Musical acoustics

Musical acoustics or music acoustics is a multidisciplinary field that combines knowledge from physics, psychophysics, organology (classification of the instruments), physiology, music theory, ethnomusicology, signal processing and instrument building, among other disciplines. As a branch of acoustics, it is concerned with researching and describing the physics of music – how sounds are employed to make music.

Examples of areas of study are the function of musical instruments, the human voice (the physics of speech and singing), computer analysis of melody, and in the clinical use of music in music therapy.

The pioneer of music acoustics was Hermann von Helmholtz, a German polymath of the 19th century who was an influential physician, physicist, physiologist, musician, mathematician and philosopher. His book On the Sensations of Tone as a Physiological Basis for the Theory of Music is a revolutionary compendium of several studies and approaches that provided a complete new perspective to music theory, musical performance, music psychology and the physical behaviour of musical instruments.

Methods and fields of study

Musical acoustics studies how sounds work in music. It looks at the physics of musical instruments, how we hear different frequencies in music, and how to create musical sounds using computers. It also explores how our minds understand music, which is called music cognition or psychoacoustics.

Physical aspects

When two different musical notes are played together, their sound waves mix and create a new sound. Our ears and brains can usually tell these notes apart and hear them clearly.

Notes that repeat perfectly are made up of several simple waves called the main note and its higher notes, which are called overtones. The main note is the lowest sound, while the overtones vibrate faster. Real musical instruments almost make these perfect repeating notes, but the overtones are not always exact.

Subjective aspects

Changes in air pressure against the ear and how our body processes these changes create what we call sound. Most sounds we think of as music come from regular vibrations, giving them a clear pitch. These sounds travel through the air as waves. A simple sound wave, called a sine wave, makes the air pressure go up and down evenly, sounding like a pure tone. Things like tuning forks or whistling can make pure tones. The speed of these pressure changes is called the frequency of the tone, measured in hertz. Frequency mainly decides how high or low a pitch sounds. The frequency of musical instruments can shift with altitude because of changes in air pressure.

Pitch ranges of musical instruments

This chart shows the pitch ranges of different musical instruments. Most instruments start at C₀, but some very large ones, like certain pipe organs and the subcontrabass tuba, can go even lower, down to C₋₁ or B♭₋₁. These low notes are very deep and hard to hear.

Harmonics, partials, and overtones

The fundamental is the main frequency at which a wave vibrates. Overtones are additional sounds that occur at higher frequencies than the fundamental. All the frequencies that make up a sound wave, including the fundamental and the overtones, are called partials. Together, they create what is known as the harmonic series.

Overtones that are exact multiples of the fundamental are called harmonics. Sometimes, overtones are close to being harmonics but not exact, and they are still often called harmonics. Other times, overtones may not be close to harmonics at all and are just called partials or inharmonic overtones. The fundamental frequency is the first harmonic and the first partial. The way we number partials and harmonics can change if there are inharmonic partials. Overtones are counted based on how they appear above the fundamental.

Harmonics and non-linearities

When a repeating sound wave includes only certain vibrations called odd harmonics, the wave looks the same if you flip it over. If the wave includes even-numbered vibrations, it looks different on top and bottom.

Some systems can change the shape of a wave in a way that creates extra vibrations, called harmonics. This is known as a non-linear system. If the change is the same on both sides, only odd harmonics are created. If the change is different on each side, even harmonics may appear along with odd ones.

Harmony

Main article: Harmony

When two notes are played together and their frequencies are simple fractions of each other, like 2/1, 3/2, or 5/4, they sound pleasant together. This is called harmony. For example, a note at 200 Hz and another at 300 Hz (a perfect fifth) create a wave that repeats every 1/100 of a second.

Notes from musical instruments also have overtones, or extra sounds that occur alongside the main note. When two notes share some of these overtones, it adds to the pleasant feeling of harmony. However, if the notes are slightly off, the combined sound can create a pulsing effect called beating, which sounds unpleasant or dissonant. The faster this pulsing happens, the more unpleasant it feels.

Scales

Main article: Musical scale

A musical composition often uses notes from a group called a scale. Since people usually can't tell the exact pitch of a note, a scale is known by how the pitches relate to each other.

Main article: Just intonation

The diatonic scale has been used for a long time. It includes seven notes within an octave. In just intonation, this scale can be made using simple ratios between notes, like the perfect fifth (3/2), perfect fourth (4/3), and the major third (5/4). These ratios come from natural patterns in sound.

Other scales can also be made, like the minor scale. Some scales change the ratios to fit certain needs. These are called temperaments, with equal temperament being common. While these scales don't keep the exact sound ratios, they can make playing instruments easier.

For many instruments, the player mainly controls when and how hard they play a note. After that, the sound fades away on its own. The beginning of the note is usually what listeners notice most.