Harmonic vs Fundamental Quiz
Two pure tones play from a single harmonic series — one is the fundamental (the low root, f0) and the other is one of its harmonics (an integer multiple: 2f, 3f, 4f…). Listen, decide which tone is the fundamental and which is the overtone — or name the harmonic number — then reveal the spectrum. Three difficulty levels build your ear from easy octaves up to high harmonics whose candidate numbers sit close together (up to the 12th).
ℹ The harmonic series is exact math: the nth harmonic is exactly n×f0 (here tuned to 12-TET, A4 = 440 Hz for the note labels). But telling two tones apart by ear is uncalibrated and depends entirely on your headphones, speakers, volume and listening conditions — identifying a high harmonic relative to its fundamental gets genuinely hard because the candidate harmonic numbers are tightly spaced, and tiny speakers may not reproduce the lowest fundamentals at all. Your score is a personal practice metric, not a test, certification or hearing diagnosis, and it is stored only in your own browser. Use a moderate volume; headphones help.
The quiz
A round is 8 questions. Pick a level and type, then start. You can change them between rounds.
Round complete
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Quick refresher
- Fundamental (f0) — the lowest, root pitch of the series; the harmonic number is 1.
- Harmonic / overtone — a higher partial at an exact integer multiple: 2× (one octave up), 3× (an octave + a fifth), 4× (two octaves), and so on.
- The higher the harmonic, the harder it is to judge how many times higher than the fundamental it sits — and in “name the harmonic number” mode the candidate harmonics get closer together, so picking the right one is harder. That is the skill this game builds.
How It Works
Every pitched sound — a plucked string, a sung note, a blown pipe — is built from a fundamental frequency (f0) plus a stack of harmonics sitting at exact integer multiples of it: 2f0, 3f0, 4f0, and upward. That integer relationship is what makes the harmonic series exact mathematics rather than a matter of opinion. The fundamental is the pitch you usually name; the harmonics give the sound its timbre.
This quiz plays two pure sine tones drawn from one series: the fundamental (f0) and one of its harmonics — for example f0 and 2f0, or f0 and 5f0. The lower tone is always the fundamental. Your job is to decide which tone is the fundamental and which is the overtone, or, in the harder mode, to name the higher tone's harmonic number relative to the fundamental you hear.
- Pick a level and question type. Each level plays the fundamental against an increasingly high harmonic. Level 1 contrasts it with a low harmonic (2nd–3rd) — a wide, easy gap. Level 2 uses a nearby low harmonic (3rd–5th). Level 3 reaches up to the 12th, where the candidate harmonic numbers are tightly spaced.
- Listen. Play Tone A and Tone B separately, or play them back to back. Compare which sits lower.
- Answer. Choose the fundamental, or tap the harmonic number. You get instant feedback.
- Reveal. A spectrum diagram shows both tones on the harmonic ladder so you can see exactly how they relate, with a one-line explanation.
- Repeat & track. Finish the 8-question round to log your accuracy. Your best and last scores persist locally.
Tones are generated with the Web Audio API as oscillators with a short click-free fade, tuned to 12-TET with A4 = 440 Hz so the note labels (like “A2” or “E4”) line up with standard tuning. Nothing is recorded and there is no microphone — the tool only plays sound out.