Harmonic Series Calculator

What Is the Harmonic Series?

In music, the harmonic series is the set of frequencies that are integer multiples of a fundamental note. These overtones shape the timbre of every pitched instrument.

Harmonic Series Formula

For fundamental frequency $f$, the $n$th partial is:

$$f_n = n \times f$$

The first partial is the fundamental itself. Each successive partial is one octave higher every time $n$ doubles.

Try the Tone Generator, Chord Calculator, or BPM Calculator for more music tools.

Frequently Asked Questions

What are the first harmonics of A440?

The first four partials are 440 Hz (A4), 880 Hz (A5), 1320 Hz (E6), and 1760 Hz (A6).

What is the difference between just intonation and equal temperament?

Just intonation uses simple integer ratios between notes. Equal temperament divides the octave into 12 equal semitone steps, slightly adjusting pure ratios for keyboard compatibility.

What are overtones?

Overtones are partial frequencies above the fundamental. They are what give each instrument its distinctive sound character.

Why do cents matter in the harmonic series?

Cents measure how far a just-intonation partial deviates from the nearest equal-temperament note. Large cent values indicate more dissonant intervals.

How many partials should I generate?

Sixteen partials cover most audible overtones for analysis. Higher partials contribute less to perceived timbre but matter for synthesis and acoustic research.

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What Is the Harmonic Series?

Harmonic Series Formula

Frequently Asked Questions

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