Musical acoustics 1379269 204075571 2008-04-07T21:23:00Z Kozuch 1339567 clean up using [[Project:AutoWikiBrowser|AWB]] '''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 [[Interpersonal communication|speech]] and [[singing]]), computer analysis of [[melody]]. == Methods and fields of study == *[[Range (music)|Frequency Range of Music]] *[[Frequency analysis]] *Computer [[Musical analysis|analysis]] of musical structure *[[Synthesis#Synthesis in electronics and acoustics|Synthesis]] of musical sounds *[[Music cognition]], based on physics (also known as [[psychoacoustics]]) == 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 [[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 [[note]] consists of several related sine waves (which mathematically add to each other) called the [[fundamental]] and the [[harmonic]]s, [[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 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 "[[music]]al" is dominated by [[periodicity|periodic]] or regular vibrations rather than non-periodic ones (called a [[definite pitch]]), and we refer to the transmission mechanism as 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 fork]]s or [[whistling]]. The rate at which the air pressure varies governs is the [[frequency]] of the tone, which is measured in oscillations per second, called [[hertz]]. Frequency is a primary determinate of the perceived [[Pitch (music)|pitch]]. Frequency can change with Altitude due to changes in air pressure. This is called the Adiabatic [[Lapse Rate]] == Frequency Range of Music == {{Vocal and instrumental pitch ranges}} [[Image:Spectrogram of violin.png|thumb|300px|A [[spectrogram]] of [[media:Violin for spectrogram.ogg|violin playing]]. The bright lines along the bottom are the fundamentals of each note, and the other bright lines are (nearly) harmonic overtones; collectively, they are [[frequency spectrum|spectra]].]] == 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 [[partial]]s. Overtones which 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:Symmetricandasymmetricwaveforms.png|frame|A half-wave symmetric and asymmetric waveform. The red contains only the fundamental and odd harmonics, the green contains the fundamental, odd, and even harmonics.]] [[Image:Perfect fifth graphs.png|frame|200 and 300 Hz waves and their sum, showing the periods of each.]] [[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.]] 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. The opposite is also true. 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|Harmony}} If two notes are simultaneously played, with frequency [[ratio]]s 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 [[consonance|consonant]]. For instance, a note vibrating at 200&nbsp;Hz and a note vibrating at 300&nbsp;Hz (a [[perfect fifth]], or 3/2 ratio, above 200&nbsp;Hz) will add together to make a wave that repeats at 100&nbsp;Hz: every 1/100 of a second, the 300&nbsp;Hz wave will repeat thrice and the 200&nbsp;Hz wave will repeat twice. Note that the total wave repeats at 100&nbsp;Hz, but there is not actually a 100&nbsp;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&nbsp;Hz will have harmonics at: :(200,) 400, 600, 800, 1000, 1200, … A note with fundamental frequency of 300&nbsp;Hz will have harmonics at: :(300,) 600, 900, 1200, 1500, … The two notes have the harmonics 600 and 1200 in common, 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 [[beat (acoustics)|beating]], and is considered to be unpleasant, or [[Consonance and dissonance|dissonant]]. The frequency of beating is calculated as the difference between the frequencies of the two notes. For the example above, |200&nbsp;Hz - 300&nbsp;Hz| = 100&nbsp;Hz. As another example, a combination of 3425&nbsp;Hz and 3426&nbsp;Hz would beat once per second (|3425&nbsp;Hz - 3426&nbsp;Hz| = 1&nbsp;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. [[Hermann von Helmholtz|Helmholtz]] proposed that maximum dissonance would arise between two pure tones when the beat rate is roughly 35&nbsp;Hz. [http://www.music-cog.ohio-state.edu/Music829B/roughness.html] == 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 which do not adhere to just intonation, and instead have their intervals adjusted to meet other needs are known as [[Musical temperament|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]]. == Further reading == *[[Carl Seashore|Seashore, Carl Emil]], "The Psychology of Music", McGraw-Hill, 1938. ISBN 0486218511 ([[Dover Publications]] reprint) == See also == *[[Sound]] *[[Acoustics]] *[[Harmony]] *[[Mathematics of musical scales]] *[[Vibrating string]] *[[Open tube]] *[[Closed tube]] *[[String resonance (music)]] == External links == *[http://www.physics.umd.edu/deptinfo/facilities/lecdem/misc/phys102/index.htm Physics of music course - links and illustrations - University of Maryland] *[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]] *[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://www.ph.ed.ac.uk/acoustics/MSc/ Acoustics and Music Technology courses - University of Edinburgh] *[http://www.speech.kth.se/music/music_about.html Speech, Music and Hearing - About the music acoustics group] *[http://www.sankey.ws/energy.html The physics of harpsichord sound] *[http://bach.tuning.googlepages.com/ Equal beating tuning] *[http://www.fortunecity.com/tinpan/lennon/362/english/acoustics.htm Music & Acoustics] *[http://www.humanspeakers.com/whatis/sound.htm Sound & Hearing] *[http://donskiff.com/quest_2.htm Visual music] *[http://www.acoustics.salford.ac.uk/schools/ Acoustics, audio and video group - University of Salford] *[http://rr.smitech.org/ The research repository of stringed musical instrument technology - An open access of research articles] [[Category:Sound]] [[Category:Acoustics]] [[Category:Music]] [[Category:Mathematics of music]] [[ca:Acústica musical]] [[el:Μουσική ακουστική]] [[es:Acústica musical]] [[fr:Acoustique musicale]] [[sv:Musikakustik]]