Timbre and harmonics
This activity allows students to understand why the same note sounds different depending on the instrument that produces it. It develops the ability to analyze the spectrum of a sound and to link acoustics and musical perception.
Activity Summary
The student compares the sound spectra of different instruments playing the same note (A at 880 Hz) using FizziQ. Starting with a pure sound generated by the synthesizer then successively analyzing the spectrum of a flute, a guitar and a piano, the student discovers that it is the richness and distribution of harmonics which define the characteristic timbre of each instrument.
Introduction
Close your eyes and listen to a flute, a guitar, and a piano each playing the same note. Despite the identical pitch, you instantly recognize which instrument is playing. This remarkable ability of the human auditory system depends on timbre, the quality of a sound that distinguishes different instruments. Physically, timbre is determined by the unique pattern of harmonics, their relative amplitudes, and how they evolve over time during the attack, sustain, and decay of a note. A flute produces a nearly pure tone with few harmonics, giving it a smooth, hollow quality. A guitar string generates a rich series of harmonics that decay at different rates, creating its warm brightness. A piano hammer excites a complex pattern of harmonics with a sharp attack and gradual decay. By comparing the frequency spectra of these instruments playing the same note, students can see the physical basis of what their ears already know: it is the recipe of harmonics, not the fundamental frequency, that gives each instrument its unique voice.
Learning Objectives
- Identify the fundamental frequency and harmonics in each spectrum
- Observe how the number and relative amplitudes of harmonics differ between instruments
- Understand that timbre is determined by harmonic content, not fundamental frequency
- Compare a pure synthesized tone with real instrument tones to understand spectral richness
Scientific Concepts
Instruments and sensors
Scientific instruments
- Sound spectrum analyzer (FFT)
- Synthesizer
Sensors
- Microphone
FizziQ Features
- Sound library — Provides the pre-recorded flute, guitar and piano notes at A5 (880 Hz) used for spectral comparison.
- Experiment notebook — Used to record each spectrum, build the harmonic-amplitude comparison table and plot the bar chart of results.
Required Materials
- - Smartphone or tablet with FizziQ installed (spectrum analyzer and synthesizer) - Sound library recordings of flute, guitar and piano playing the same note (built into FizziQ) - Note: the protocol remains adaptable to any comparable spectral analysis tool.
Experimental Protocol
Open the app **Synthesizer** and generate a pure **880 Hz** tone (A5). Open the **Spectrum Analyzer** and observe: there should be a **single peak** at 880 Hz.
Record or sketch this spectrum. This is the reference: a pure tone with **no harmonics**.
Load the **flute** recording playing A5 (880 Hz) from the Sound Library. Analyze its spectrum.
Count the number of **visible harmonic peaks** and note their relative amplitudes. The flute should show **few harmonics** (2-4 visible peaks).
Load the **guitar** recording playing the same note. Analyze its spectrum.
The guitar should show **many more harmonics** (6-10 visible peaks), with the amplitudes decreasing more gradually.
Load the **piano** recording playing the same note. Analyze its spectrum.
The piano typically shows a **rich harmonic series** with a distinctive amplitude pattern.
Create a **comparison table**: for each instrument, list the amplitude (relative to the fundamental) of harmonics 1 through 8.
Listen to all four sounds (pure tone, flute, guitar, piano) in sequence. Can you now connect the spectral differences with the perceived timbre differences?
Plot a **bar chart** of harmonic amplitudes for each instrument to visually compare their spectral signatures.
Discuss: what physical properties of each instrument (string, air column, hammer, bow) determine its harmonic pattern?
Expected Results
The pure synthesizer tone should show a single peak at 880 Hz with no other frequency components. The flute typically shows 2-4 harmonics, with the fundamental dominant and upper harmonics rapidly decreasing in amplitude. The guitar shows 6-10 harmonics with a more gradual roll-off and possibly enhanced mid-range harmonics. The piano shows a complex harmonic pattern that depends on the specific register and dynamic level. All instruments should share the same fundamental frequency (880 Hz ± 2 Hz) but differ dramatically in their harmonic content. Students should observe a clear correlation between the number and strength of harmonics and the perceived richness or brightness of the sound.
