View source for Musical acoustics

{{Short description|Application of acoustics to music}}
'''Musical acoustics''' or '''music acoustics''' is a multidisciplinary field that combines knowledge from [[physics]],<ref>{{Cite book|url=https://books.google.com/books?id=cCW5Ng0UfYYC|title=Fundamentals of Musical Acoustics|last=Benade|first=Arthur H.|author-link=Arthur Benade |date=1990|publisher=Dover Publications|isbn=9780486264844|language=en}}</ref><ref>{{Cite book|url=https://books.google.com/books?id=9CRSRYQlRLkC|title=The Physics of Musical Instruments|last1=Fletcher|first1=Neville H.|last2=Rossing|first2=Thomas|date=2008-05-23|publisher=Springer Science & Business Media|isbn=9780387983745|language=en}}</ref><ref>{{Cite book|url=https://books.google.com/books?id=iiCZwwFG0x0C|title=The Musician's Guide to Acoustics|last1=Campbell|first1=Murray|last2=Greated|first2=Clive|date=1994-04-28|publisher=OUP Oxford|isbn=9780191591679|language=en}}</ref> [[psychophysics]],<ref>{{Cite book|url=https://www.springer.com/gp/book/9780387094700|title=The Physics and Psychophysics of Music: An Introduction|last=Roederer|first=Juan|date=2009|publisher=Springer-Verlag|isbn=9780387094700|edition=4|location=New York|language=en}}</ref> [[organology]]<ref>{{Cite book|url=https://books.google.com/books?id=5h3FGwAACAAJ|title=Acústica musical|last=Henrique|first=Luís L.|date=2002|publisher=Fundação Calouste Gulbenkian|isbn=9789723109870|language=pt}}</ref> (classification of the instruments), [[physiology]],<ref>{{Cite book|title=The Biology of Musical Performance and Performance-Related Injury|last=Watson, Lanham|first=Alan H. D., ML|publisher=Scarecrow Press|year=2009|isbn=9780810863590|location=Cambridge}}</ref> [[music theory]],<ref name=":0">{{Cite book|url=https://www.cambridge.org/core/books/on-the-sensations-of-tone-as-a-physiological-basis-for-the-theory-of-music/6B5630E5D439286A8946CEB9D62BE6EC|title=On the Sensations of Tone as a Physiological Basis for the Theory of Music by Hermann L. F. Helmholtz|last1=Helmholtz|first1=Hermann L. F.|last2=Ellis|first2=Alexander J.|date=1885|website=Cambridge Core|doi=10.1017/CBO9780511701801 |hdl=2027/mdp.39015000592603 |isbn=9781108001779 |language=en|access-date=2019-11-04}}</ref> [[ethnomusicology]],<ref>{{Cite book|url=https://www.press.uchicago.edu/ucp/books/book/chicago/O/bo3774458.html|title=On Concepts and Classifications of Musical Instruments|last=Kartomi|first=Margareth|publisher=University of Chicago Press|year=1990|isbn=9780226425498|location=Chicago}}</ref> [[signal processing]] and instrument building,<ref>{{Cite book|title=Musical Instrument Design: Practical Information for Instrument Design|last=Hopkin|first=Bart|publisher=See Sharp Press|year=1996|isbn=978-1884365089}}</ref>  among other disciplines.  As a branch of [[acoustics]], it is concerned with researching and describing the physics of [[music]] – how [[sound]]s are employed to make music. Examples of areas of study are the function of [[musical instruments]], the [[human voice]] (the physics of [[Interpersonal communication|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 ''[[iarchive:onsensationsofto00helmrich|On the Sensations of Tone as a Physiological Basis for the Theory of Music]]''<ref name=":0" /> 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==

*The [[physics]] of [[musical instruments]]
*[[Range (music)|Frequency range of music]]
*[[Fourier analysis]]
*Computer [[Musical analysis|analysis]] of musical structure
*[[Sound synthesis|Synthesis]] of musical sounds
*[[Music cognition]], based on physics (also known as [[psychoacoustics]])

==Physical aspects==

[[File:Sound spectrography of infrasound recording 30301.webm|thumb|Sound spectrography of infrasound recording 30301]]

