Harmonics Lab

Settings

Analysis FFT size

Window Peak threshold above noise floor 15 dB Dynamic range 60 dB Input gate (silence below) −70 dBFS Detect multiple notes (chords) Max notes 4 Lowest fundamental Display smoothing 0.5

Display Frequency range – Hz Level floor −100 dB Harmonics to show per note 16 Note spelling Sargam script Sa fine-tune 0 ¢ Show roughness band under spectrum Show tuning-degree ticks on spectrum

Microphone Input device

Echo cancellation, noise suppression and automatic gain are requested off — they would distort the overtones.

Spectrum every peak named · coloured combs = harmonic series of each detected note

Play something.

Start the Microphone and play an instrument or sing — or open the Tone Lab to generate notes and chords in any tuning.

Scroll to zoom · drag to pan · double-click to reset · click a peak to pin its harmonic series · Space freeze

What you are seeing

A pitched sound is not one frequency. A string or air column vibrates at its fundamental f₀ and simultaneously at 2f₀, 3f₀, 4f₀… — the harmonic series. Their relative strengths are the timbre. The spectrum shows every partial as a peak; the coloured comb above marks the harmonic numbers of each detected note.

Harmonics 1, 2, 4, 8 are octaves (Sa). 3 and 6 are Pa (a pure fifth, +2.0¢ from equal temperament). 5 is Ga (a pure major third, −13.7¢). 7 is a "natural" komal Ni, −31.2¢ — no piano key matches it. 11 sits almost exactly between Ma and tivra Ma. The Harmonic ladder tab lists all of this for whatever you play.

Consonance, made visible

When two notes sound together, their harmonic series interleave. If the frequency ratio is simple — 2:1, 3:2, 4:3, 5:4 — many partials land on exactly the same frequencies and fuse. Partials that land close but not together (within about a critical band) beat, which we hear as roughness.

Open Overtone overlap and play a fifth: green coincidences everywhere. Play a minor second: red beating bands. In equal temperament the fifth's 3rd/2nd harmonics are 0.9 Hz apart at C4 — a slow beat you can see in the interval card. Switch the Tone Lab to Just intonation and it vanishes.

Tuning systems

Equal temperament divides the octave into 12 identical steps, so every key works but only the octave is pure. Just intonation takes intervals straight from the harmonic series (5/4, 3/2…) — perfectly beat-free chords, tied to one Sa, exactly like a tanpura-tuned raga. Pythagorean stacks pure fifths. Meantone and Werckmeister are historical compromises.

Choose a tuning at the top: note labels and cents then refer to that tuning's degrees, ticks on the spectrum show where its notes lie, and the Tone Lab plays in it.

Tips for accurate readings

Use a quiet room and keep the mic 20–50 cm from the instrument. Avoid Bluetooth headsets (their codecs low-pass and distort).
Bigger FFT (Settings) = finer frequency resolution but slower response. 32768 separates partials only 3 Hz apart; 8192 follows fast melodies.
Pitch is refined from the phase advance between two overlapping frames: steady tones read to better than 0.1¢.
An octave above a sounding note can't be detected as a separate note: every partial coincides with the lower note's even harmonics. That perfect overlap is why the octave is the most consonant interval.
Freeze (Space) and hover the spectrum to read any peak exactly.

Roughness model: Plomp & Levelt (1965), parameterised by W. Sethares, Tuning, Timbre, Spectrum, Scale (2005). Multi-note detection: harmonic summation with iterative explanation (after A. Klapuri, 2006). Validation suite: tests/tests.html.