.00 |
Tips
- You can enter positive or negative cent values. A negative value means a transposition downward, or a flat (lower) tuning offset.
- To find the concert pitch of a transposing instrument (e.g. B♭ clarinet, E♭ saxophone), enter its transposition interval in semitones (e.g. -2 for B♭ clarinet) as the transpose amount.
- The frequency ratio field accepts any decimal fraction used by non-equal-tempered tunings, such as just intonation or Pythagorean tuning (e.g. enter 1.5 for a 3:2 ratio).
- Clicking the sample button fills in 440Hz and 12 semitones, so you can immediately verify the tool against the well-known result that transposing up an octave exactly doubles the frequency.
- If a tuner shows a reading like "15 cents flat," typing that number directly into the cents field instantly gives you the corresponding frequency ratio.
Frequently Asked Questions
Side Note — Why Musical Intervals Are Measured in Cents, Not a Simple Hz Difference
When comparing the pitch of two notes, it is tempting to simply subtract their frequencies in Hz. But a 5Hz gap between 440Hz and 445Hz sounds like an almost imperceptible difference, while the very same 5Hz gap between 220Hz and 225Hz sounds noticeably out of tune. That is because human pitch perception tracks the ratio between frequencies, not the raw difference — a property that a logarithmic unit like the cent was invented to capture numerically.
The cent was devised by the 19th-century English acoustician Alexander Ellis, who defined an octave (a 2:1 frequency ratio) as exactly 1200 cents. The number 1200 has no special physical significance; it was chosen purely so that it would divide evenly by the 100-cent semitones of 12-tone equal temperament, making transposition, tuning system comparisons, and pitch-deviation descriptions all reducible to simple cent arithmetic.
Expressing the gap between equal temperament and just intonation in cents makes the mismatch easy to see. A just perfect fifth, tuned to the simple 3:2 frequency ratio, comes out to roughly 702 cents, while equal temperament mechanically splits the octave into 12 identical pieces and lands exactly on 700 cents. That tiny 2-cent gap is precisely what produces the faint beating heard in chords on equally-tempered instruments like the piano, and it is why string players and a cappella ensembles often deliberately bend away from equal temperament to make a chord ring more purely.
Calculating a transposing instrument's concert pitch is a direct application of this same semitone-and-cent logic. Instruments like the B♭ clarinet or E♭ saxophone sound at a different pitch than what is written on the page, simply because each instrument has a fixed transposition interval built into its design; multiplying the written frequency by the corresponding frequency ratio yields the actual sounding pitch. That is also why, in an orchestra, instruments in different keys reading the same written note on the page are, in fact, sounding entirely different pitches.