[[Image:Spectrogram showing shared partials.png|frame|A spectrogram of a violin playing a note and then a perfect fifth above it. The shared partials are highlighted by the white dashes.]]
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. Any repeating sound wave that is not a sine wave can be modeled by many different sine waves of the appropriate frequencies and amplitudes (a [[frequency spectrum]]). In [[human]]s the [[hearing (sense)|hearing]] apparatus (composed of the [[ear]]s 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 [[Musical note|note]] consists of several related sine waves (which mathematically add to each other) called the [[fundamental frequency|fundamental]] and the [[harmonic]]s, [[Harmonic series (music)#Partial|partial]]s, or [[overtone]]s. The sounds have [[harmonic]] [[frequency spectrum|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 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.{{Citation needed|date=January 2009}}

==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 [[music]]al is dominated by [[Periodic function|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 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 fork]]s 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 (music)|pitch]]. Frequency of musical instruments can change with altitude due to changes in air pressure.

==Pitch ranges of musical instruments==

{{Vocal and instrumental pitch ranges}}

== Harmonics, partials, and overtones ==

[[Image:Moodswingerscale.svg|thumb|upright=1.3|[[Scale of harmonics]]]]

The [[fundamental frequency|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 [[Harmonic series (music)#Partial|partial]]s. Together they form the [[harmonic series (music)|harmonic series]].

Overtones that are perfect integer multiples of the fundamental are called [[harmonic]]s. 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 ==
[[Image:Symmetric_and_asymmetric_waveforms.svg|thumb|A symmetric and asymmetric waveform. The red (upper) wave contains only the fundamental and odd harmonics; the green (lower) wave contains the fundamental and even harmonics.]]

When a periodic wave is composed of a fundamental and only odd harmonics ({{mvar|f}}, {{math|3 ''f''}}, {{math|5 ''f''}}, {{math|7 ''f''}}, ...), 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 ({{math|2 ''f''}}, {{math|4 ''f''}}, {{math|6 ''f''}}, ...), it is ''asymmetrical''; the top half of the plotted wave form does not mirror image the bottom.

Conversely, a system that 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 are all odd. If it affects the harmonics asymmetrically, at least one even harmonic is produced (and probably also odd harmonics).

==Harmony==

{{Main|Harmony}}

If two notes are simultaneously played, with frequency [[ratio]]s that are simple fractions (e.g. {{small| {{sfrac| 2 | 1 }} }}, {{small| {{sfrac| 3 | 2 }} }}, or {{small| {{sfrac| 5 | 4 }} }}), the composite wave is still periodic, with a short period – and the combination sounds [[consonance and dissonance|consonant]]. For instance, a note vibrating at 200&nbsp;[[Hertz (unit)|Hz]] and a note vibrating at 300&nbsp;Hz (a [[perfect fifth]], or {{nobr|{{small| {{sfrac| 3 | 2 }} }} ratio,}} above 200&nbsp;Hz) add together to make a wave that repeats at 100&nbsp;Hz: Every {{small| {{sfrac| 1 | 100 }} }} of a second, the 300&nbsp;Hz wave repeats three times and the 200&nbsp;Hz wave repeats twice. Note that the ''combined'' wave repeats at 100&nbsp;Hz, even though there is no actual 100&nbsp;Hz sinusoidal component contributed by an individual sound source.

Additionally, the two notes from acoustical instruments will have overtone partials that will include many that share the same frequency. For instance, a note with the frequency of its fundamental harmonic at 200&nbsp;[[Hertz (unit)|Hz]] can have harmonic overtones at: 400, 600, 800, {{gaps|1|000}}, {{gaps|1|200}}, {{gaps|1|400}}, {{gaps|1|600}}, {{gaps|1|800}}, ...&nbsp;[[Hertz (unit)|Hz]].
A note with fundamental frequency of 300&nbsp;Hz can have overtones at: 600, 900, {{gaps|1|200}}, {{gaps|1|500}}, {{gaps|1|800}}, ...&nbsp;[[Hertz (unit)|Hz]].
The two notes share harmonics at 600, {{gaps|1|200}}, {{nobr|{{gaps|1|800}} Hz,}} and more that coincide with each other, further along in the each series.

Although the mechanism of human hearing that accomplishes it is still incompletely understood, practical musical observations for nearly {{nobr|{{gaps|2|000}} years}}<ref>{{cite book |first=Gaius Claudius |last=Ptolemy |author-link=Claudius Ptolemy |id=year {{nobr|{{circa|180 {{sc|ce}}}}}} |trans-title=Harmonics |script-title=he:{{math|Ἁρμονικόν}} |title=Harmonikon  |title-link=Harmonics}}</ref> 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 [[beat (acoustics)|beating]], and is considered unpleasant, or [[consonance and dissonance|dissonant]].

