World Library  
Flag as Inappropriate
Email this Article

Physics of music

Article Id: WHEBN0000442849
Reproduction Date:

Title: Physics of music  
Author: World Heritage Encyclopedia
Language: English
Subject: Musical tuning, Harmony, Index of music articles, Audio system measurements, List of cycles, Multiphonics, Acoustic wave
Collection:
Publisher: World Heritage Encyclopedia
Publication
Date:
 

Physics of music

Musical acoustics or music acoustics is the branch of acoustics concerned with researching and describing the physics of music – how sounds employed as music work. 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.

Methods and fields of study

Physical aspects

Whenever two different pitches are played at the same time, their sound waves interact with each other – the highs and lows in the air pressure reinforce each other to produce a different sound wave. As a result, any given sound wave which is more complicated than a sine wave can be modelled by many different sine waves of the appropriate frequencies and amplitudes (a frequency spectrum). In humans the hearing apparatus (composed of the ears and brain) can usually isolate these tones and hear them distinctly. When two or more tones are played at once, a variation of air pressure at the ear "contains" the pitches of each, and the ear and/or brain isolate and decode them into distinct tones.

When the original sound sources are perfectly periodic, the note consists of several related sine waves (which mathematically add to each other) called the fundamental and the harmonics, partials, or overtones. The sounds have harmonic frequency spectra. The lowest frequency present is the fundamental, and is the frequency at which the entire wave vibrates. The overtones vibrate faster than the fundamental, but must vibrate at integer multiples of the fundamental frequency in order for the total wave to be exactly the same each cycle. Real instruments are close to periodic, but the frequencies of the overtones are slightly imperfect, so the shape of the wave changes slightly over time.

Subjective aspects

Variations in air pressure against the ear drum, and the subsequent physical and neurological processing and interpretation, give rise to the subjective experience called sound. Most sound that people recognize as musical is dominated by periodic or regular vibrations rather than non-periodic ones; that is, musical sounds typically have a definite pitch). The transmission of these variations through air is via a sound wave. In a very simple case, the sound of a sine wave, which is considered to be the most basic model of a sound waveform, causes the air pressure to increase and decrease in a regular fashion, and is heard as a very pure tone. Pure tones can be produced by tuning forks or whistling. The rate at which the air pressure oscillates is the frequency of the tone, which is measured in oscillations per second, called hertz. Frequency is the primary determinant of the perceived pitch. Frequency of musical instruments can change with altitude due to changes in air pressure.

Pitch ranges of musical instruments

ImageSize = width:700 height:2000 PlotArea = left:0 right:0 top:0 bottom:20 AlignBars = justify Colors =

 id:b value:rgb(0.85,0.85,0.85) # instruments
 id:f value:gray(0.8) # background bar
 id:heading value:rgb(0,0.6,0.5) # class
 id:subhead value:rgb(0,0.7,0.5) # subclass
 id:2x-subhead value:rgb(0,0.8,0.5) # sub-subclass
 id:3x-subhead value:rgb(0,0.9,0) # sub-sub-subclass
 id:4x-subhead value:rgb(0,1,0.5) # families
 id:paleGray  value:rgb(0.86,0.86,0.86) # grids

BarData =

 bar:pitch
 bar:Hz
 barset:ranges
 bar:pitch2
 bar:Hz2

Period = from:0 till:651 ScaleMajor = increment:72 start:2 gridcolor:paleGray TimeAxis = orientation:horizontal

Define $cc2 = 2 Define $cc1 = 74 Define $cc = 146 Define $c = 218 Define $c1 = 290 Define $c2 = 362 Define $c3 = 434 Define $c4 = 506 Define $c5 = 578 Define $c6 = 650 Define $dd2 = 14 Define $dd1 = 86 Define $dd = 158 Define $d = 230 Define $d1 = 302 Define $d2 = 374 Define $d3 = 446 Define $d4 = 518 Define $d5 = 590 Define $ee2 = 26 Define $ee1 = 98 Define $ee = 170 Define $e = 242 Define $e1 = 314 Define $e2 = 386 Define $e3 = 458 Define $e4 = 530 Define $e5 = 602 Define $ff2 = 32 Define $ff1 = 104 Define $ff = 176 Define $f = 248 Define $f1 = 320 Define $f2 = 392 Define $f3 = 464 Define $f4 = 536 Define $f5 = 608 Define $gg2 = 44 Define $gg1 = 116 Define $gg = 188 Define $g = 260 Define $g1 = 332 Define $g2 = 404 Define $g3 = 476 Define $g4 = 548 Define $g5 = 620 Define $aa2 = 56 Define $aa1 = 128 Define $aa = 200 Define $a = 272 Define $a1 = 344 Define $a2 = 416 Define $a3 = 488 Define $a4 = 560 Define $a5 = 632 Define $hh2 = 68 Define $hh1 = 140 Define $hh = 212 Define $h = 284 Define $h1 = 356 Define $h2 = 428 Define $h3 = 500 Define $h4 = 572 Define $h5 = 644

