Harmonic Series Calculator

It is the set of frequencies that are whole-number multiples of a fundamental. Harmonic n has frequency n times the fundamental, so a 100 Hz root gives 100, 200, 300, 400 Hz and onward. These overtones are what give a violin, trumpet or voice its distinctive timbre.

For harmonic n the interval above the fundamental is 1200 times the base-2 logarithm of n, measured in cents. The second harmonic is exactly 1200 cents (one octave), the fourth is 2400 cents (two octaves), and the third is about 1902 cents.

The third harmonic sits about 1902 cents above the root. That is one octave (1200 cents) plus roughly 702 cents, which is a near-just perfect fifth. This is why brass and string overtones naturally outline major triads.

They are closely related but numbered differently. The fundamental is harmonic 1, and its overtones start above it: the first overtone is harmonic 2, the second overtone is harmonic 3, and so on. This tool numbers every partial from the fundamental as harmonic 1.

Up to 64. The Harmonics field must be a whole number from 1 to 64; anything higher shows a limit message. High harmonics crowd together in pitch and, for a high fundamental, quickly climb past the roughly 20 kHz ceiling of human hearing.

Any finite number greater than zero. If the field is blank, zero, negative or not a number, the tool shows a prompt to enter a fundamental greater than zero instead of a table. There is no upper bound on the frequency itself.

The engine keeps six decimal places internally, then the table rounds frequency to two decimals and cents to one decimal for readability. Whole-number fundamentals like 110 Hz produce exact integer harmonics, so no rounding is visible for them.

No. The whole series is computed in your browser with plain arithmetic, so nothing you type is uploaded. The tool works offline once the page has loaded.

Yes. Enter the open-string frequency as the fundamental to see the natural harmonics you get by lightly touching the string at its halfway, third and quarter points, which correspond to harmonics 2, 3 and 4.