Harmonic Series Calculator
Calculate the first N harmonics of any fundamental frequency. Shows each harmonic's frequency in Hz and its closest musical note name.
How to use this tool
- Enter fundamental frequency and number of harmonics in the fields above.
- Results update instantly as you type — or click Calculate.
- Read your harmonic frequencies and the full breakdown beneath it.
Generate the harmonic series of any fundamental frequency to explore overtones and timbre.
Formula
Harmonic frequency: fn = f0 × n
Nearest MIDI note: midi = 69 + 12 × log2(f / 440)
Octave: oct = floor(round(midi) / 12) − 1
How it works
The calculator multiplies the fundamental frequency by each integer n from 1 to the requested number of harmonics, producing the classic overtone series found in all acoustic instruments. Each resulting frequency is converted to a MIDI note number using the equal-temperament formula referenced to A4 = 440 Hz, then mapped to a note name and octave number.
Up to 32 harmonics can be computed. Note names are based on 12-tone equal temperament, so harmonics that fall between semitones (such as the 7th harmonic) are shown as the nearest tempered pitch, which may differ noticeably from the pure harmonic interval.
Worked example
Worked example
- Fundamental f0 = 110 Hz, computing 4 harmonics.
- H1: 110 × 1 = 110.0 Hz. MIDI = 69 + 12 × log2(110/440) = 69 − 24 = 45 → A2.
- H2: 110 × 2 = 220.0 Hz. MIDI = 69 + 12 × log2(220/440) = 69 − 12 = 57 → A3.
- H3: 110 × 3 = 330.0 Hz. MIDI = 69 + 12 × log2(330/440) ≈ 64 → E4.
- H4: 110 × 4 = 440.0 Hz. MIDI = 69 + 12 × log2(440/440) = 69 → A4.
H1: 110.0 Hz (A2), H2: 220.0 Hz (A3), H3: 330.0 Hz (E4), H4: 440.0 Hz (A4)
Key terms
- Fundamental frequency
- The lowest frequency in a harmonic series (the first harmonic, n=1), from which all overtones are derived.
- Harmonic
- A frequency that is an integer multiple of the fundamental. The nth harmonic has frequency n × f0.
- Overtone series
- The naturally occurring sequence of harmonics produced by vibrating strings, air columns, and other resonant systems.
- Equal temperament
- The standard Western tuning system dividing each octave into 12 equal semitones, so each semitone is a factor of 2^(1/12).
- MIDI note number
- An integer 0–127 representing a pitch, where middle C is 60 and A4 (440 Hz) is 69.
Frequently asked questions
- What is the harmonic series?
- The harmonic series is the sequence of frequencies that are integer multiples of a fundamental: f, 2f, 3f, 4f, ... These overtones give instruments their characteristic tone colour.
- Which harmonic is the octave?
- The 2nd harmonic (2× fundamental) is exactly one octave above. The 3rd harmonic is an octave + perfect fifth above.