Editing Dynamic range (section)

== Audio ==
[[Audio engineer]]s use ''dynamic range'' to describe the ratio of the amplitude of the loudest possible [[Audio distortion|undistorted]] signal to the [[noise floor]], say of a [[microphone]] or [[loudspeaker]].<ref>Ballou Glen M., ''Handbook for Sound Engineers'', 3rd edition, Focal Press 2002, pp. 1107-1108</ref> Dynamic range is therefore the [[signal-to-noise ratio]] (SNR) for the case where the signal is the loudest possible for the system. For example, if the ceiling of a device is 5&nbsp;V (rms) and the noise floor is 10&nbsp;μV (rms) then the dynamic range is 500000:1, or 114&nbsp;dB:

<math display=block>20 \times \log_{10} \left(\frac{\rm 5\,V}{10 \, \mu \mathrm{V}}\right) = 20 \times \log_{10}(500000) = 20 \times 5.7 = 114 \,\mathrm{dB}</math>

In digital audio theory the dynamic range is limited by [[quantization error]]. The maximum achievable dynamic range for a digital audio system with ''Q''-bit uniform quantization is calculated as the ratio of the largest sine-wave rms to rms noise is:<ref name=seeber/>

<math display=block> \mathrm{DR_{ADC}} = 20 \times \log_{10} \left(\frac{2^Q}{1}\right) = \left ( 6.02 \cdot Q \right )\ \mathrm{dB} \,\!</math>

However, the usable dynamic range may be greater, as a properly [[dither]]ed recording device can record signals well below the noise floor.

The 16-bit [[compact disc]] has a theoretical undithered dynamic range of about 96&nbsp;dB;<ref name="Fries2005"/>{{efn|The 96&nbsp;dB figure is for a [[Triangle wave|triangle]] or [[sine wave]]. Dynamic range is 98&nbsp;dB for [[sine wave]]<ref name=seeber/> (see [[Quantization (signal processing)#Quantization noise model|Quantization noise model]]).}} however, the ''perceived'' dynamic range of 16-bit audio can be 120&nbsp;dB or more with [[Noise shaping|noise-shaped]] [[dither]], taking advantage of [[Equal-loudness contour|the frequency response of the human ear]].<ref>{{cite web |url=https://www.xiph.org/~xiphmont/demo/neil-young.html |title=24/192 Music Downloads ...and why they make no sense |last=Montgomery |first=Chris |author-link=Chris Montgomery |date=March 25, 2012 |website=xiph.org |access-date=26 May 2013 |quote=With use of shaped dither, which moves quantization noise energy into frequencies where it's harder to hear, the effective dynamic range of 16 bit audio reaches 120dB in practice, more than fifteen times deeper than the 96dB claim. 120dB is greater than the difference between a mosquito somewhere in the same room and a jackhammer a foot away.... or the difference between a deserted 'soundproof' room and a sound loud enough to cause hearing damage in seconds. 16 bits is enough to store all we can hear, and will be enough forever. |url-status=dead |archive-url=https://web.archive.org/web/20130707161555/http://xiph.org/~xiphmont/demo/neil-young.html |archive-date=7 July 2013 }}</ref><ref>{{Cite web
 |url         = https://www.meridian-audio.com/meridian-uploads/ara/coding2.pdf
 |title       = Coding High Quality Digital Audio
 |last        = Stuart
 |first       = J. Robert
 |date        = 1997
 |publisher   = Meridian Audio Ltd
 |access-date = 2016-02-25
 |quote       = One of the great discoveries in PCM was that, by adding a small random noise (that we call dither) the truncation effect can disappear. Even more important was the realisation that there is a ''right'' sort of random noise to add, and that when the right dither is used, the resolution of the digital system becomes ''infinite''.
 |url-status     = dead
 |archive-url  = https://web.archive.org/web/20160407163817/https://www.meridian-audio.com/meridian-uploads/ara/coding2.pdf
 |archive-date = 2016-04-07
}}</ref>

Digital audio with undithered 20-bit quantization is theoretically capable of 120&nbsp;dB dynamic range, while 24-bit digital audio affords 144&nbsp;dB dynamic range.<ref name=HuberRunstein513/> Most [[Digital audio workstation]]s process audio with 32-bit [[floating-point]] representation which affords even higher dynamic range and so loss of dynamic range is no longer a concern in terms of [[digital audio processing]]. Dynamic range limitations typically result from improper [[gain staging]], recording technique including [[ambient noise]] and intentional application of [[dynamic range compression]].

