Relationship between Music & Life

[Anilkumar]

I was just digging in to find the Relationship between Music & Life. I found some interesting areas which I thought I should share with you and seek help. I don't know if this classical physics forum is the right place for this thread, but I have posted it here for obvious reasons. I leave it to the Moderators to give it the appropriate place they think is.

 

MUSIC

 

Pitch:

 

Pitch is a perceptual property that allows the ordering of sounds on a frequency-related scale. Pitches are compared as "higher" and "lower" in the sense associated with musical melodies, which require "sound whose frequency is clear and stable enough to be heard as not noise". Pitch is a major auditory attribute of musical tones, along with duration, loudness, and timbre.

 

Pitch may be quantified as a frequency, but pitch is not a purely objective physical property; it is a subjective psychoacoustical attribute of sound. Historically, the study of pitch and pitch perception has been a central problem in psychoacoustics, and has been instrumental in forming and testing theories of sound representation, processing, and perception in the auditory system.

 

Musical Notes:

 

Music is is mainly composed of 'Notes', which are said to be the 'Atoms' of Music. A note is;

• A sign used in musical notation to represent the relative duration and pitch of a sound.
• A pitched sound itself.

In traditional music theory pitch classes are represented by the first seven letters of the Latin alphabet (A, B, C, D, E, F and G) (some countries use other names). The eighth note, or octave is given the same name as the first, but has double its frequency. In Italian, Portuguese, Greek, French, Russian, Flemish, Romanian, Spanish, Persian, Arabic, Hebrew, Bulgarian and Turkish notation the notes of scales are given in terms of Do-Re-Mi-Fa-Sol-La-Si rather than C-D-E-F-G-A-B similar to the Indian 'Swaras', Sa-Re-Ga-Ma-Pa-Dha-Ni-Sa.

 

When notes are written out in a score, each note is assigned a specific vertical position. Each line or space is assigned a note name. These names are memorized by musicians and allow them to know at a glance the proper pitch to play on their instruments for each note-head marked on the page.

 

 

The Musical score above shows the notes C, D, E, F, G, A, B, C and then in reverse order.

 

Listen to the music/sound of the above score here.

 

Musical tone:

 

A musical tone is a steady periodic sound. A musical tone is characterized by its duration, pitch, intensity (or loudness), and timbre (or quality). A simple tone, or pure tone, has a sinusoidal waveform. A compound tone is any musical tone that is not sinusoidal, but is periodic, such that it can be described as a sum of simple tones with harmonically related frequencies.

 

Now let us move on to Musical melody.

 

Tone color/Timbre/Tone quality:

 

In simple terms, timbre is what makes a particular musical sound different from another, even when they have the same pitch and loudness. For instance, it is the difference between a guitar and a piano playing the same note at the same loudness. Experienced musicians are able to distinguish between different instruments based on their varied timbres, even if those instruments are playing notes at the same pitch and loudness.

 

Musical melody:

 

A melody also tune, voice, or line, is a linear succession of musical tones which is perceived as a single entity. It also is an exponential succession of musical tones which is perceived as two entities. In its most literal sense, a melody is a combination of pitch and rhythm, while, more figuratively, the term has occasionally been extended to include successions of other musical elements such as tone color.

 

Mathematics and Physics of music :

 

Music theorists sometimes use mathematics to understand music. Mathematics is "the basis of sound". In all technicality, music can be composed of notes at any arbitrary frequency. Since the physical causes of music are vibrations of mechanical systems, they are often measured in hertz (Hz), with 1 Hz = 1 complete vibration per second. For historical and other reasons, especially in Western music, only twelve notes of fixed frequencies are used. These fixed frequencies are mathematically related to each other, and are defined around the central note, A4. The current "standard pitch" or modern "concert pitch" for this note is 440 Hz, although this varies in actual practice. Without the boundaries of rhythmic structure – a fundamental equal and regular arrangement of pulse repetitivity, accent, phrase and duration – music would be impossible. A musical scale is a discrete set of pitches used in making or describing music. Each pitch corresponds to a particular frequency, expressed in hertz (Hz), sometimes referred to as cycles per second (c.p.s.). A scale has an interval of repetition, normally the octave. The octave of any pitch refers to a frequency exactly twice that of the given pitch.

 

Cymatics :

 

Cymatics (from Greek:"wave") is the study of visible sound and vibration. Typically the surface of a plate, diaphragm, or membrane is vibrated, and regions of maximum and minimum displacement are made visible in a thin coating of particles, paste, or liquid. Different patterns emerge in the excitatory medium depending on the geometry of the plate and the driving frequency.

