The tone of an instrument

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.

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.

Visão geral da atividade:

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.

Nível:

Middle school

FizziQ

Autor:

Duração (minutos):

30

O que os alunos farão:

- Compare the frequency spectra of different instruments playing the same note using FizziQ
- 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

Conceitos científicos:

- Musical timbre
- Harmonics
- Sound spectrum
- Fourier synthesis and analysis
- Instrumental acoustics

Sensores:

- Microphone (frequency analysis)
- FizziQ spectrum analyzer (FFT)
- FizziQ synthesizer (for pure tone reference)

Materiais necessários:

- Smartphone with the FizziQ application
- Various musical instruments or sound library recordings
- FizziQ experience notebook

Procedimento experimental:

Open FizziQ's 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?

Resultados esperados:

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.

Questões científicas:

- Why does a flute sound hollow compared to a violin? What spectral feature explains this?
- 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?

Explicações científicas:

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."

Atividades de extensão:

Perguntas frequentes:

Q: The fundamental frequencies of the different instruments do not match exactly. Is this a problem?
R: 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.

Q: I see peaks in the spectrum that are not at harmonic frequencies. What are they?
R: 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.

Q: The synthesizer produces a tone that sounds very different from any real instrument. Why?
R: 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.

Q: Can two different instruments ever sound exactly the same?
R: 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.