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==Physics and perception==
Apparent source width is the aurally perceived extent of a sound source. Sometimes, it is defined as the impression that a source sounds larger than its visible size.<ref name="blau">{{cite journal |last1=Blau |first1=Matthias |title=Correlation of apparent source width with objective measures in synthetic sound fields |journal=Acta Acustica United with Acustica |date=2004 |volume=90 |issue=4 |page=720 |url=http://www.ingentaconnect.com/content/dav/aaua/2004/00000090/00000004/art00015# |accessdate=31 May 2018}}</ref> The impression results from several auditory cues, which are affected by sound radiation characteristics of the source itself and by characteristics of the room. Since the term ''apparent source width'' has been used a lot in the field of subjective room acoustics to characterize how the room affects the perception of source size, the term ''perceived source extent'' has been introduced to highlight that the perception results from both the sound source and the room.<ref name="psfs">{{cite book |last1=Ziemer |first1=Tim |title=Psychoacoustic Music Sound Field Synthesis |volume=7 |date=2020 |publisher=Springer |___location=Cham |isbn=978-3-030-23033-3 |doi=10.1007/978-3-030-23033-3 |series=Current Research in Systematic Musicology |s2cid=201136171 }}</ref>
The [[auditory system]] has mechanisms that separate the processing of late [[reverberation]] from the processing of direct sound and early [[Reflection (physics)|reflections]] referred to as [[precedence effect]]. While the late reverberation contributes to the [[perception]] of '''{{vanchor|listener envelopment}}''' and reverberance, the direct sound and the early reflections mostly affect [[Sound localization|source localization]], intimacy and the apparent source width.<ref name="beranek">{{cite book|last1=Beranek|first1=Leo Leroy|s2cid=191844675|title=Concert Halls and Opera Houses: Music, Acoustics, and Architecture|date=2004|publisher=Springer|___location=New York|doi=10.1007/978-0-387-21636-2|isbn=978-1-4419-3038-5|edition=Second}}</ref> The balance of early and late arriving sound affects the perceived clarity, warmth and brilliance.
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The auditory system does not process all early sounds together to derive a source ___location. In complicated acoustical scenes, the auditory system integrates those parts of sound that share temporal, spectral, and spatial properties into one so-called auditory stream. An auditory stream is the counterpart to a visible object in [[Gestalt psychology]]. Several auditory streams are segregated from one another. The process of integration and segregation is referred to as [[auditory scene analysis]] and is believed to be the original function of the ear.<ref name="braun">{{cite book |last1=Braun |first1=Christopher B. |last2=Grande |first2=Terry |editor1-last=Webb |editor1-first=Jacqueline F. |editor2-last=Fay |editor2-first=Richard R. |editor3-last=Popper |editor3-first=Arthur N. |title=Fish Bioacoustics |date=2008 |doi=10.1007/978-0-387-73029-5_4 |publisher=Springer |___location=New York |isbn=978-0-387-73029-5 |page=105 |chapter=Evolution of peripheral mechanisms for the enhancement of sound reception}}</ref> Each auditory stream can have its own apparent source width. One auditory stream may contain the direct sound and early reflections of a single musical instrument or a [[musical ensemble]].
A high strength of low frequencies and incoherence of the left and the right ear of one auditory stream, especially of its direct sound and early reflections, increase the apparent source width.<ref name=blau/><ref name=ziemer/><ref name=beranek/> Even in absence of room acoustical reflections the pure direct sound of musical instruments already affects the perceived source extent.<ref name="ziemer">{{cite book|last1=Ziemer|first1=Tim|editor1-last=Schneider|editor1-first=Albrecht|title=Studies in Musical Acoustics and Psychoacoustics|volume=4|doi=10.1007/978-3-319-47292-8_10|date=2017|publisher=Springer|___location=Cham|isbn=978-3-319-47292-8|pages=299–340|chapter=Source Width in Music Production. Methods in Stereo, Ambisonics, and Wave Field Synthesis|series=Current Research in Systematic Musicology}}</ref> Unlike hypothetical [[Point source#Sound|monopole source]] musical instruments radiate their sound not evenly in all directions. Rather the overall [[Amplitude|volume]] and the [[frequency spectrum]] differ in each direction. This is referred to as sound radiation characteristics or radiation patterns.<ref name=ziemer/><ref name="ziemerdiss">{{cite thesis|type=PhD|doi=10.13140/RG.2.1.1997.9769|last1=Ziemer|first1=Tim|title=Implementation of the Radiation Characteristics of Musical Instruments in Wave Field Synthesis Applications|date=2015|publisher=Univ. Diss.|___location=Hamburg|url=https://ediss.sub.uni-hamburg.de/volltexte/2016/7939/|accessdate=25 May 2018}}</ref><ref name="bader">{{cite journal|last1=Bader|first1=Rolf|title=Radiation characteristics of multiple and single sound hole vihuelas and a classical guitar|journal=The Journal of the Acoustical Society of America|date=2012|volume=131|issue=1|pages=819–828|doi=10.1121/1.3651096|pmid=22280704|bibcode=2012ASAJ..131..819B}}</ref> These may create incoherent signals at the ears and, consequently, the impression of a wide source. The sound radiation characteristics of musical instruments are typically given as [[radiation pattern]] in a two- to three-dimensional [[polar coordinate system]].<ref name="meyer">{{cite book|last1=Meyer|first1=Jürgen|doi=10.1007/978-0-387-09517-2|title=Acoustics and the Performance of Music. Manual for Acousticians, Audio Engineers, Musicians, Architects and Musical Instrument Makers|date=2009|publisher=Springer|___location=Bergkirchen|isbn=978-0-387-09516-5|s2cid=60810170 |edition=Fifth |url=http://cds.cern.ch/record/1339014}}</ref><ref name="patynen">{{cite journal|last1=Pätynen|first1=Jukka|last2=Lokki|first2=Tapio|s2cid=119661613|title=Directivities of Symphony Orchestra Instruments|journal=Acta Acustica United with Acustica|date=2010|volume=96|issue=1|pages=138–167|doi=10.3813/aaa.918265}}</ref><ref name="ziemerj">{{cite journal|last1=Ziemer|first1=Tim|last2=Bader|first2=Rolf|title=Psychoacoustic Sound Field Synthesis for Musical Instrument Radiation Characteristics|journal=Journal of the Audio Engineering Society|date=2017|volume=65|issue=6|pages=482–496|doi=10.17743/jaes.2017.0014}}</ref><ref name="zotter">{{cite thesis|type=PhD|institution=University of Music and Performing Arts Graz|last1=Zotter|first1=Franz|title=Analysis and Synthesis of Sound-Radiation with Spherical Arrays|date=2009|___location=Graz|url=https://iem.kug.ac.at/en/projects/workspace/projekte-bis-2008/dsp/analysis-and-synthesis-of-sound-radiation-with-spherical-arrays.html|accessdate=25 May 2018}}</ref>
==Subjective room acoustics==
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