CapoWhy two guitars a few cents apart beat against each other
When two notes are close but not identical, their waveforms drift in and out of alignment, and the volume rises and falls at exactly the difference between their frequencies. Two strings four hertz apart beat four times a second. Tuning by ear is really just slowing that beat until it stops.
- Play the demo. Pick 440, then 432, then both.
- With both, count the pulses per second.
- That count is the difference in hertz.
Ask two guitarists to tune to each other and watch what they do: they play the same note on both instruments and listen for a wobble, then turn a peg until the wobble slows down and disappears. Almost nobody is taught why that works, and it is one of the tidiest pieces of acoustics there is.
Two reference pitches about 32 cents apart. Play each on its own — most people cannot tell which is which. Play both and the difference becomes obvious immediately: a slow pulsing you can count.
Synthesised live in your browser with the Web Audio API — the same technology Capo uses. Nothing is downloaded.
Two waves, drifting
Sound is pressure going up and down. Two notes at exactly the same frequency go up and down together, and the peaks reinforce: one steady, slightly louder note. Two notes at slightly different frequencies start together, drift apart until one is pushing while the other pulls, then drift back into step.
When they are in step you get a loud moment. When they are opposed you get a quiet one. That cycle from loud to quiet and back is the beat, and it happens at exactly the difference between the two frequencies. 440 Hz against 444 Hz beats four times a second. Against 441 Hz, once a second.
Why this makes ears better than tuners at the last stage
A tuner reading 441 against 440 has to resolve a quarter of a percent. Your ear does not measure anything — it just counts a pulse that is happening once a second, which is trivially easy. As the strings converge the beat slows to nothing, and "no beat at all" is a far sharper target than any needle.
This is why a good string section can be more precisely in tune with each other than any of them are with a tuner.
Cents, and why 432 is about a third of a semitone
Musicians measure these gaps in cents: one hundredth of a semitone, twelve hundred to the octave. The gap between A = 440 and A = 432 is about −31.8 cents, which is roughly a third of a semitone — small enough that few people identify it in isolation, large enough that it clashes audibly against a tuned instrument within a bar.
Capo’s Fine control covers ±50 cents, which is exactly the gap that whole semitones leave behind. Anything larger is a semitone move; anything inside it is a tuning move.
What beating cannot tell you
Beating tells you two notes differ. It does not tell you which one is sharp. For that you need a reference you trust, or you need to move one and see whether the beat speeds up or slows down — slower means you are heading the right way.
And it says nothing about whether 432 Hz sounds better than 440. It does not; it sounds lower. What it does explain is why playing a 432 track against a 440-tuned instrument sounds actively wrong rather than merely different.
أسئلة
What is a beat frequency?
Why is tuning by ear more precise than a tuner?
How many cents is 440 Hz to 432 Hz?
تابِع القراءة
Why slowed audio sounds underwater
Slowing a tape drops the pitch. Holding the pitch steady is a harder trick, and the artefacts it leaves have a cause.
Why the pitch dial stops at twelve
A short note on a default: one octave each way, four if you ask for it, and a ceiling set by where the audio stops being usable.
How to learn a song by ear without naming a single note
You do not need perfect pitch or theory. You need a slow loop, one string, and a way of asking the recording yes-or-no questions.