Timbre

Timbre is what makes it possible to distinguish two sounds of the same pitch, the same intensity and the same duration: a violin and a saxophone playing the same A remain recognizable. It depends on the spectrum of the sound and on its evolution over time.

Discover FizziQ

How to measure it in class

FizziQ gives access both to the frequency spectrum and to the oscillogram, the two faces of timbre: the distribution of the harmonics and the evolution of the amplitude over time.

Steps:

Have the same note, for example an A at 440 Hz, played by two different instruments and record each sound with FizziQ.
Display the frequency spectrum of each recording: the peak of the fundamental is in the same place, but the amplitudes of the harmonics differ.
For each instrument, record the relative amplitude of the first five harmonics and compare the two profiles.
Display the complete oscillogram of each note and identify the three phases of the envelope: attack, sustain, decay.
Compare the attack durations: a few milliseconds for a piano or a plucked guitar, several tens of milliseconds for a bowed or wind instrument.
Listen again to an excerpt taken from the middle of the note, without the attack, and try to identify the instrument by ear.

Scientific activities on this topic

Two activities allow you to explore what makes the sound signature of an instrument.

Learn more

The timbre of a musical instrument, often called its “sound quality” or “tonal color,” is what allows distinguishing one instrument from another when they produce the same note. Timbre is the element that makes each instrument unique and identifiable to the ear.

The same note played by two different instruments has different timbres because the number of harmonics and their relative intensities differ. The two sounds, although having the same fundamental frequency, do not sound alike to the ear. This difference can be observed by comparing the frequency spectra in FizziQ.

Timbre cannot be reduced to the spectrum. This is the most frequent error about this notion. The temporal envelope of the sound, that is, the way its amplitude evolves during the note, plays a role at least as important. Three phases can be distinguished: the attack, very brief, during which the sound establishes itself; the sustain, where the amplitude is maintained or decreases slowly; the decay, when the sound dies away. The classic experiment is telling: if you record a piano note and remove its first few tens of milliseconds, the remaining sound becomes very difficult to identify and many listeners mistake it for an organ or a wind instrument. Yet the spectrum has not changed. Conversely, playing a piano recording backwards makes the instrument unrecognizable, even though the spectral content is identical.

The spectrum itself is in fact not fixed during the note: the high harmonics often appear first and die away faster than the fundamental. It is this joint evolution of the spectrum and the amplitude that FizziQ’s spectrogram makes it possible to visualize.

The timbre of an instrument comes from several acoustic and physical characteristics that influence how sound waves are produced and propagated by the instrument. Here are some of the main factors that contribute to an instrument’s timbre:

Shape and material of the sound source: The way the instrument generates sound vibrations plays a crucial role in its timbre. For example, the steel strings of a guitar will vibrate differently from those of a violin, and this will affect the timbre of each instrument.
Shape and size of the resonance chamber: The shape and size of the instrument’s resonance chamber, such as the body of a violin or the bell of a trumpet, influence how sound waves are amplified and modified, contributing to the characteristic timbre of the instrument.
Sound emission characteristics: The attack modes, sustain (note maintenance), and decay of the note are important aspects of an instrument’s timbre. For example, the way a musician plays a transverse flute can create a different timbre from that of a clarinet player.
Specific components of the instrument: Some instruments have unique components that influence their timbre. For example, the harmonics in a guitar’s sound result from the vibration of the strings and their interaction with the resonance chamber and frets.
Musician’s technique: The way a musician plays an instrument, including their style, phrasing, expression, and articulation, can also influence the instrument’s timbre.
Characteristics of instrument materials: The materials used to construct the instrument, such as wood, metal, plastic, or skin, impact the timbre by influencing how vibrations propagate through the instrument.

The timbre of an instrument is influenced by many factors, such as the shape and size of the instrument, the materials used to make it, how it is played (for example, with or without vibrato), and the sound effects used (for example, reverb or distortion). The timbre of an instrument can also change depending on the pitch of the note played, and some instruments have timbres that are more characteristic than others (for example, the low and round sound of the tuba is easily recognizable).

Formula

Timbre is not a quantity measurable by a single number: it is described by a set of descriptors. The sound is first decomposed into harmonics:

s(t) = Σ Aₙ(t) sin(2π n f₀ t + φₙ)

where:

Aₙ(t): amplitude of the harmonic of rank n, variable during the note (Pa)
n: rank of the harmonic
f₀: fundamental frequency, which sets the pitch (Hz)
φₙ: phase of the harmonic of rank n (rad)

A common descriptor of timbre is the spectral centroid, which reflects the more or less bright character of the sound:

f_c = Σ (fₙ × Aₙ) / Σ Aₙ

where:

f_c: spectral centroid (Hz)
fₙ: frequency of the harmonic of rank n (Hz)
Aₙ: amplitude of that harmonic (Pa)

Application examples

A violin and a flute playing the same A at 440 Hz give very different spectra: the violin is rich up to rank 10 or beyond, the flute dies out from the first ranks.
The attack of a piano note lasts about 10 ms, that of a bowed violin several tens of milliseconds: this is a decisive clue for identification by ear.
A piano note stripped of its attack becomes very difficult to recognize, even though its spectrum is unchanged.
The clarinet, rich in odd harmonics, has a hollow timbre clearly distinct from that of the oboe, which has all the ranks.
Automatic recognition of an instrument or a speaker relies on timbre descriptors calculated from the spectrum and its temporal evolution.
The timbre of the same voice changes when different vowels are articulated: the resonances of the mouth reinforce zones of the spectrum called formants, without changing the pitch.

FAQ

Q: Timbre is just the spectrum, right? A: No, not only. Two sounds with identical spectra can be perceived as coming from different instruments if their temporal envelopes differ. The attack is particularly decisive for identification.

Q: Does timbre depend on the note played? A: Yes. The same instrument does not have exactly the same timbre in the low and high registers, because the number of audible harmonics and the response of the resonance chamber change with pitch.

Q: How does a synthesizer imitate an instrument? A: By reproducing both the spectrum and the envelope. Synthesizers explicitly model the attack, sustain and decay phases, because a correct spectrum with a wrong envelope does not sound right.

Q: Is timbre a measurable physical quantity? A: It is a perceptual quantity, described by several measurable descriptors: relative amplitudes of the harmonics, spectral centroid, attack duration. No single number sums it up.

Q: Why do we recognize a voice on the telephone despite the poor quality? A: The telephone only transmits a narrow band, about 300 to 3400 Hz, but it contains the formants and the attack characteristics that carry most of the timbre information.

Pure Tone - Complex Sound - Harmonic Sound - Fundamental Frequency - Spectrogram - Sound Signal Envelope - Vocal Formant - Pitch (Sound Height)