Dynamic range in analog audio is the difference between low-level thermal noise in the electronic circuitry and high-level signal saturation resulting in increased distortion and, if pushed higher, [[Clipping (audio)|clipping]].<ref>Huber, Runstein 2009, [https://books.google.com/books?id=W9U7A-rSXtEC&pg=PA416 pp. 416, 487] {{webarchive|url=https://web.archive.org/web/20171120223132/https://books.google.com/books?id=W9U7A-rSXtEC&pg=PA416 |date=2017-11-20 }}</ref> Multiple noise processes determine the noise floor of a system. Noise can be picked up from microphone self-noise, preamp noise, wiring and interconnection noise, media noise, etc.

Early 78 rpm phonograph discs had a dynamic range of up to 40&nbsp;dB,<ref>[http://www.aes.org/e-lib/browse.cfm?elib=308 Audio Engineering Society. E-Library. Jerry B. Minter. April 1956. ''Recent Developments in Precision Master Recording Lathes''] {{webarchive|url=https://web.archive.org/web/20081211094752/http://www.aes.org/e-lib/browse.cfm?elib=308 |date=2008-12-11 }}</ref> soon reduced to 30&nbsp;dB and worse due to wear from repeated play. Vinyl microgroove phonograph records typically yield 55-65&nbsp;dB, though the first play of the higher-fidelity outer rings can achieve a dynamic range of 70&nbsp;dB.<ref>{{cite book |title=A Century of Recorded Music: Listening to Musical History |last=Day |first=Timothy |year=2002 |publisher=Yale University Press |isbn=978-0-300-09401-5 |page=23 |url=https://books.google.com/books?id=EYdtlP6hvPoC |url-status=live |archive-url=https://web.archive.org/web/20171120223132/https://books.google.com/books?id=EYdtlP6hvPoC |archive-date=2017-11-20 }}</ref>

German magnetic tape in 1941 was reported to have had a dynamic range of 60&nbsp;dB,<ref name="First100Years"/> though modern-day restoration experts of such tapes note 45-50&nbsp;dB as the observed dynamic range.<ref>{{citation |url=http://www.aes.org/journal/suppmat/hess_2001_7.pdf |publisher=Audio Engineering Society |author=Richard L. Hess |date=July–August 2001 |title=The Jack Mullin/Bill Palmer tape restoration project |archive-url=https://web.archive.org/web/20081201123950/http://www.aes.org./journal/suppmat/hess_2001_7.pdf |archive-date=2008-12-01}}</ref> [[Ampex]] tape recorders in the 1950s achieved 60&nbsp;dB in practical usage,<ref name="First100Years"/> In the 1960s, improvements in tape formulation processes resulted in 7&nbsp;dB greater range,<ref name=Eargle/>{{rp|158}} and Ray Dolby developed the [[Dolby noise reduction system#Dolby A|Dolby A-Type noise reduction system]] that increased low- and mid-frequency dynamic range on magnetic tape by 10&nbsp;dB, and high-frequency by 15&nbsp;dB, using [[companding]] (compression and expansion) of four frequency bands.<ref name=Eargle/>{{rp|169}} The peak of professional analog magnetic recording tape technology reached 90&nbsp;dB dynamic range in the midband frequencies at 3% distortion, or about 80&nbsp;dB in practical broadband applications.<ref name=Eargle/>{{rp|158}} The [[Dolby noise reduction system#Dolby SR|Dolby SR noise reduction system]] gave a 20&nbsp;dB further increased range resulting in 110&nbsp;dB in the midband frequencies at 3% distortion.<ref name=Eargle/>{{rp|172}}

[[Compact Cassette]] tape performance ranges from 50 to 56&nbsp;dB depending on tape formulation, with [[type IV tape]] tapes giving the greatest dynamic range, and systems such as [[XDR (audio)|XDR]], [[dbx (noise reduction)|dbx]] and [[Dolby noise reduction system]] increasing it further. Specialized bias and record head improvements by Nakamichi and Tandberg combined with Dolby C noise reduction yielded 72&nbsp;dB dynamic range for the cassette.{{citation needed|date=September 2018}}

A [[dynamic microphone]] is able to withstand high sound intensity and can have a dynamic range of up to 140&nbsp;dB. Condenser microphones are also rugged but their dynamic range may be limited by the overloading of their associated electronic circuitry.<ref>{{cite book |author1=Huber |author2=Runstein |date=2010 |url=https://books.google.com/books?id=W9U7A-rSXtEC&pg=PA127 |page=127 |archive-url=https://web.archive.org/web/20171120223132/https://books.google.com/books?id=W9U7A-rSXtEC&pg=PA127 |archive-date=2017-11-20 |title=Modern Recording Techniques |url-status=live |publisher=Taylor & Francis|isbn=9780240810690 }}</ref> Practical considerations of acceptable distortion levels in microphones combined with typical practices in a recording studio result in a useful dynamic range of 125&nbsp;dB.<ref name=Eargle/>{{rp|75}}

