Harmonic Series Frequency
Calculator
Results
- Harmonic frequency (Hz)
- 550
- Semitones above the fundamental
- 27.863137
- Cents above the fundamental
- 2,786.313713
Music and audio results
| Harmonic frequency (Hz) | 550 |
| Semitones above the fundamental | 27.863137 |
| Cents above the fundamental | 2,786.313713 |
formula-map diagram
- Harmonic frequency (Hz)
- 550
- Semitones above the fundamental
- 27.863137
- Cents above the fundamental
- 2,786.313713
Musical and acoustic relationship
Formula
fₙ = n × f₁= 550
Note
This result is a simplified model: it applies the displayed standard formula to the values you entered, assuming twelve-tone equal temperament, a speed of sound of 343 m/s in dry air at 20 °C, an ideal free field with no reflections or air absorption, purely resistive speaker loads and Sabine's diffuse-field assumption. Real rooms, instruments, codecs and amplifiers depart from these idealisations, so measure with proper instruments for critical work.
More in Music and audio
See all →Frequently asked questions
What is the harmonic series, and how are the frequencies calculated?+
The harmonic series is the set of frequencies that are whole-number multiples of a fundamental frequency, so the nth harmonic equals n times the fundamental. A 100 Hz fundamental has harmonics at 200 Hz (2nd), 300 Hz (3rd), 400 Hz (4th), and so on indefinitely.
Why do some instruments sound 'brighter' or 'richer' than others playing the same note?+
An instrument's timbre comes from the relative loudness of its different harmonics above the fundamental, not just the fundamental frequency itself, so a violin and a flute playing the same fundamental pitch sound completely different because they emphasize different harmonics. The harmonic series is the mathematical backbone of what timbre actually is.
Why does the 2nd harmonic sound like the same note an octave up?+
The 2nd harmonic is exactly double the fundamental frequency, and doubling frequency is by definition one octave higher, which is why it blends so naturally with the fundamental that our ears often perceive it as reinforcing the same note rather than a separate pitch. This is also why octave doubling in orchestration sounds so seamless.
Why aren't the higher harmonics exactly in tune with the standard 12-note scale?+
The natural harmonic series follows pure whole-number ratios, but equal temperament (the tuning system behind modern pianos and fretted instruments) rounds those ratios to fit 12 equal semitone steps per octave, so higher harmonics like the 7th or 11th fall noticeably 'out of tune' compared to their nearest equal-tempered note. This mismatch is why brass and string players sometimes need to lip- or finger-adjust natural harmonics to sound in tune with a piano.
How is this used practically, for example on a guitar or in synthesis?+
Guitarists play natural harmonics by lightly touching a string at points that correspond to simple harmonic ratios (like the 12th fret for the 2nd harmonic, or the 7th fret for the 3rd), and synthesizer additive synthesis builds complex tones from scratch by combining harmonics at calculated frequencies and amplitudes. Knowing the exact harmonic frequencies makes both techniques precise rather than trial-and-error.