Timbre means the nature or quality of a sound.

Timbre applies to the sound of a musical instrument. A note with the same pitch played on two different musical instruments has a different timbre. Timbre is what distinguishes the sound of a piano from that of a trumpet. Every musical instrument has a unique timbre.

A collection of instruments has a different timbre to a single instrument. It is what distinguishes the sound of music played by a rock band from the same music played by a classical orchestra.

Timbre applies to speech and singing as well as to instruments. It is the factor that distinguishes a familiar voice from that of a stranger.

Timbre is a major factor in performing music. It is a somewhat overlooked factor in writing music. Changing the instruments in a piece of music always changes the timbre of the sound. Sometimes the change in timbre is subtle, more often than not it is significant. Changing timbre by changing instruments is the missing link between writing and performing music.

In simple terms, timbre is what distinguishes two sounds with the same frequency from each other.

This section explores the technical definition of timbre. Every sound consists of sine waves with different frequencies. A single sine wave is also called a partial. The dominant partial in a sound is the fundamental frequency, or fundamental for short. The fundamental is the perceived pitch of a sound. Partials in a pitched sound form a harmonic series. Partials in an unpitched sound are inharmonic.

Audio: partial (0:02)

Figure: partial

partial plays a single note, middle C, twice, first on a piano then on a sine wave instrument. The partial figure shows the score followed by the spectrograms of each of the two sounds. The piano contains multiple partials in a harmonic series, the sine wave contains a single partial.

Partial is another name for a sine wave that forms part of a sound.

A sine wave contains one partial. All other sounds contain multiple partials.

Each individual sine wave in a sound is called a partial, because it is a part of the complete sound.

The timbre of a sound is determined by how many partials are present and how they relate to each other in terms of their relative amplitude.

Audio: fundamental (0:04)

Figure: fundamental

fundamental plays a note on a guitar followed by the sound of a crash symbol. The fundamental figure shows the score followed by the spectrograms of the two sounds. There is a peak at 110Hz in the guitar spectrogram, which represents the fundamental, the pitch of the note. The crash cymbal spectrogram demonstrates no obvious fundamental frequency. Its sound has no discernible pitch and is unpitched sound.

A fundamental frequency, or fundamental for short, is the lowest perceived frequency in a sound.

The pitch of a note is the perceived frequency of its fundamental.

The fundamental frequency is usually the lowest perceived frequency in a note and it is usually the partial with the highest amplitude. Occasionally, the fundamental is not the highest amplitude and, sometimes, it is missing altogether. The listener still perceives a fundamental but pitch is a perception of sound, and the ear and brain can and do play tricks such as supplying a perceived fundamental when one is missing, a phenomenon known as the missing fundamental.

An unpitched sound has no obvious fundamental frequency and is thus unpitched.

Audio: harmonic series (0:04)

Harmonic series
Figure: harmonic series

harmonic series plays concert pitch on a trumpet then on a violin. The harmonic series figure shows the spectrogram of each instrument. Both spectrograms show the regular spacing between partials that is the hallmark of a harmonic series. However, the number of partials in each instrument differs and the relative amplitude of each partial differs. This indicates that each instrument has a different timbre.

The harmonic series is a series of partials whose frequency is an integer (whole number) multiple of the fundamental.

A partial that is part of a harmonic series is also called a harmonic or an overtone.

In harmonic series the partials in both instruments form a harmonic series. The fundamental is 440Hz, the second partial is 880Hz, twice the fundamental, and the third partial is 1320Hz, three times the fundamental. A harmonic series continues in this fashion.

The trumpet has fewer partials, 19, than the violin, which has 35. This is one reason for the difference in timbres. Another is that the relative amplitude of each partial in each instrument is different. The amplitude of the partials in the trumpet spectrogram decrease in a fairly straight line. The violin partials also decrease in amplitude but the line is more uneven and ragged than the trumpet.

A harmonic series is a mathematical property of sound. It is a real phenomenon but can be treated in a rather rigid fashion. For example, there are two interesting features of the harmonic series that are just visible in the harmonic series spectrograms:

  1. The fundamental of the trumpet is not the loudest partial. You can see that the fundamental, which is on the extreme left of the trumpet spectrogram, is slightly lower in amplitude than the second partial to its right, which is the loudest partial.
  2. The lowest frequency of the harmonic series in the violin is not 440Hz but 55Hz. You can just see a bunch of low frequency partials lurking in the bottom left-hand corner of the violin spectrogram but their amplitudes are so small that they are dwarfed by the eighth partial.

Pitched musical instruments are manufactured to generate partials in a harmonic series. The material from which an instrument is made is a major factor in determining which partials are present in the sound.

The harmonic series provides an objective explanation for that most mysterious and elusive of terms, timbre. A harmonic series is a remarkable physical property of sound. It explains why some frequencies are more closely related than others, and it explains why some notes are more closely related than others. A harmonic series is the basis for designing tuning systems which, in turn, determine the notes that are available for writing melody and harmony. And it provides a scientific basis for music theory.

Audio: inharmonic (0:02)

Figure: inharmonic

inharmonic plays inharmonic sound. The inharmonic figure, its spectrogram, shows no evidence of a harmonic series and the sound is inharmonic, unpitched sound.

Inharmonic is a real mouthful, but it is simply the opposite of harmonic.

An inharmonic sound contains frequencies that are not in a harmonic series.

Unpitched sound is inharmonic, pitched sound is harmonic.

Inharmonic sound need not sound unpleasant, harmonic sound need not sound pleasant. Harmonicity is a technical feature of sound not a perception of sound.