Scientific Questions
- What physical properties of a vibrating string determine which harmonics are strongest?
- How does the point where a guitar string is plucked affect the harmonic content?
- Why does a pure synthesized tone sound artificial compared to real instruments?
- What role does the temporal evolution (attack, sustain, decay) play in timbre perception beyond the spectrum?
- Could you identify an instrument from its spectrum alone, without hearing it?
Scientific Background
Timbre, the quality that allows you to distinguish a trumpet from a violin playing the same note, is one of the most complex aspects of musical acoustics. Physically, two main parameters define timbre: 1) Spectral composition: the number, frequency and relative amplitude of harmonics; 2) Temporal evolution: how the sound evolves from attack to extinction.
A pure sound, like that generated by FizziQ's synthesizer, is a simple sine wave containing only one frequency. Its spectrum shows a single peak.
It is a rare sound in nature, perceived as "hollow" or "artificial". Real instruments produce complex sounds composed of a fundamental and harmonics.
The flute generates a relatively pure sound with few low amplitude harmonics, hence its soft and "pure" sound. The guitar produces numerous harmonics but of regularly decreasing amplitude, creating a warm sound.
The piano has a very rich harmonic profile with some particularly amplified due to the rigidity of the strings and the resonance box. The oboe, with its double reed, generates a spectrum dominated by odd harmonics, giving it its characteristic nasal timbre.
These differences in timbre can be explained by the physics of each instrument: the shape of the exciter (reed, bow, hammer), the structure of the resonator (tube, body, soundboard), and the materials used. FizziQ's sound spectrum tool uses the Fourier transform to break down these complex sounds into their frequency components, making these acoustic differences visible and providing a scientific understanding of why each instrument has its unique "voice."
Extensions
- Analyze how the spectrum of a guitar changes depending on whether the string is plucked near the bridge or near the neck
- Record and compare your voice singing a vowel with an instrument playing the same note
- Investigate how a mute changes the timbre of a brass instrument by comparing spectra with and without the mute
- Create a synthetic tone with FizziQ by adding harmonics one by one until it sounds like a real instrument
Frequently Asked Questions
The fundamental frequencies of the different instruments do not match exactly. Is this a problem?
Small differences of ±2-3 Hz are normal due to tuning variations. The important observation is the relative harmonic content, not the exact fundamental frequency.
I see peaks in the spectrum that are not at harmonic frequencies. What are they?
These may be room resonances, background noise, or in the case of piano strings, slight inharmonicity of the higher partials. Focus on the peaks that fall near integer multiples of the fundamental.
The synthesizer produces a tone that sounds very different from any real instrument. Why?
A pure sine wave lacks harmonics entirely and has no temporal evolution (attack and decay). Both features are essential to natural-sounding timbre. Real instruments always produce multiple harmonics and have characteristic time envelopes.
Can two different instruments ever sound exactly the same?
In theory, if two instruments produced identical spectra with identical temporal envelopes, they would sound the same. In practice, the physical mechanisms are so different that this never occurs naturally.
Detailed Description
The student compares the sound spectra of different instruments playing the same note (A at 880 Hz) using FizziQ. Starting with a pure sound generated by the synthesizer then successively analyzing the spectrum of a flute, a guitar and a piano, the student discovers that it is the richness and distribution of harmonics which define the characteristic timbre of each instrument. FizziQ provides the synthesizer to generate the pure reference tone, the spectrum analyzer to display each FFT spectrum, and the built-in sound library to access the flute, guitar and piano recordings needed for the comparison.
This activity is part of our sound resources. To dig deeper into measuring and analyzing sound (waveform, spectrum, spectrogram, decibels) and find all twelve experiments, read our complete guide to measuring and analyzing sound with a smartphone or computer.
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