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Art and culture · Music and sound

The octave: why does it sound like "the same note"?

When a man and a child sing the same song, their frequencies differ but the melody sounds the same. Discover the secret of doubling the frequency, the octave, and find the A's on a piano yourself.

  • 15 min
  • 2 simulations
  • Mini quiz

Updated:

Preview

The question

A father and his young daughter sing the birthday song together. The father's voice is clearly deep, the daughter's high. Even so, it sounds as if they are singing "the same song, on the same notes"; nobody thinks they are singing different melodies. Yet if we measured them, the two voices would have very different frequencies. How can different frequencies sound like the same note?

Try it yourself

No account needed: change the values and check your answer. Some simulations ask for a prediction before they start; it doesn't matter whether it's right or wrong.

Sound lab

A, one octave up

Change the frequency of the second tone with the slider or the plus and minus buttons. Watch the waves and the frequency ratio; if you like, press Play to hear the two sounds together. When you're ready, press Check.

Prediction

Predict first

What do you think the frequency of the same note one octave above a 220 Hz note should be?

It doesn’t matter whether you’re right; the simulation opens once you choose.

Number line

The piano's lowest A

Drag the marker or move it with the arrow keys, then press Check.

Prediction

Predict first

What happens to the frequency when you go down four octaves from 440 Hz?

It doesn’t matter whether you’re right; the simulation opens once you choose.

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Frequently asked

5 questions

Does each octave add the same number of hertz?

No, an octave multiplies the frequency by two. Going from 220 Hz to 440 Hz is one octave, but the next A is 880 Hz, not 660 Hz. That is why octaves are not evenly spaced on the frequency axis; your ear responds to ratios, not differences.

Are two notes an octave apart the same sound?

No. They share the same note name and sound related, but their frequencies differ: the upper note has twice the frequency of the lower one, so it is one octave higher.

Why does twice the frequency sound like "the same note"?

A 220 Hz sound also produces overtones at 440, 660 and 880 Hz. The overtones of a 440 Hz sound are 880, 1320 and 1760 Hz. All the frequencies of the upper note are already among the overtones of the lower one, so the brain hears such overlapping sounds as members of the same family.

If its name means "eighth", why does an octave on the piano have 12 semitones?

The name comes from it being the eighth note in the seven-note scale of Western music. Today's piano, however, divides the octave into 12 equal semitones; the frequency ratio between two neighbouring keys is about 1.0595. Turkish makam music uses even finer intervals.

Why do you hear an octave higher when you press the exact middle of a string?

With the same tension and thickness, a string's frequency is inversely proportional to the vibrating length. Halve the length and the string vibrates twice as fast, so the frequency doubles. That is why the 12th fret on a guitar sits exactly in the middle of the string.