Psychoacoustics is an interdisciplinary field between physical acoustics, anatomy and psychology concerned with how humans perceive and interpret sound. One of the key aspects of psychoacoustic is the study of timbre and how humans perceive them.
Timbre is operationally defined as the attribute that distinguishes sounds of equal pitch, loudness, location and duration. The timbre of each nonmonotonic sound source is created by a blend of overtones (harmonics) at varying amplitude and attack to create a unique waveform.
Functionally, timbre is a key determinant of sound identity (ie. sound of a piano or a violin, or an oboe), and plays a pivotal role in speech as it is the principal determinant of phonetic identity. Technically, timbre of a sound is represented in both spectral, temporal, and spectro-temporal dimensions.
The plot below shows the time-frequency auditory spectrogram of piano and violin notes. The temporal and spectral slices shown on the right are marked. (B) The plots show magnitude cortical responses of four piano notes (left panels), played in normal (left) and Staccato (right) at F4 (top) and F#4 (bottom); and four violin notes (right panels), played in normal (left) and Pizzicato (right) also at pitch F4 (top) and F#4 (bottom). The white asterisks (upper leftmost notes in each quadruplet) indicate the notes shown in part (A) of this figure.
It can be seen that the piano has most of the energy sustained at the fundamental while the violin has energy distributed more evenly over many harmonics, hence the difference in sound.
We now understand timbre to have two broad characteristics that contribute to the perception of music: First, the distribution of energy across different harmonics not only serves as a recognition between instruments but also enables the recognition of a multifarious set of abstract tonal attributes (brightness, nasality, richness). Second, the temporal characteristics, especially the transient & note onset, or what musicians call the “nature of attack” is one of the primary perceptual vehicles for the identiﬁcation, and location tracking over time of a sound source. This is important for bass & plucked string instruments such as guitars that contain little or no steady state sound at all . In this case, the shape of the amplitude envelope at the beginning of the sound will be key to the perceived pitch & tone quality.
In the next post, we will talk about how digital music are recorded and in later posts, we will discuss further into how a Digital to analog converter (DAC) and amplifier can best recreate the timbre and maximize the musical experience.
Harvey E.White & Donald H.White - Physics and Music: The Science of Musical Sound