Define $max = 650 PlotData=

 align:center textcolor:black fontsize:10 mark:(line,black) width:10 shift:(0,-4)
 barset:ranges
 color:heading from:$ee  till:$c3  text:human voice
 color:b from:$ee  till:$e1  text:bass
 color:b from:$aa  till:$a1  text:baritone
 color:b from:$c   till:$c2  text:tenor
 color:b from:$e   till:$e2  text:alto
 color:b from:$a   till:$a2  text:mezzo-soprano
 color:b from:$c1  till:$c3  text:soprano
 color:heading from:$aa2 till:$c5  text:chordophone
 color:3x-subhead from:$ee1 till:$a4  text:bowed
 color:4x-subhead from:$ee1 till:$a4 text:violin family
 color:b from:$ee1 till:$a   text:double bass
 color:b from:$cc  till:$g2  text:cello
 color:b from:$c   till:$d4  text:viola
 color:b from:$g   till:$a4  text:violin
 color:3x-subhead from:$hh2 till:$f4  text:plucked
 color:b from:$hh2 till:$f4  text:harp
 color:b from:$ff1 till:$f3  text:harpsichord
 color:b from:$ee1 till:$g1  text:bass guitar
 color:b from:$ee  till:$e3  text:guitar
 color:b from:$g   till:$d4  text:mandolin
 color:b from:$d   till:$a2  text:5-string banjo
 color:3x-subhead from:$aa2 till:$c5  text:struck
 color:b from:$aa2 till:$c5  text:piano
 color:b from:$d till:$d3  text:hammered dulcimer
 color:b from:$aa2 till:$a4  text:cymbalum
 color:heading from:$cc2 till:$c6 text:aerophone
 color:subhead from:$cc2 till:$c6  text:woodwind instrument
 color:2x-subhead from:$aa2 till:$f3  text:double reed
 color:3x-subhead from:$hh2 till:$e3 text:exposed
 color:4x-subhead from:$hh2 till:$f2 text:bassoons
 color:b from:$hh2 till:$c1  text:contrabassoon
 color:b from:$hh1 till:$f2   text:bassoon
 color:4x-subhead from:$e till:$e3 text:oboes
 color:b from:$e   till:$h2  text:cor anglais
 color:b from:$a   till:$f3  text:heckelphone
 color:b from:$h   till:$e3  text:oboe
 color:2x-subhead from:$dd2 till:$a4  text:single reed
 color:4x-subhead from:$dd2 till:$a4 text:clarinet family
 color:b from:$dd2 till:$h   text:octocontrabass clarinet
 color:b from:$gg2 till:$h   text:octacontra-alto clarinet
 color:b from:$dd1 till:$h1  text:contrabass clarinet
 color:b from:$gg1 till:$h1  text:contra-alto clarinet
 color:b from:$dd  till:$h2  text:bass clarinet
 color:b from:$gg  till:$h2  text:alto clarinet
 color:b from:$d   till:$h3  text:soprano clarinet
 color:b from:$c1  till:$a4  text:sopranino clarinet
 color:4x-subhead from:$aa2 till:$e4 text:saxophone family
 color:b from:$aa2 till:$e   text:subcontrabass saxophone
 color:b from:$dd1 till:$d1  text:contrabass saxophone
 color:b from:$aa1 till:$e1  text:bass saxophone
 color:b from:$dd  till:$d2  text:baritone sax
 color:b from:$aa  till:$e2  text:tenor saxophone
 color:b from:$d   till:$d3  text:alto saxophone
 color:b from:$e   till:$h2  text:mezzo-soprano saxophone
 color:b from:$a   till:$e3  text:soprano saxophone
 color:b from:$d1  till:$d4  text:sopranino saxophone
 color:b from:$a1  till:$e4  text:sopranissimo saxophone
 color:2x-subhead from:$cc  till:$d4  text:free reed
 color:b from:$cc  till:$c4  text:harmonium
 color:b from:$gg  till:$a3  text:accordion
 color:b from:$c   till:$d4  text:16-hole harmonica
 color:b from:$c1  till:$c4  text:typical C harmonica
