Let me take you down
May 29, 2026 at 11:50 PM by Dr. Drang
I just learned that people are listening to music pitched slightly down because it makes them feel better. Instead of the A above middle C being set at 440 Hz, they have it tuned down to 432 Hz.
This strikes me as odd, but how you feel is how you feel. Do whatever you want, as long as it doesn’t hurt anyone. I was interested, though, in the math behind this pitch change.
In the equal-tempered scale, the frequency ratio of a semitone, which I’ll call is the twelfth root of two:
This is the ratio of frequencies of adjacent piano keys.
The ratio of 440 Hz to 432 Hz is
so the pitch difference you get from moving down to 432 Hz is distinctly less than a semitone. How can we characterize that difference?
Small differences in pitch are measured in cents. There are 100 cents in a semitone, so the frequency ratio of one cent, , is
To get the number of cents we move down in going from 440 Hz to 432 Hz, we solve this equation for n:
Taking the base-2 logarithm of both sides yields
and therefore
So going from A440 tuning to A432 tuning means going down about 32 cents or about a third of a semitone. Not a lot, but you (probably) can hear it.
Here’s two seconds of A440:
And here’s two seconds of A432:
It’s easier to hear the difference when they’re played simultaneously because the beat frequency is distinct:
Given the name of this blog, I would be remiss if I didn’t mention the famous splice in “Strawberry Fields Forever.” There were two takes that John Lennon liked: a slower version in a lower key and a faster version in a higher key. He wanted the final song to have part of one and part of the other. Right. As luck would have it, though, producer George Martin and engineer Geoff Emerick learned that adjusting the tape speeds to bring the two tempos together also put them in the same key.