 

The apparatus employed can be simple, such as the ancient Chinese spouting bowl, or Chinese singing fountain, in which copper handles are rubbed and cause the copper bottom elements to vibrate. Other examples are a Chladni Plate or advanced such as the CymaScope, a laboratory instrument that makes visible the inherent geometries within sound and music.

 

The study of the patterns produced by vibrating bodies has a venerable history. One of the earliest to record that an oscillating body displayed regular patterns was Galileo Galilei. In Dialogue Concerning the Two Chief World Systems (1632), he wrote:

 

"As I was scraping a brass plate with a sharp iron chisel in order to remove some spots from it and was running the chisel rather rapidly over it, I once or twice, during many strokes, heard the plate emit a rather strong and clear whistling sound: on looking at the plate more carefully, I noticed a long row of fine streaks parallel and equidistant from one another. Scraping with the chisel over and over again, I noticed that it was only when the plate emitted this hissing noise that any marks were left upon it; when the scraping was not accompanied by this sibilant note there was not the least trace of such marks."

 

On July 8, 1680, Robert Hooke was able to see the nodal patterns associated with the modes of vibration of glass plates. Hooke ran a bow along the edge of a glass plate covered with flour, and saw the nodal patterns emerge.

 

Ernst Florens Friedrich Chladni (1756–1827) was a German physicist and musician. His important works include research on vibrating plates and the calculation of the speed of sound for different gases. For this some call him the "Father of Acoustics".

 

 

In 1787, Ernst Chladni repeated the work of Robert Hooke and published "Entdeckungen über die Theorie des Klanges" ("Discoveries in the Theory of Sound"). In this book, Chladni describes the patterns seen by placing sand on metal plates which are made to vibrate by stroking the edge of the plate with a bow.

 

Cymatics was explored by Hans Jenny in his 1967 book, Kymatik (translated Cymatics). Inspired by systems theory and the work of Ernst Chladni, Jenny began an investigation of periodic phenomena but especially the visual display of sound. He used standing waves, piezoelectric amplifiers, and other methods and materials.

 

One of Chladni's best-known achievements was inventing a technique to show the various modes of vibration of a rigid surface. A plate or membrane vibrating at resonance is divided into regions vibrating in opposite directions, bounded by lines of zero vibration called nodal lines. Chladni repeated the pioneering experiments of Robert Hooke of Oxford University who, on July 8, 1680, had observed the nodal patterns associated with the vibrations of glass plates. Hooke ran a bow along the edge of a plate covered with flour, and saw the nodal patterns emerge.

 

Node:

 

A node is a point along a standing wave where the wave has minimal amplitude. For instance, in a vibrating guitar string, the ends of the string are nodes. By changing the position of the end node through frets, the guitarist changes the effective length of the vibrating string and thereby the note played. The opposite of a node is an anti-node, a point where the amplitude of the standing wave is a maximum. These occur midway between the nodes.

 

Click here for the Gif image of a wave showing nodes.

 

The red dots are the wave nodes.

 

Chemistry:

 

In chemistry, quantum mechanical waves, or "orbitals", are used to describe the wave-like properties of electrons. Many of these quantum waves have nodes as well. The number and position of these nodes give rise to many of the properties of an atom or bond. For example, bonding orbitals with small nodes solely around nuclei are very stable, and are known as "bonds". In contrast, bonding orbitals with large nodes between nuclei will not be stable due to electrostatic repulsion and are known as "anti-bonding orbitals" because they will be so unstable as to cause a bond to break. It is due to this that the noble gases will not as likely form bonds between other noble gases. Another such quantum mechanical concept is the particle in a box where the number of nodes of the wavefunction can help determine the quantum energy state—zero nodes corresponds to the ground state, one node corresponds to the 1st excited state, etc.

 

Chladni patterns:

 

Chladni's technique, first published in 1787 in his book, Entdeckungen über die Theorie des Klanges ("Discoveries in the Theory of Sound"), consisted of drawing a bow over a piece of metal whose surface was lightly covered with sand. The plate was bowed until it reached resonance, when the vibration causes the sand to move and concentrate along the nodal lines where the surface is still, outlining the nodal lines.

 

Variations of this technique are still commonly used in the design and construction of acoustic instruments such as violins, guitars, and cellos. Since the 20th century it has become more common to place a loudspeaker driven by an electronic signal generator over or under the plate to achieve a more accurate adjustable frequency.

