# Video; Timbre of musical instruments

The spectrum analyzer is a very efficient tool for the study of the physical nature of a sound.

A periodic signal can be decomposed into the sum of sinusoidal signals.

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This is decomposition by Fourier series.

The spectrum analyzer enables us to display the components as lines.

The abscissa is no longer graduated in time, but in frequency.

We therefore speak of a frequency analysis, as opposed to the temporal analysis provided by the oscilloscope.

The collection of lines characterizes the spectrum of the signal. For this reason, frequency analysis is also called spectral analysis.

Each line is a sinusoidal component, also called a “harmonic”.

The first line, or first harmonic, is the fundamental. It has the base frequency, f0,  of the periodic signal.

The harmonics that follow are sinusoids of frequencies that are multiples of the fundamental frequency.

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Spectral analysis enables us to distinguish a note played on a piano,

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from the same note played on a violin.

The spectra are different. The lines are at the same frequencies, but their respective amplitudes are different.

This characteristic determines the timbre of a musical instrument.