 color:2x-subhead from:$cc2 till:$c6 text:flutes
 color:3x-subhead from:$cc2 till:$c5 text:side blown
 color:4x-subhead from:$cc2 till:$c5 text:western concert flute family
 color:b from:$cc2 till:$c   text:hyperbass flute
 color:b from:$cc1 till:$c1  text:double contrabass flute
 color:b from:$gg1 till:$g1  text:subcontrabass flute
 color:b from:$cc  till:$c2  text:contrabass flute
 color:b from:$gg  till:$g2  text:contra-alto flute
 color:b from:$c   till:$c3  text:bass flute
 color:b from:$g   till:$g3  text:alto flute
 color:b from:$c1  till:$c4  text:flute
 color:b from:$c2  till:$c5  text:piccolo
 color:3x-subhead from:$cc2 till:$c6 text:internal duct (fipple)
 color:4x-subhead from:$f   till:$c5  text:recorders
 color:b from:$f   till:$c3  text:bass recorder
 color:b from:$c1  till:$g3  text:tenor recorder
 color:b from:$f1  till:$c4  text:alto recorder
 color:b from:$c2  till:$g4  text:soprano (descant) recorder
 color:b from:$f2  till:$c5  text:sopranino recorder
 color:b from:$cc2 till:$c6  text:organ*
 color:subhead from:$ff2 till:$h4  text:brass instrument
 color:4x-subhead from:$aa2 till:$f2  text:tubas
 color:b from:$aa2 till:$h text:contrabass tuba
 color:b from:$dd1 till:$g1 text:bass tuba
 color:b from:$ee1  till:$f2  text:tenor wagner tuba
 color:b from:$ff1  till:$f1 text:cimbasso
 color:4x-subhead from:$aa2  till:$d2  text:trombones
 color:b from:$aa2 till:$c2  text:contrabass trombone
 color:b from:$hh2  till:$f2  text:bass trombone
 color:b from:$ee  till:$f2  text:tenor trombone
 color:b from:$ff  till:$d2  text:alto trombone
 color:4x-subhead from:$ff1 till:$h2  text:horns
 color:b from:$hh1  till:$f2  text:horn
 color:b from:$ff1  till:$f2  text:baritone horn
 color:b from:$ff1  till:$f2  text:euphonium
 color:b from:$aa   till:$e2  text:alto horn
 color:b from:$g   till:$c3  text:flugelhorn
 color:4x-subhead from:$ee  till:$h4  text:trumpets
 color:b from:$ee  till:$h1  text:bass trumpet
 color:b from:$e   till:$h3  text:cornet
 color:b from:$e   till:$h3  text:trumpet
 color:b from:$h1  till:$h4  text:piccolo trumpet
 color:heading from:$cc  till:$c1  text:membranophone
 color:4x-subhead from:$cc  till:$c1  text:timpani
 color:b from:$cc till:$c text:D drum
 color:b from:$ee till:$e text:G drum
 color:b from:$aa till:$a text:C drum
 color:b from:$c  till:$g text:F drum
 color:b from:$c  till:$c1 text:A drum
 color:b from:$g  till:$c1 text:B drum
 color:heading from:$cc  till:$f5  text:idiophone
 color:2x-subhead from:$cc till:$c5 text:sticks or bars
 color:3x-subhead from:$cc till:$c5 text:xylophone family
 color:b from:$cc  till:$c4  text:marimba
 color:b from:$c1  till:$c5  text:xylophone
 color:2x-subhead from:$c till:$f5 text:plaques
 color:b from:$c3 till:$c4 text:crotales
 color:3x-subhead from:$c till:$f5 text:metallophones
 color:b from:$c   till:$f5  text:celesta
 color:b from:$c   till:$f3  text:vibraphone
 color:b from:$c2  till:$f5  text:glockenspiel
 color:2x-subhead from:$e till:$g2 text:tubes
 color:b from:$e   till:$g2  text:tubular bells
 color:2x-subhead from:$cc till:$g2 text:vessels
 color:b from:$cc till:$g2 text:gong
 color:f textcolor:blue align:left fontsize:S mark:(line,white) shift:(3,-4)
 
