scientific pitch notation
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Scientific pitch notation (SPN), also known as American standard pitch notation (ASPN) and international pitch notation (IPN), is a method of specifying musical pitch by combining a musical
note Note, notes, or NOTE may refer to: Music and entertainment * Musical note, a pitched sound (or a symbol for a sound) in music * ''Notes'' (album), a 1987 album by Paul Bley and Paul Motian * ''Notes'', a common (yet unofficial) shortened version ...
name (with accidental if needed) and a number identifying the pitch's
octave In music, an octave ( la, octavus: eighth) or perfect octave (sometimes called the diapason) is the interval between one musical pitch and another with double its frequency. The octave relationship is a natural phenomenon that has been refer ...
. Although scientific pitch notation was originally designed as a companion to
scientific pitch Scientific pitch, also known as philosophical pitch, Sauveur pitch or Verdi tuning, is an absolute concert pitch standard which is based on middle C ( C4) being set to 256 Hz rather than 261.62 Hz, making it approximately 37.6 cents ...
(see below), the two are not synonymous. Scientific pitch is a pitch standard—a system that defines the specific
frequencies Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...
of particular pitches (see below). Scientific pitch notation concerns only how pitch names are notated, that is, how they are designated in printed and written text, and does not inherently specify actual frequencies. Thus, the use of scientific pitch notation to distinguish octaves does not depend on the pitch standard used.


Nomenclature

The notation makes use of the traditional tone names (A to G) which are followed by numbers showing which
octave In music, an octave ( la, octavus: eighth) or perfect octave (sometimes called the diapason) is the interval between one musical pitch and another with double its frequency. The octave relationship is a natural phenomenon that has been refer ...
they are part of. For standard
A440 A440 or A-440 may refer to: * A440 (pitch standard) * A440 highway (Australia), a road in Victoria, Australia * Quebec Autoroute 440 (Laval) * Quebec Autoroute 440 (Quebec City) See also * Apollo 440 Apollo 440 (also known as Apollo Four Fo ...
pitch
equal temperament An equal temperament is a musical temperament or tuning system, which approximates just intervals by dividing an octave (or other interval) into equal steps. This means the ratio of the frequencies of any adjacent pair of notes is the same, wh ...
, the system begins at a frequency of 16.35160 Hz, which is assigned the value C0. The octave 0 of the scientific pitch notation is traditionally called the sub-contra octave, and the tone marked C0 in SPN is written as '',,C'' or ''C,,'' or ''CCC'' in traditional systems, such as Helmholtz notation. Octave 0 of SPN marks the low end of what humans can actually perceive, with the average person being able to hear frequencies no lower than 20 Hz as pitches. The octave number increases by 1 upon an ascension from B to C. Thus, ''A0'' refers to the first A ''above'' C0 and
middle C C or Do is the first note and semitone of the C major scale, the third note of the A minor scale (the relative minor of C major), and the fourth note (G, A, B, C) of the Guidonian hand, commonly pitched around 261.63  Hz. The actual frequen ...
(the one-line octave's C or simply ) is denoted as ''C4'' in SPN. For example, C4 is one note above B3, and A5 is one note above G5. The octave number is tied to the alphabetic character used to describe the pitch, with the division between note letters ‘B’ and ‘C’, thus: :* "B3" and all of its possible variants (B, B, B, B, B) would properly be designated as being in octave "3". :* "C4" and all of its possible variants (C, C, C, C, C) would properly be designated as being in octave "4". :* In equal temperament "C" is same frequency as "B".


