How to Look Up the Frequency of a Note

You need to set a tone generator to A4, or check what frequency a resonance corresponds to, or work out whether a recording is at concert pitch. All three need the same lookup and the same understanding of how the numbers relate.

Frequencies are multiplicative

Every octave doubles the frequency. A4 is 440 Hz, A5 is 880, A3 is 220.

Within an octave, equal temperament divides that doubling into twelve equal ratios rather than twelve equal steps in hertz. Each semitone multiplies frequency by the twelfth root of two, about 1.05946.

f = 440 × 2^(n/12)

Where n is the number of semitones from A4, positive or negative.

The consequence is that the same musical interval spans wildly different numbers of hertz depending on where you are. A semitone at the bottom of the piano is a couple of hertz; the same semitone three octaves up is dozens. Which is why hertz is a poor unit for describing a tuning difference.

Cents make intervals comparable

A cent is a hundredth of a semitone, so 1200 cents to the octave. It’s logarithmic, which means a cent represents the same perceived interval anywhere in the range.

That makes it the useful unit for tuning:

• Around 5 cents is where most listeners start noticing a difference on a sustained tone
• 10-15 cents sounds noticeably out
• 100 cents is a full semitone

Baroque pitch at A4 = 415 Hz sits almost exactly 100 cents — a full semitone — below modern concert pitch, which is why baroque players read a written A and produce something a modern ear hears as A♭.

Why A440, and why it isn’t universal

Pitch standards varied enormously across Europe historically — church organs, opera houses and instrument makers each had their own, and surviving instruments span a wide range.

A440 was adopted as an international standard in the twentieth century to end that. In practice orchestras still vary slightly, with several tuning a few hertz sharp for a perceived brightness, and period ensembles deliberately using historical pitches.

So a recording that sounds slightly off against a tuner may be at a different reference rather than out of tune.

Equal temperament is a compromise

Dividing the octave into twelve equal ratios makes every key equally usable. It also means no interval except the octave is perfectly in tune.

A pure major third is a 5:4 frequency ratio. In equal temperament it’s about 14 cents sharp of that — audible as a slight beating on a sustained chord, which is why a barbershop quartet or a string ensemble adjusting by ear sounds different from a piano.

Just intonation gives pure intervals in one key and unusable ones in others. Equal temperament spreads the error evenly so nothing is perfect and nothing is unbearable, which is the trade that made keyboard music in all twelve keys possible.

Common mistakes to avoid

• Describing a tuning difference in hertz, which means different things at different pitches.
• Assuming a recording is out of tune when it’s at a different reference pitch.
• Mixing scientific pitch notation conventions — middle C is C4 in the standard system, and some software calls it C3.
• Expecting equal temperament thirds to sound pure.
• Forgetting that instruments drift with temperature, sometimes by more than the difference you’re chasing.

How to do it with Note Frequency Chart

The Note Frequency Chart shows frequencies at any reference pitch with cents deviation.

1. Pick the note and octave in scientific pitch notation, where middle C is C4.
2. Set the concert pitch reference if you’re not at A440.
3. Read the frequency, and the cents deviation if comparing tuning systems.
4. Use cents rather than hertz when describing how far out something is.

Other audio tools are in the tools directory.

Frequently asked questions

Why is A440 the standard?

It was adopted internationally in the twentieth century, replacing a range of local pitches. Orchestras still vary slightly around it, and some tune deliberately sharper for brightness.

What is a cent?

A hundredth of a semitone — 1200 to the octave. It’s logarithmic, so a cent represents the same perceived interval anywhere in the range, unlike a fixed number of hertz.

Why is equal temperament a compromise?

Because it makes every key equally usable by making no interval except the octave perfectly in tune. Just intonation gives purer thirds and fifths in one key and unusable intervals in others.

Final thought

Talk in cents, not hertz. Five hertz means nothing without knowing which note you’re near, and five cents means the same thing everywhere.

Try the free Note Frequency Chart