Harmonic Series Frequency Calculator
The harmonic series is the set of frequencies that are integer multiples of a fundamental frequency. The nth harmonic has frequency fn = n x f1, where f1 is the fundamental. Harmonics are the basis of musical timbre, natural overtone singing, resonant string and wind instrument acoustics, and harmonic distortion analysis in audio equipment. Enter a fundamental frequency and the calculator lists the first ten harmonics.
Harmonic frequency formula
fn = n × f1
Where n is the harmonic number (1, 2, 3, ...) and f1 is the fundamental frequency. The second harmonic (n=2) is one octave above the fundamental; the fourth harmonic (n=4) is two octaves above.
Harmonics and musical intervals
- Harmonic 2: one octave above fundamental
- Harmonic 3: octave + perfect fifth above fundamental
- Harmonic 4: two octaves above fundamental
- Harmonic 5: two octaves + major third above fundamental
- Harmonic 6: two octaves + perfect fifth above fundamental
Frequently asked questions
What is the harmonic series?
The harmonic series is the set of frequencies that are integer multiples of a fundamental frequency: f1, 2f1, 3f1, 4f1, and so on. The fundamental is the first harmonic; the second harmonic is twice the fundamental, the third is three times, etc.
How does the harmonic series relate to musical timbre?
The amplitude and phase of each harmonic relative to the fundamental determines the timbre (tone color) of a sound. A pure sine wave has no harmonics; a sawtooth wave contains all harmonics; a square wave contains only odd harmonics. This is why different instruments sound different at the same pitch.
Is the harmonic series the same as the overtone series?
Almost. Overtones are harmonics above the fundamental. The first overtone is the second harmonic (2x fundamental), the second overtone is the third harmonic (3x fundamental), etc. Overtone numbering starts at 1 above the fundamental, so harmonic n = overtone n-1.
What is the harmonic series in music theory?
In music theory, the harmonic series corresponds roughly to intervals: the second harmonic is an octave above, the third is a fifth above that (perfect fifth above the octave), the fourth is another fourth, etc. Natural harmonics on strings and brass instruments follow this series.
Why do higher harmonics matter in audio engineering?
Harmonic distortion in amplifiers and speakers adds energy at harmonic frequencies. Even-order harmonics (2nd, 4th) are generally musically consonant; odd-order harmonics (3rd, 5th) can sound harsh. Total Harmonic Distortion (THD) is the ratio of harmonic energy to fundamental energy.
Official sources
- AES: Audio Engineering Society.
- OpenStax University Physics Vol. 1, Chapter 17: Sound.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.