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 A transposing instrument is a musical instrument for which music notation is not written at concert pitch (concert pitch is the pitch on a non-transposing instrument such as the piano). For example, playing a written middle C on a transposing ...
s that are used in writing the music for instruments such as the
clarinet The clarinet is a musical instrument in the woodwind family. The instrument has a nearly cylindrical bore and a flared bell, and uses a single reed to produce sound. Clarinets comprise a family of instruments of differing sizes and pitches ...
and
guitar The guitar is a fretted musical instrument that typically has six strings. It is usually held flat against the player's body and played by strumming or plucking the strings with the dominant hand, while simultaneously pressing selected stri ...
. It is also easily translated into staff notation, as needed. In describing musical pitches, nominally
enharmonic In modern musical notation and tuning, an enharmonic equivalent is a note, interval, or key signature that is equivalent to some other note, interval, or key signature but "spelled", or named differently. The enharmonic spelling of a written n ...
spellings can give rise to anomalies where, for example in
meantone temperament Meantone temperament is a musical temperament, that is a tuning system, obtained by narrowing the fifths so that their ratio is slightly less than 3:2 (making them ''narrower'' than a perfect fifth), in order to push the thirds closer to pure. M ...
s C is a lower frequency than B; 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 refers to the C below middle C, whereas "C" in ABC Notation refers to middle C itself. With scientific pitch notation, middle C is ''always'' C, and C 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 is much easier to quickly distinguish visually from C, than is, for example, from , 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 or higher than E are outside most humans'
hearing range Hearing range describes the range of frequencies that can be heard by humans or other animals, though it can also refer to the range of levels. The human range is commonly given as 20 to 20,000 Hz, although there is considerable variati ...
, 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 The Chandra X-ray Observatory (CXO), previously known as the Advanced X-ray Astrophysics Facility (AXAF), is a Flagship-class space telescope launched aboard the during STS-93 by NASA on July 23, 1999. Chandra is sensitive to X-ray sources 1 ...
observed the waves of pressure fronts propagating away from a black hole, their one oscillation every 10 million years was described by
NASA The National Aeronautics and Space Administration (NASA ) is an independent agency of the US federal government responsible for the civil space program, aeronautics research, and space research. NASA was established in 1958, succeeding t ...
as corresponding to the B fifty-seven octaves below middle C (B or 3.235  fHz).


Similar systems

There are pitch-octave notation conventions that appear similar to scientific pitch notation but are based on an alternative octave convention that differs from scientific pitch notation, usually by one octave. For example, middle C ("C4" in ISPN) appears in some
MIDI MIDI (; Musical Instrument Digital Interface) is a technical standard that describes a communications protocol, digital interface, and electrical connectors that connect a wide variety of electronic musical instruments, computers, and re ...
software as "C5" (MIDI note 60). This convention is probably related to a similar convention in sample-based trackers, where C5 is the basic pitch at which a sample plays (8287.12 Hz in
MOD Mod, MOD or mods may refer to: Places * Modesto City–County Airport, Stanislaus County, California, US Arts, entertainment, and media Music * Mods (band), a Norwegian rock band * M.O.D. (Method of Destruction), a band from New York City, US ...
), forcing the musician to treat samples at any other pitch as
transposing instrument A transposing instrument is a musical instrument for which music notation is not written at concert pitch (concert pitch is the pitch on a non-transposing instrument such as the piano). For example, playing a written middle C on a transposing i ...
s when using them in songs. Alternately, both
Yamaha Yamaha may refer to: * Yamaha Corporation, a Japanese company with a wide range of products and services, established in 1887. The company is the largest shareholder of Yamaha Motor Company (below). ** Yamaha Music Foundation, an organization estab ...
and the software
MaxMSP Max, also known as Max/MSP/Jitter, is a visual programming language for music and multimedia developed and maintained by San Francisco-based software company Cycling '74. Over its more than thirty-year history, it has been used by composers, pe ...
define middle C as C3.
Apple An apple is an edible fruit produced by an apple tree (''Malus domestica''). Apple fruit tree, trees are agriculture, cultivated worldwide and are the most widely grown species in the genus ''Malus''. The tree originated in Central Asia, wh ...
's GarageBand also defines middle C (261.6256 Hz) as C3. Using scientific pitch notation consistently, the MIDI NoteOn message assigns MIDI note 0 to C−1 (five octaves below C4 or Middle C; lowest note on the two largest organs of the world; about one octave below the human hearing threshold: its overtones, however, are audible), MIDI note 21 to A0 (the bottom key of an 88-key piano), MIDI note 60 to C4 (Middle C), MIDI note 69 to A4 (A440), MIDI note 108 to C8 (the top key of an 88-key piano), and MIDI note 127 to G9 (beyond the piano; one octave above the highest note on some keyboard glockenspiels; some notes above the highest-pitched organ pipes). This creates a linear pitch space in which an octave spans 12
semitone A semitone, also called a half step or a half tone, is the smallest musical interval commonly used in Western tonal music, and it is considered the most dissonant when sounded harmonically. It is defined as the interval between two adjacent no ...
s, where each semitone is the distance between adjacent keys of the piano keyboard. Distance in this space corresponds to musical pitch distance in an equal-tempered scale, 2 semitones being a whole step, and 1 semitone being a half step. An equal-tempered semitone can also be subdivided further into 100 cents. Each cent is semitone or octave. This measure of pitch allows the expression of ''
microtones Microtonal music or microtonality is the use in music of microtones—intervals smaller than a semitone, also called "microintervals". It may also be extended to include any music using intervals not found in the customary Western tuning of tw ...
'' not found on standard piano keyboards.