 bar:pitch 
 from:0 till:$max
 at:$cc2  text:C0
 at:$cc1  text:C1
 at:$cc   text:C2
 at:$c    text:C3
 at:$c1   text:C4
 at:$c2   text:C5
 at:$c3   text:C6
 at:$c4   text:C7
 at:$c5   text:C8
 bar:Hz
 from:0 till:$max
 at:23    text:20
 at:65    text:30
 at:105   text:44
 at:153   text:70
 at:190   text:100
 at:232   text:150
 at:262   text:200
 at:304   text:300
 at:344   text:440
 at:392   text:700
 at:430   text:1000
 at:472   text:1500
 at:502   text:2000
 at:544   text:3000
 at:583   text:4400 Hz
 bar:pitch2 # exact copy of bar:pitch 
 from:0 till:$max
 at:$cc2  text:C0
 at:$cc1  text:C1
 at:$cc   text:C2
 at:$c    text:C3
 at:$c1   text:C4
 at:$c2   text:C5
 at:$c3   text:C6
 at:$c4   text:C7
 at:$c5   text:C8
 bar:Hz2 # exact copy of bar:Hz 
 from:0 till:$max
 at:23    text:20
 at:65    text:30
 at:105   text:44
 at:153   text:70
 at:190   text:100
 at:232   text:150
 at:262   text:200
 at:304   text:300
 at:344   text:440
 at:392   text:700
 at:430   text:1000
 at:472   text:1500
 at:502   text:2000
 at:544   text:3000
 at:583   text:4400 Hz

*This chart only displays down to C0, though the Octocontrabass clarinet extends down to the B♭ below that C. Also some pipe organs, such as the Boardwalk Hall Auditorium Organ, extend down to C−1 (one octave below C0).


Harmonics, partials, and overtones


The fundamental is the frequency at which the entire wave vibrates. Overtones are other sinusoidal components present at frequencies above the fundamental. All of the frequency components that make up the total waveform, including the fundamental and the overtones, are called partials. Together they form the harmonic series.

Overtones which are perfect integer multiples of the fundamental are called harmonics. When an overtone is near to being harmonic, but not exact, it is sometimes called a harmonic partial, although they are often referred to simply as harmonics. Sometimes overtones are created that are not anywhere near a harmonic, and are just called partials or inharmonic overtones.

The fundamental frequency is considered the first harmonic and the first partial. The numbering of the partials and harmonics is then usually the same; the second partial is the second harmonic, etc. But if there are inharmonic partials, the numbering no longer coincides. Overtones are numbered as they appear above the fundamental. So strictly speaking, the first overtone is the second partial (and usually the second harmonic). As this can result in confusion, only harmonics are usually referred to by their numbers, and overtones and partials are described by their relationships to those harmonics.

Harmonics and non-linearities


When a periodic wave is composed of a fundamental and only odd harmonics (f, 3f, 5f, 7f, ...), the summed wave is half-wave symmetric; it can be inverted and phase shifted and be exactly the same. If the wave has any even harmonics (0f, 2f, 4f, 6f, ...), it will be asymmetrical; the top half will not be a mirror image of the bottom.

Conversely, a system which changes the shape of the wave (beyond simple scaling or shifting) creates additional harmonics (harmonic distortion). This is called a non-linear system. If it affects the wave symmetrically, the harmonics produced will only be odd, if asymmetrically, at least one even harmonic will be produced (and probably also odd).

Harmony

Main article: Harmony

If two notes are simultaneously played, with frequency ratios that are simple fractions (e.g. 2/1, 3/2 or 5/4), then the composite wave will still be periodic with a short period, and the combination will sound consonant. For instance, a note vibrating at 200 Hz and a note vibrating at 300 Hz (a perfect fifth, or 3/2 ratio, above 200 Hz) will add together to make a wave that repeats at 100 Hz: every 1/100 of a second, the 300 Hz wave will repeat thrice and the 200 Hz wave will repeat twice. Note that the total wave repeats at 100 Hz, but there is not actually a 100 Hz sinusoidal component present.