 

Samples of Chladni figures produced by sound vibrations in fine powder on a guitar:

 

 

Psychoacoustics:

 

Psychoacoustics is the scientific study of sound perception. More specifically, it is the branch of science studying the psychological and physiological responses associated with sound (including speech and music). It can be further categorized as a branch of psychophysics.

 

Often listeners are able to identify the kind of instrument even across "conditions of changing pitch and loudness, in different environments and with different players". In the case of the clarinet, an acoustic analysis of the waveforms shows they are irregular enough to suggest three instruments rather than one. David Luce (1963) suggests that this implies "certain strong regularities in the acoustic waveform of the above instruments must exist which are invariant with respect to the above variables". However, Robert Erickson argues that there are few regularities and they do not explain our "powers of recognition and identification". He suggests the borrowing from studies of vision and visual perception the concept of subjective constancy (Erickson 1975).

 

Psychoacoustic experiments from the 1960s onwards tried to elucidate the nature of timbre. One method involves playing pairs of sounds to listeners and then using a multidimensional scaling algorithm to aggregate their dissimilarity judgments into a timbre space; the most consistent outcomes from such experiments are that brightness or spectral energy distribution (Grey 1977), and the "bite", or rate and synchronicity (Wessel 1979) and rise time (Lakatos 2000), of the attack are important factors.

 

Hearing is not a purely mechanical phenomenon of wave propagation, but is also a sensory and perceptual event; in other words, when a person hears something, that something arrives at the ear as a mechanical sound wave traveling through the air, but within the ear it is transformed into neural action potentials. These nerve pulses then travel to the brain where they are perceived. Hence, in many problems in acoustics, such as for audio processing, it is advantageous to take into account not just the mechanics of the environment, but also the fact that both the ear and the brain are involved in a person's listening experience.

 

The inner ear, for example, does significant signal processing in converting sound waveforms into neural stimuli, so certain differences between waveforms may be imperceptible. Data compression techniques, such as MP3, make use of this fact.In addition, the ear has a nonlinear response to sounds of different intensity levels, this nonlinear response is called loudness. Telephone networks and audio noise reduction systems make use of this fact by nonlinearly compressing data samples before transmission, and then expanding them for playback. Another effect of the ear's nonlinear response is that sounds that are close in frequency produce phantom beat notes, or intermodulation distortion products.

 

The human ear can nominally hear sounds in the range 20 Hz (0.02 kHz) to 20,000 Hz (20 kHz). The upper limit tends to decrease with age; most adults are unable to hear above 16 kHz. The lowest frequency that has been identified as a musical tone is 12 Hz under ideal laboratory conditions. Tones between 4 and 16 Hz can be perceived via the body's sense of touch.

 

Frequency resolution of the ear is 3.6 Hz within the octave of 1000 – 2000 Hz. That is, changes in pitch larger than 3.6 Hz can be perceived in a clinical setting. However, even smaller pitch differences can be perceived through other means. For example, the interference of two pitches can often be heard as a (low) frequency difference pitch. This effect of phase variance upon the resultant sound is known as beating.

 

The intensity range of audible sounds is enormous. Human ear drums are sensitive to variations in the sound pressure, and can detect pressure changes from as small as a few micropascals to greater than 1 bar.

 

The psychoacoustic model provides for high quality lossy signal compression by describing which parts of a given digital audio signal can be removed (or aggressively compressed) safely — that is, without significant losses in the (consciously) perceived quality of the sound.

 

It can explain how a sharp clap of the hands might seem painfully loud in a quiet library, but is hardly noticeable after a car backfires on a busy, urban street.

 

Click on this

[6284 KB] to see for yourself the patterns of sound emerging.

 

Also see this Harvard university link here for knowing how it works.

 

Please give your opinion and throw more light to show further the relation between Music & Life.

 

Thank you.

 

Resources: Wikipedia.

Edited October 16, 2012 by Anilkumar

[Anilkumar]

Here is a Johns Hopkins University, recent research news on the subject;

 

Excerpts -

 

Helping the song remain the same: New insights about timbre could improve hearing prosthetics:

". . . Based on experiments in both animals and humans, they devised a computer model that can accurately mimic how specific brain regions process sounds as they enter our ears and get transformed into brain signals that allow us to recognize the type of sounds we are listening to. The model was able to correctly identify which instrument is playing (out of a total of 13 instruments) to an accuracy rate of 98.7 percent. . ."

Edited November 6, 2012 by Anilkumar