The frequency of beating is calculated as the difference between the frequencies of the two notes. When two notes are close in pitch they beat slowly enough that a human can measure the frequency ''difference'' by ear, with a [[stopwatch]]; beat timing is how tuning pianos, harps, and [[harpsichord]]s to complicated [[temperament (music)|temperaments]] was managed before affordable [[electronic tuner|tuning meters]].
* For the example above, {{nobr|{{math| {{big|'''&#x7C;'''}} 200 }}[[Hertz (unit)|Hz]]{{math| − 300 }}Hz{{math| {{big|'''&#x7C;'''}} &thinsp;{{=}}&thinsp; 100}} Hz .}}

* As another example from [[modulation]] theory, a combination of {{nobr|&thinsp;{{gaps|3|425}} Hz&thinsp;}} and {{nobr|&thinsp;{{gaps|3|426}} Hz&thinsp;}} would beat once per second, since {{nobr| &thinsp;{{math| {{big|'''&#x7C;'''}} {{gaps|3|425}} }}Hz{{math| − {{gaps|3|426}} }}Hz{{math| {{big|'''&#x7C;'''}} &thinsp;{{=}}&thinsp; 1}} Hz .}}

The difference between consonance and dissonance is not clearly defined, but the higher the beat frequency, the more likely the interval is dissonant. [[Hermann von Helmholtz|Helmholtz]] proposed that maximum dissonance would arise between two pure tones when the beat rate is roughly 35&nbsp;Hz.<ref>{{cite web |title=Roughness |series=Music&nbsp;829B |type=course notes |website=music-cog.ohio-state.edu |publisher=[[Ohio State University]] |url=http://www.music-cog.ohio-state.edu/Music829B/roughness.html }}</ref>

==Scales==

{{Main|Musical scale}}

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

{{Main|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).<!-- Though many musicians know that the diatonic scale is Tone Tone Semi-Tone Tone Tone Tone Semi-Tone. Present the relation-ship of tones and semi-tones... we should add this here along with our sources for the preceding section (user:CyclePat) --> 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.

{| class="wikitable"
|-
! 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 that do not adhere to just intonation, and instead have their intervals adjusted to meet other needs are called [[Musical temperament|''temperaments'']], of which [[equal temperament]] is the most used. Temperaments, though they obscure the acoustical purity of just intervals, often have desirable properties, such as a closed [[circle of fifths]].

==See also==

{{Portal|Music}}

*[[Acoustic resonance]]
*[[Cymatics]]
*[[Mathematics of musical scales]]
*[[String resonance]]
*[[Vibrating string]]
*[[3rd bridge]] (harmonic resonance based on equal string divisions)
*[[Basic physics of the violin]]

== References ==
<references />

==External links==
*[http://www.phys.unsw.edu.au/music/ Music acoustics - sound files, animations and illustrations - University of New South Wales]
*[http://www.phys.cwru.edu/ccpi/ Acoustics collection - descriptions, photos, and video clips of the apparatus for research in musical acoustics by Prof.] [[Dayton Miller]]
*[https://web.archive.org/web/20010613120620/http://www.public.coe.edu/~jcotting/tcmu/ The Technical Committee on Musical Acoustics (TCMU) of the Acoustical Society of America (ASA)]
*[http://ccrma.stanford.edu/marl/ The Musical Acoustics Research Library (MARL)]
*[http://www2.ph.ed.ac.uk/acoustics/ Acoustics Group/Acoustics and Music Technology courses - University of Edinburgh]
*[http://acoustics.open.ac.uk Acoustics Research Group - Open University]
*[http://www.speech.kth.se/music/music_about.html The music acoustics group at Speech, Music and Hearing KTH]
*[http://www.johnsankey.ca/energy.html The physics of harpsichord sound]
*[http://donskiff.com/quest_2.htm Visual music]
*[http://SavartJournal.org/ Savart Journal - The open access online journal of science and technology of stringed musical instruments]
*[http://www.animations.physics.unsw.edu.au/waves-sound/interference/ Interference and Consonance] from [http://www.animations.physics.unsw.edu.au/ Physclips]
*[http://www.cursodeacusticamusical.blogspot.com// Curso de Acústica Musical] (Spanish)

{{Acoustics}}

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[[Category:Musical terminology]]