Harmonic vs Fundamental Quiz

This harmonic vs fundamental quiz plays two pure tones 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

Difficulty

Question type

A round is 8 questions. Pick a level and type, then start. You can change them between rounds.

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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 (tone color). This is why a violin and an oboe playing the same note sound different — they share the same fundamental but have different harmonic content, or overtone spectra. Understanding this relationship is foundational for music producers, audio engineers, and composers working with additive synthesis or orchestration. As an overtone ear training exercise and ear training game, the quiz helps you internalize these relationships so you can identify fundamental frequency from harmonic number purely by ear.

This harmonic series 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 harmonic number quiz mode, to name the higher tone's harmonic number relative to the fundamental you hear. To see the exact frequencies and note names for any harmonic series, pair this quiz with the harmonic series calculator.

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. The tones are pure sinusoids with no additional harmonics added — isolating each partial as a sine wave is what makes the frequency-ratio discrimination task possible. Nothing is recorded and there is no microphone — the tool only plays sound out. If you want to explore what the harmonic spectrum of a real instrument or microphone signal looks like, the harmonic overtone detector can identify which partials are present in a live sound.

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.

How does this quiz help with music theory ear training?

Recognizing harmonic ratios by ear is the foundation of interval recognition training: the 2nd harmonic is an octave (2:1), the 3rd harmonic relative to the 2nd is a perfect 5th (3:2), and the 5th harmonic gives a pure major 3rd (5:4). By practicing with isolated sine tones — stripped of the timbre cues a real instrument provides — you train your auditory cortex to perceive frequency ratios directly, making interval recognition on real instruments easier. This complements traditional solfège and relative pitch training.

Why do I hear a "beating" or wobbling sound when both tones play together?

When you use “Play both” and the two tones are close in frequency (or at a non-integer ratio due to rounding), small amplitude fluctuations — called beats — can arise. At this quiz's large integer ratios, true beating between the fundamental and harmonic is minimal. What you may hear instead is the combination tone (difference frequency) your auditory system generates internally — for example, 5f₀ and f₀ produce an internal combination tone at 4f₀. This is normal and is a property of nonlinear auditory processing, not an audio glitch.

What is the best way to get a perfect score on Level 3?

In “Which is the fundamental?” mode, Level 3 is about picking the lower tone — straightforward with headphones. In “Name the harmonic number” mode, the practical strategy is to estimate the interval: an octave = 2×, an octave + a 5th = 3×, two octaves = 4×, two octaves + a major 3rd = 5×, and so on. Counting octaves first narrows the range, then the remaining interval pins the harmonic number. Regular practice with the frequency identification quiz builds the pitch-naming skills that underpin this estimation.

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