Boneyard Tools

Harmonic Series Calculator

Enter a fundamental frequency and how many harmonics to list. Each harmonic is a whole-number multiple of the fundamental, shown in hertz with the interval in cents above the root.

How to use the harmonic series calculator

  1. Enter the fundamental frequency in hertz, for example 110.
  2. Choose how many harmonics to list, up to 64.
  3. Read each harmonic in hertz and its interval in cents above the fundamental.

Examples

Harmonics of 110 Hz

110 Hz, 8 harmonics
110, 220, 330, 440, 550, 660, 770, 880 Hz

Second harmonic interval

Any fundamental, harmonic 2
1200 cents (one octave)

Frequently asked questions

What is the harmonic series?

It is the set of frequencies that are whole-number multiples of a fundamental. Harmonic n has frequency n times the fundamental, so the series is f, 2f, 3f and so on.

How is the cents value above the fundamental found?

For harmonic n the interval above the fundamental is 1200 x log2(n) cents. The second harmonic is 1200 cents, an octave, and the third is about 1902 cents.

Why does the third harmonic sound like a fifth?

The third harmonic is about 1902 cents above the root, which is an octave plus a near-just perfect fifth of about 702 cents. It is why brass and string overtones outline triads.

Are harmonics and overtones the same thing?

Closely related. The first overtone is the second harmonic, the second overtone is the third harmonic, and so on. Harmonics are numbered from the fundamental as harmonic one.

How many harmonics can I list?

Up to 64. Higher harmonics get very close together in pitch and quickly exceed the range of hearing for high fundamentals.

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