Additionally, the two notes will have many of the same partials. For instance, a note with a fundamental frequency of 200 Hz will have harmonics at:

(200,) 400, 600, 800, 1000, 1200, …

A note with fundamental frequency of 300 Hz will have harmonics at:

(300,) 600, 900, 1200, 1500, …

The two notes share harmonics at 600 and 1200Hz, and more will coincide further up the series.

The combination of composite waves with short fundamental frequencies and shared or closely related partials is what causes the sensation of harmony.

When two frequencies are near to a simple fraction, but not exact, the composite wave cycles slowly enough to hear the cancellation of the waves as a steady pulsing instead of a tone. This is called beating, and is considered to be unpleasant, or dissonant.

The frequency of beating is calculated as the difference between the frequencies of the two notes. For the example above, |200 Hz - 300 Hz| = 100 Hz. As another example, a combination of 3425 Hz and 3426 Hz would beat once per second (|3425 Hz - 3426 Hz| = 1 Hz). This follows from modulation theory.

The difference between consonance and dissonance is not clearly defined, but the higher the beat frequency, the more likely the interval to be dissonant. [1]

Scales

Main article: Musical scale

The material of a musical composition is usually taken from a collection of pitches known as a scale. Because most people cannot adequately determine absolute frequencies, the identity of a scale lies in the ratios of frequencies between its tones (known as intervals).

Main article: Just intonation

The diatonic scale appears in writing throughout history, consisting of seven tones in each octave. In just intonation the diatonic scale may be easily constructed using the three simplest intervals within the octave, the perfect fifth (3/2), perfect fourth (4/3), and the major third (5/4). As forms of the fifth and third are naturally present in the overtone series of harmonic resonators, this is a very simple process.

The following table shows the ratios between the frequencies of all the notes of the just major scale and the fixed frequency of the first note of the scale.

C D E F G A B C
1 9/8 5/4 4/3 3/2 5/3 15/8 2

There are other scales available through just intonation, for example the minor scale. Scales which do not adhere to just intonation, and instead have their intervals adjusted to meet other needs are known as temperaments, of which equal temperament is the most used. Temperaments, though they obscure the acoustical purity of just intervals often have other desirable properties, such as a closed circle of fifths.

See also

External links

  • Music acoustics - sound files, animations and illustrations - University of New South Wales
  • Dayton Miller
  • The Technical Committee on Musical Acoustics (TCMU) of the Acoustical Society of America (ASA)
  • The Musical Acoustics Research Library (MARL)
  • Acoustics Group/Acoustics and Music Technology courses - University of Edinburgh
  • Acoustics Research Group - Open University
  • The music acoustics group at Speech, Music and Hearing KTH
  • The physics of harpsichord sound
  • Visual music
  • Savart Journal - The open access online journal of science and technology of stringed musical instruments
  • Creative Commons Licence
  • Physclips

Template:Acoustics

This article was sourced from Creative Commons Attribution-ShareAlike License; additional terms may apply. World Heritage Encyclopedia content is assembled from numerous content providers, Open Access Publishing, and in compliance with The Fair Access to Science and Technology Research Act (FASTR), Wikimedia Foundation, Inc., Public Library of Science, The Encyclopedia of Life, Open Book Publishers (OBP), PubMed, U.S. National Library of Medicine, National Center for Biotechnology Information, U.S. National Library of Medicine, National Institutes of Health (NIH), U.S. Department of Health & Human Services, and USA.gov, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for USA.gov and content contributors is made possible from the U.S. Congress, E-Government Act of 2002.
 
Crowd sourced content that is contributed to World Heritage Encyclopedia is peer reviewed and edited by our editorial staff to ensure quality scholarly research articles.
 
By using this site, you agree to the Terms of Use and Privacy Policy. World Heritage Encyclopedia™ is a registered trademark of the World Public Library Association, a non-profit organization.
 



Copyright © World Library Foundation. All rights reserved. eBooks from World Library are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.