Editing Scientific pitch notation (section)

==Use==
Scientific pitch notation is often used to specify the range of an instrument. It provides an unambiguous means of identifying a note in terms of textual notation rather than frequency, while at the same time avoiding the [[transposition convention]]s that are used in writing the music for instruments such as the [[clarinet]] and [[guitar]]. It is also easily translated into staff notation, as needed. In describing musical pitches, nominally [[enharmonic]] spellings can give rise to anomalies where, for example in [[Pythagorean intonation]] C{{music|b}}<sub>4</sub> is a lower frequency than B{{sub|3}}; but such paradoxes usually do not arise in a scientific context.

Scientific pitch notation avoids possible confusion between various derivatives of Helmholtz notation which use similar symbols to refer to different notes. For example, "C" in Helmholtz's original notation<ref>{{cite book |title=Die Lehre von den Tonempfindungen als physiologische Grundlage für die Theorie der Musik |trans-title=On the Sensations of Tone as a Physiological Basis for the Theory of Music |author-link=Hermann von Helmholtz |first=Hermann |last=von Helmholtz |orig-year=1870 |year=1912 |publisher=Whitefish, MT. Kellinger |edition=4 |isbn=978-1-4191-7893-1 |lang=en |translator=[[Alexander J. Ellis|Ellis, A.J.]] |via=[[Internet Archive]] |url=https://archive.org/stream/onsensationston01helmgoog#page/n5/mode/2up}}</ref> refers to the C two octaves below middle C, whereas "C" in [[ABC Notation]] refers to middle C itself. With scientific pitch notation, middle C is ''always'' C{{sub|4}}, and C{{sub|4}} is never any note but middle C. This notation system also avoids the "fussiness" of having to visually distinguish between four and five primes, as well as the typographic issues involved in producing acceptable subscripts or substitutes for them. C{{sub|7}} is much easier to quickly distinguish visually from C{{sub|8}}, than is, for example, {{nowrap|c′′′′}} from {{nowrap|c′′′′′}}, and the use of simple integers (e.g. C7 and C8) makes subscripts unnecessary altogether.

Although pitch notation is intended to describe sounds audibly perceptible as pitches, it can also be used to specify the frequency of non-pitch phenomena. Notes below E{{sub|0}} or higher than E{{music|b}}<sub>10</sub> are outside most humans' [[hearing range]], although notes slightly outside the hearing range on the low end may still be indirectly perceptible as pitches due to their overtones falling within the hearing range. For an example of truly inaudible frequencies, when the [[Chandra X-ray Observatory]] observed the waves of pressure fronts propagating away from a black hole, their one oscillation every 10&nbsp;million years was described by [[NASA]] as corresponding to the B{{music|b}} fifty-seven octaves below middle C (B{{music|b}}<sub>−53</sub>) or 3.235&nbsp;[[femto-|fHz]]).<ref name="nasa">{{cite press release |publisher=NASA |url=https://science.nasa.gov/science-news/science-at-nasa/2003/09sep_blackholesounds/ |title=Black hole sound waves |quote=Sound waves 57 octaves lower than middle-C are rumbling away from a supermassive black hole in the Perseus cluster.}}</ref>


The notation is sometimes used in the context of [[meantone temperament]], and does not always assume [[equal temperament]] nor the standard concert A<sub>4</sub> of 440&nbsp;[[Hertz|Hz]]; this is particularly the case in connection with earlier music.

The standard proposed to the Acoustical Society of America<ref name="JASA"/> explicitly states a logarithmic scale for frequency, which excludes meantone temperament, and the base frequency it uses gives A<sub>4</sub> a frequency of exactly 440&nbsp;Hz. However, when dealing with earlier music that did not use equal temperament, it is understandably easier to simply refer to notes by their closest modern equivalent, as opposed to specifying the difference using cents every time.{{efn|The conventions of musical pitch notation require the use of sharps and flats on the [[circle of fifths]] closest to the [[key (music)|key]] currently in use, and forbid substitution of notes with the same frequency in equal temperament, such as A{{music|#}} and B{{music|b}}. These rules have the effect of (usually) producing more nearly [[Just intonation|consonant pitches]] when using [[meantone temperament|meantone]] systems, and other non-[[equal temperament]]s. In almost all [[meantone temperament]]s, the so-called [[enharmonic]] notes, such as A{{music|#}} and B{{music|b}}, are a different pitch, with A{{music|#}} at a ''lower'' frequency than the enharmonic B{{music|b}}. With the single exception of [[equal temperament]] (which fits in among meantone systems as a special case) enharmonic notes always have slightly different frequencies.}}