Meantone temperament

The notation is sometimes used in the context of
meantone temperament Meantone temperament is a musical temperament, that is a tuning system, obtained by narrowing the fifths so that their ratio is slightly less than 3:2 (making them ''narrower'' than a perfect fifth), in order to push the thirds closer to pure. M ...
, and does not always assume
equal temperament An equal temperament is a musical temperament or tuning system, which approximates just intervals by dividing an octave (or other interval) into equal steps. This means the ratio of the frequencies of any adjacent pair of notes is the same, wh ...
nor the standard concert A4 of 440  Hz; this is particularly the case in connection with earlier music. The standard proposed to the Acoustical Society of America explicitly states a logarithmic scale for frequency, which excludes meantone temperament, and the base frequency it uses gives A4 a frequency of exactly 440 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.


Table of note frequencies

The table below gives notation for pitches based on standard
piano key frequencies This is a list of the fundamental frequencies in hertz (cycles per second) of the keys of a modern 88-key standard or 108-key extended piano in twelve-tone equal temperament, with the 49th key, the fifth A (called A4), tuned to 440 Hz (refe ...
: standard concert pitch and
twelve-tone equal temperament Twelve-tone equal temperament (12-TET) is the musical system that divides the octave into 12 parts, all of which are equally tempered (equally spaced) on a logarithmic scale, with a ratio equal to the 12th root of 2 ( ≈ 1.05946). That resultin ...
. When a piano is tuned to
just intonation In music, just intonation or pure intonation is the tuning of musical intervals Interval may refer to: Mathematics and physics * Interval (mathematics), a range of numbers ** Partially ordered set#Intervals, its generalization from numbers to ...
, C4 refers to the same key on the keyboard, but a slightly different frequency. Keys which do not appear on any piano (medium gray) or only on an extended 108-key piano (light gray) are highlighted. Mathematically, given the number of semitones above middle C, the fundamental frequency in hertz is given by 440 \cdot 2^ (see
twelfth root of two The twelfth root of two or \sqrt 2/math> (or equivalently 2^) is an algebraic irrational number, approximately equal to 1.0594631. It is most important in Western music theory, where it represents the frequency ratio (musical interval) of a semi ...
). Given the MIDI NoteOn number , the frequency of the note is normally 440 \cdot 2^ Hz, using standard tuning.


