Harmonic Series Calculator
Calculate the harmonic series from a fundamental frequency. Understand overtones and their relationships to the fundamental note.
Harmonic Series
C3
261.63 Hz
C4
523.26 Hz
G4
784.89 Hz
C5
1046.52 Hz
E5
1308.15 Hz
G5
1569.78 Hz
A#6
1831.41 Hz
C6
2093.04 Hz
How to Use This Calculator
- Select the fundamental note or enter its frequency in Hz.
- Enter the number of harmonics you want to calculate (typically 8-16).
- The calculator displays each harmonic with its frequency, note name, and ratio to the fundamental.
- Use this to understand timbre, intervals, and the physics of sound.
Harmonic Series Formula
Harmonics are integer multiples of the fundamental frequency:
Example: Fundamental C4 (261.63 Hz): 1st harmonic = 261.63 Hz (fundamental), 2nd harmonic = 523.26 Hz (C5, octave), 3rd harmonic = 784.89 Hz (G5, perfect 5th), 4th harmonic = 1046.52 Hz (C6, two octaves).
Full Description
The harmonic series is a fundamental concept in music and physics. When you play a note on any instrument, you don\'t just hear one frequency—you hear the fundamental frequency plus a series of overtones (harmonics) that are integer multiples of the fundamental. These harmonics create the timbre (tone color) that makes different instruments sound unique.
The harmonic series forms the basis of musical intervals and harmony. The 2nd harmonic is an octave, the 3rd is a perfect 5th, the 4th is two octaves, the 5th is a major 3rd, and so on. Understanding harmonics helps explain why certain intervals sound consonant (harmonious) and others sound dissonant. It also explains the physics behind tuning systems and why equal temperament was developed.
This calculator helps you explore the harmonic series for any fundamental frequency. Enter a note or frequency, and it calculates all the harmonics with their frequencies, note names, and ratios. Use it to understand timbre, learn about intervals, study tuning systems, or explore the physics of sound. The harmonic series is essential knowledge for any serious musician or audio engineer.
Frequently Asked Questions
What is the harmonic series?
The harmonic series is a sequence of frequencies that are integer multiples of a fundamental frequency. When you play a note, you actually hear the fundamental plus all its harmonics (overtones), which give the note its characteristic timbre.
What are harmonics used for?
Harmonics create the timbre (tone color) of instruments. Different instruments emphasize different harmonics, creating their unique sounds. Harmonics are also used in music theory to understand intervals, chord construction, and tuning systems.
How do harmonics relate to intervals?
The 2nd harmonic is an octave above the fundamental. The 3rd harmonic is a perfect 5th above the octave. The 4th harmonic is two octaves above. The 5th harmonic is a major 3rd. These relationships form the basis of musical intervals and harmony.
Why do some harmonics sound out of tune?
In equal temperament (modern tuning), some intervals are slightly adjusted from their pure harmonic ratios. For example, a perfect 5th in equal temperament is 700 cents, while the pure harmonic ratio (3:2) is 701.96 cents. This small difference creates the "temperament" in equal temperament.