Harmonic Frequencies Calculator

Formula first

Overview

Harmonic frequencies are the integer multiples of a fundamental frequency, forming a sequence known as the harmonic series. In music synthesis, these frequencies represent the individual sine wave components that combine to create the complex timbre and character of a periodic sound.

Symbols

Variables

$f_n$ = Harmonic Freq., n = Harmonic Number, $f_1$ = Fundamental

Apply it well

When To Use

When to use: Use this formula when analyzing the spectral content of periodic waveforms or designing sounds in additive synthesis. It is applicable to ideal vibrating systems, such as strings and air columns, where overtones occur at exact integer multiples of the base frequency.

Why it matters: Understanding this relationship allows sound designers to manipulate the 'color' of a sound by adding or removing specific harmonics. It is critical for audio engineers when using equalizers to target specific resonant frequencies or when creating synthetic versions of acoustic instruments.

Avoid these traps

Common Mistakes

• Counting the fundamental as '0' instead of '1'.
• Convert units and scales before substituting, especially when the inputs mix Hz.
• Interpret the answer with its unit and context; a percentage, rate, ratio, and physical quantity do not mean the same thing.

One free problem

Practice Problem

A synthesizer is set to produce a sawtooth wave with a fundamental frequency of 440 Hz. Calculate the frequency of the 3rd harmonic.

Solve for: fn

Hint: Multiply the fundamental frequency by the harmonic number n.

The full worked solution stays in the interactive walkthrough.

References

Sources

1. Wikipedia: Harmonic series (music)
2. Britannica: Harmonic
3. The Science of Sound by Thomas D. Rossing
4. Fundamentals of Physics by Halliday, Resnick, and Walker
5. Wikipedia: Harmonic (music)
6. Britannica: Harmonic (music)
7. Halliday, Resnick, Walker: Fundamentals of Physics
8. Halliday, Resnick, Walker Fundamentals of Physics