In 1981, researchers at Ampex determined that a dynamic range of 118&nbsp;dB on a dithered digital audio stream was necessary for subjective noise-free playback of music in quiet listening environments.<ref>[http://www.aes.org/e-lib/browse.cfm?elib=11981 Audio Engineering Society. E-Library. Louis D. Fielder. May 1981. ''Dynamic Range Requirement for Subjective Noise Free Reproduction of Music''] {{webarchive|url=https://web.archive.org/web/20081211094725/http://www.aes.org/e-lib/browse.cfm?elib=11981 |date=2008-12-11 }}</ref>

Since the early 1990s, it has been recommended by several authorities, including the [[Audio Engineering Society]], that measurements of dynamic range be made with an audio signal present, which is then filtered out in the noise floor measurement used in determining dynamic range.<ref>AES-6id-2000</ref> This avoids questionable measurements based on the use of blank media, or muting circuits.

The term ''dynamic range'' may be confusing in audio production because it has two conflicting definitions, particularly in the understanding of the [[loudness war]] phenomenon.<ref name="SOS_Dynamic_Range"/><ref name="DerutyTardieuAES"/> ''Dynamic range'' may refer to micro-dynamics,<ref name="Katz"/><ref>{{cite web |author=Ian Shepherd |url=http://productionadvice.co.uk/loudness-war-dynamic-range/ |title=Why the Loudness War hasn't reduced 'Loudness Range' |access-date=2014-02-06 |url-status=dead |archive-url=https://web.archive.org/web/20140209113438/http://productionadvice.co.uk/loudness-war-dynamic-range/ |archive-date=2014-02-09 |date=2011-08-18 }}</ref><ref>{{cite magazine |author=Jason Victor Serinus |url=http://www.stereophile.com/content/winning-loudness-wars |title=Winning the Loudness Wars |magazine=Stereophile |access-date=2014-02-06 |url-status=dead |archive-url=https://web.archive.org/web/20140209155445/http://www.stereophile.com/content/winning-loudness-wars |archive-date=2014-02-09 }}</ref> related to [[crest factor]],<ref>{{cite web |url=http://www.sfxmachine.com/docs/loudnesswar/loudness_war.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://www.sfxmachine.com/docs/loudnesswar/loudness_war.pdf |archive-date=2022-10-09 |url-status=live |title=The Loudness War: Background, Speculation and Recommendations |author=Earl Vickers |publisher=[[Audio Engineering Society]] |work=AES 2010: Paper Sessions: Loudness and Dynamics |location=San Francisco |date=November 4, 2010 |access-date=July 14, 2011}}</ref><ref>{{Cite web |title=Dynamic Range Meter |url=http://www.pleasurizemusic.com/free-downloads |url-status=dead |archive-url=https://web.archive.org/web/20141027152639/http://www.pleasurizemusic.com/free-downloads |archive-date=2014-10-27 |access-date=2018-11-27 }}</ref> whereas the [[European Broadcasting Union]], in EBU3342 Loudness Range, defines ''dynamic range'' as the difference between the quietest and loudest volume, a matter of macro-dynamics.<ref name="SOS_Dynamic_Range"/><ref name="DerutyTardieuAES"/><ref name="EBU3342"/><ref>{{cite journal|date=26 July 2012|title=Measuring the Evolution of Contemporary Western Popular Music|journal=Scientific Reports|volume=2|page=521|arxiv=1205.5651|pmid=22837813|pmc=3405292|bibcode=2012NatSR...2E.521S|doi=10.1038/srep00521|last1=Serrà|first1=J|last2=Corral|first2=A|last3=Boguñá|first3=M|last4=Haro|first4=M|last5=Arcos|first5=JL}}</ref><ref>{{cite journal|doi=10.17743/jaes.2014.0003|title=Perceptual Effects of Dynamic Range Compression in Popular Music Recordings|journal=Journal of the Audio Engineering Society|volume=62|pages=37–41|year=2014|last1=Hjortkjær|first1=Jens|last2=Walther-Hansen|first2=Mads}}</ref><ref>{{cite web |author=Esben Skovenborg |publisher=AES 132nd Convention |date=April 2012 |url=http://www.aes.org/e-lib/browse.cfm?elib=16254/ |title=Loudness Range (LRA) – Design and Evaluation |access-date=2014-10-25 |url-access=subscription  |url-status=live |archive-url=https://web.archive.org/web/20141025174340/http://www.aes.org/e-lib/browse.cfm?elib=16254%2F |archive-date=2014-10-25 }}</ref>