Enter two frequencies in Hz to see how far apart they are in cents, plus the beat frequency you would hear if both tones sounded at once.
Cents measure pitch difference on a logarithmic scale (100 cents per semitone), calculated as 1200 × log₂(f2 ÷ f1). Beat frequency is simply the absolute difference between the two frequencies in Hz, the rate at which the combined sound pulses in volume when two close pitches ring together.
Frequency 1 (Hz):
Frequency 2 (Hz):
How It Works
Cents measure pitch difference on a logarithmic scale (100 cents per semitone), calculated as 1200 × log₂(f2 ÷ f1). Beat frequency is simply the absolute difference between the two frequencies in Hz, the rate at which the combined sound pulses in volume when two close pitches ring together.
How to Use This Tool
- Enter the first frequency in Hz.
- Enter the second frequency in Hz.
- Click Calculate to see the cents difference and beat frequency.
Beats are most noticeable when the two frequencies are close together (within a few Hz); as the gap grows, the beating becomes too fast to perceive as a pulse and instead sounds like a dissonant interval.
Worked example 1: a tuner reads 442 Hz when you are aiming for 440 Hz (the A above middle C). Cents = 1200 × log₂(442 ÷ 440) ≈ 7.85 cents sharp. The beat frequency is 442 − 440 = 2 Hz, so if you sounded both tones together you would hear two pulses per second.
Worked example 2: compare 432 Hz to 440 Hz. The ratio gives about −31.8 cents, so 432 Hz tuning sits roughly a third of a semitone below standard concert pitch, and the beat frequency is 8 Hz, which is a clearly audible flutter.
Why Cents Instead of Hz?
Our ears hear pitch by ratio, not by raw Hz. A 2 Hz gap is enormous near 50 Hz (a very low bass note) but tiny near 2,000 Hz. Cents fix this problem by expressing the gap as a fraction of a semitone, so 10 cents sounds like the same amount of “off” on a low note or a high note. A semitone is 100 cents, and an octave is 1,200.
Using Beats to Tune by Ear
Beats give you a way to tune two strings, or two instruments, without a tuner. Play the two notes together and listen for a slow wobble in volume. The closer the pitches get, the slower the wobble, and when the beating disappears the notes match. Guitarists use this by comparing a fretted note against an open string, and wind and brass players use it to match a partner’s pitch. The rule of thumb: count the pulses per second, and that number is the frequency gap in Hz.
Did You Know?
- Piano tuners historically used beat frequencies by ear to tune octaves and fifths precisely, long before electronic tuners existed.
- A cent is defined as 1/100th of an equal-tempered semitone, so 1200 cents make up a full octave.
Frequently Asked Questions
Why do I hear a pulsing sound when two notes are close in pitch?
That pulsing is the beat frequency, caused by the two sound waves alternately reinforcing and canceling each other as their phases drift in and out of alignment.
What is considered “in tune”?
There is no universal cutoff, but many musicians aim for within about 5 cents of the target pitch for a note to sound acceptably in tune.
How many cents can most people hear?
Trained listeners can often notice differences of a few cents between two tones played one after the other, and much smaller differences when the tones sound together, because the beating gives it away. For most casual listeners, about 10 cents or more starts to sound out of tune.
What does a negative cents value mean?
A negative value means the second frequency is lower than the first (flat). A positive value means it is higher (sharp). The beat frequency is always positive, since it is just the size of the gap.
How do I find the frequency of my note?
Use a tuner app that shows Hz, or look up the standard frequency for the note with the Note Frequency Converter, then compare it to what your instrument produces.