Scientific pitch versus scientific pitch ''notation''

Scientific pitch Scientific pitch, also known as philosophical pitch, Sauveur pitch or Verdi tuning, is an absolute concert pitch standard which is based on middle C ( C4) being set to 256 Hz rather than 261.62 Hz, making it approximately 37.6 cents ...
(q.v.) is an absolute pitch ''standard'', first proposed in 1713 by French physicist
Joseph Sauveur Joseph Sauveur (24 March 1653 – 9 July 1716) was a French mathematician and physicist. He was a professor of mathematics and in 1696 became a member of the French Academy of Sciences. Life Joseph Sauveur was born in La Flèche, the son of a ...
. It was defined so that all Cs are integer powers of 2, with
middle C C or Do is the first note and semitone of the C major scale, the third note of the A minor scale (the relative minor of C major), and the fourth note (G, A, B, C) of the Guidonian hand, commonly pitched around 261.63  Hz. The actual frequen ...
(C4) at 256 
hertz The hertz (symbol: Hz) is the unit of frequency in the International System of Units (SI), equivalent to one event (or cycle) per second. The hertz is an SI derived unit whose expression in terms of SI base units is s−1, meaning that on ...
. As already noted, it is not dependent upon, nor a part of scientific pitch ''notation'' described here. To avoid the confusion in names, scientific pitch is sometimes also called "Verdi tuning" or "philosophical pitch". The current international pitch standard, using A4 as exactly 440  Hz, had been informally adopted by the music industry as far back as 1926, and
A440 A440 or A-440 may refer to: * A440 (pitch standard) * A440 highway (Australia), a road in Victoria, Australia * Quebec Autoroute 440 (Laval) * Quebec Autoroute 440 (Quebec City) See also * Apollo 440 Apollo 440 (also known as Apollo Four Fo ...
became the official international pitch standard in 1955. SPN is routinely used to designate pitch in this system. A4 may be tuned to other frequencies under different tuning standards, and SPN octave designations still apply (ISO 16). With changes in
concert pitch Concert pitch is the pitch (music), pitch reference to which a group of musical instruments are musical tuning, tuned for a performance. Concert pitch may vary from musical ensemble, ensemble to ensemble, and has varied widely over music history. ...
and the widespread adoption of A440 as a musical standard, new scientific frequency tables were published by the
Acoustical Society of America The Acoustical Society of America (ASA) is an international scientific society founded in 1929 dedicated to generating, disseminating and promoting the knowledge of acoustics and its practical applications. The Society is primarily a voluntary orga ...
in 1939, and adopted by the
International Organization for Standardization The International Organization for Standardization (ISO ) is an international standard development organization composed of representatives from the national standards organizations of member countries. Membership requirements are given in Ar ...
in 1955. C0, which was exactly 16 Hz under the scientific pitch standard, is now 16.352 Hz under the current international standard system.


See also

*
Music and mathematics Music theory analyzes the pitch, timing, and structure of music. It uses mathematics to study elements of music such as tempo, chord progression, form, and meter. The attempt to structure and communicate new ways of composing and hearing mus ...
*
Helmholtz pitch notation Helmholtz pitch notation is a system for naming musical notes of the Western chromatic scale. Fully described and normalized by the German scientist Hermann von Helmholtz, it uses a combination of upper and lower case letters (A to G), and the su ...
*
MIDI MIDI (; Musical Instrument Digital Interface) is a technical standard that describes a communications protocol, digital interface, and electrical connectors that connect a wide variety of electronic musical instruments, computers, and re ...
* MIDI tuning standard *
Piano key frequencies This is a list of the fundamental frequencies in hertz (cycles per second) of the keys of a modern 88-key standard or 108-key extended piano in twelve-tone equal temperament, with the 49th key, the fifth A (called A4), tuned to 440 Hz (refe ...
* Keyboard tablature *
Letter notation In music, letter notation is a system of representing a set of pitches, for example, the notes of a scale, by letters. For the complete Western diatonic scale, for example, these would be the letters A-G, possibly with a trailing symbol to indic ...


Footnotes


References


External links


English Octave-Naming Convention
– Dolmetsch Music Theory Online
Notefreqs
– A complete table of note frequencies and ratios for midi, piano, guitar, bass, and violin. Includes fret measurements (in cm and inches) for building instruments. {{DEFAULTSORT:Scientific Pitch Notation Musical notation Pitch (music)