Every cents-to-hertz calculator gives you a number. None of them explain why the same interval — say, 50 cents — is 26 Hz wide in one octave and over 200 Hz in another. The relationship between cents and hertz is logarithmic, which is a word that stops most people cold but actually makes sense once you see it on a keyboard. If you tune, use pitch correction, or have ever wondered why your ears and your tuner seem to disagree, this is why.
Go deeper: Sound, Scales, and the Language in our Musician Basics guide covers the physics behind pitch, intervals, and how we ended up with 12 notes — free.
How much is one cent? Well, 100 cents is how we measure the distance between one note and the next closest one. But that’s different than Hertz.
Hertz refers to how many times a string vibrates every second. If a string vibrates at one Hertz, it goes back and forth once every second. Sound travels at about 1100 feet per second.
By the time that cycle has completed, it’s over a thousand feet away. So when we’re talking about tuning, we have to decide whether we’re talking about cents or Hertz. A above middle C vibrates at 440 times every second.
The A above that, 880 times every second. And the A above that, 1760 times every second. This B flat vibrates at about 1864, which is about a hundred cycles different.
But that’s just about the only spot on the keyboard where that happens. Half that and half again, and you’re at about 466, which is definitely not a hundred cycles per second different than A 440. But the difference between any two adjacent notes is always 100 cents.
