Cents Between Frequencies
Calculator
Results
- Interval (cents)
- 7.851415
- Interval (semitones)
- 0.078514
- Frequency ratio
- 1.004545
Music and audio results
| Interval (cents) | 7.851415 |
| Interval (semitones) | 0.078514 |
| Frequency ratio | 1.004545 |
formula-map diagram
- Interval (cents)
- 7.851415
- Interval (semitones)
- 0.078514
- Frequency ratio
- 1.004545
Musical and acoustic relationship
Formula
cents = 1200 × log₂(f₂ ÷ f₁)= 7.8514150401265
Note
This result is a simplified model: it applies the displayed standard formula to the values you entered, assuming twelve-tone equal temperament, a speed of sound of 343 m/s in dry air at 20 °C, an ideal free field with no reflections or air absorption, purely resistive speaker loads and Sabine's diffuse-field assumption. Real rooms, instruments, codecs and amplifiers depart from these idealisations, so measure with proper instruments for critical work.
More in Music and audio
See all →Frequently asked questions
What is a cent, and how does it relate to a semitone?+
A cent is 1/100th of an equal-tempered semitone, so there are 1200 cents in an octave. It's the standard unit for describing fine tuning differences too small to express meaningfully in whole semitones.
What formula does the calculator use?+
It computes cents = 1200 x log2(f2/f1), the same logarithmic ratio used for semitones but scaled by 100. This lets you express tiny pitch deviations, like a string being 8 cents flat, with useful precision.
How many cents can the average listener detect?+
Most people notice a pitch difference starting around 5 to 10 cents, and trained musicians can often detect as little as 1 to 3 cents. Anything under about 5 cents is generally considered 'in tune' for practical purposes.
Why do electronic tuners display cents instead of Hz?+
Cents give a consistent measure of how far off a note is regardless of pitch register, since the same Hz deviation means different things at low versus high frequencies. A tuner showing '-12 cents' tells you immediately the note is noticeably flat, no matter which note it is.
Can the result be negative, and what does that mean?+
Yes, a negative value means the second frequency is lower (flatter) than the first, while a positive value means it's higher (sharper). The sign simply reflects the direction of the pitch difference, not an error in the calculation.