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.

Your progress

Saved only in this browser — nothing is uploaded. Clear it any time below.

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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.

  1. 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.
  2. Listen. Play Tone A and Tone B separately, or play them back to back. Compare which sits lower.
  3. Answer. Choose the fundamental, or tap the harmonic number. You get instant feedback.
  4. Reveal. A spectrum diagram shows both tones on the harmonic ladder so you can see exactly how they relate, with a one-line explanation.
  5. 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.

Frequently Asked Questions

What is the difference between a fundamental and a harmonic?
The fundamental (f0) is the lowest frequency in a harmonic series and the pitch you normally name. A harmonic (or overtone/partial) is a higher component at an exact integer multiple of the fundamental — the 2nd harmonic is 2×f0, the 3rd is 3×f0, and so on. In a real instrument they sound together and define the timbre; here we isolate two of them as pure tones so you can compare them.
Is the harmonic series exact, or is this subjective?
The frequencies are exact: the nth harmonic equals n×f0, no rounding. We tune to 12-TET with A4 = 440 Hz so the note names match standard tuning (note that true harmonics don't land precisely on equal-tempered notes — for example the 7th harmonic is noticeably flat of any piano key). What's subjective is your ability to hear the difference: that depends on your gear, volume and the spacing of the tones, which is exactly the skill the quiz trains.
Why is the higher harmonic so hard to identify at Level 3?
It depends on the mode. In “Which is the fundamental?” mode Level 3 stays relatively easy — the fundamental is always the clearly lower tone, so picking the lower pitch is straightforward. The real challenge is “Name the harmonic number” mode: you have to judge how many times higher the upper tone is than the fundamental, and large integer ratios (6× to 12×) are hard to pin down by ear because the candidate harmonics are tightly spaced. On top of that, many headphones and most laptop or phone speakers roll off the extremes, so a tone you “miss” may be your equipment rather than your ear. That difficulty is the point of the higher levels.
Does my score mean my hearing is good or bad?
No. This is an uncalibrated, headphone-dependent practice aid, not a hearing test or certification. The score is a personal metric to track your own progress over time on this device. If you have a real concern about your hearing, see an audiologist; for music-theory exactness, use the Harmonic Series Calculator.
Is my score saved or sent anywhere?
Nothing is uploaded and the microphone is never used — the tool only plays tones. Your accuracy and play counts are stored only in your own browser (via local storage) so the Audio Skills Progress Tracker can show them and you can compare next time. Clearing your browser data, using private mode, or pressing “Clear saved progress” erases them.