Scientific pitch notation (SPN), also known asAmerican standard pitch notation (ASPN) andinternational pitch notation (IPN), is a method of specifying musicalpitch by combining a musicalnote name (withaccidental if needed) and a number identifying the pitch'soctave.^[1][2]

Although scientific pitch notation was originally designed as a companion toscientific pitch (see below), the two are not synonymous. Scientific pitch is apitch standard—a system that defines the specificfrequencies 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.

The notation makes use of the traditional tone names (A to G) which are followed by numbers showing whichoctave they are part of.

For standardA440 pitchequal temperament, the system begins at a frequency of 16.35160Hz, which is assigned the valueC₀.

The octave 0 of the scientific pitch notation is traditionally called thesub-contra octave, and the tone marked C₀ in SPN is written as,,C orC,, orCCC in traditional systems, such asHelmholtz notation. Octave 0 of SPN marks the low end of what humans can actually perceive, with the average person being able tohear 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 Aabove C₀ andmiddle C (theone-line octave's C or simplyc′) is denoted asC₄ 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♭₄" is same frequency as "B₃".

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 thetransposition conventions that are used in writing the music for instruments such as theclarinet andguitar. It is also easily translated into staff notation, as needed. In describing musical pitches, nominallyenharmonic spellings can give rise to anomalies where, for example inPythagorean intonation C♭₄ is a lower frequency than B₃; 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^[3] refers to the C two octaves below middle C, whereas "C" inABC Notation refers to middle C itself. With scientific pitch notation, middle C isalways C₄, and C₄ 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. C₇ is much easier to quickly distinguish visually from C₈, than is, for example,c′′′′ fromc′′′′′, 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 E₀ or higher than E♭₁₀ 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 theChandra X-ray Observatory observed the waves of pressure fronts propagating away from a black hole, their one oscillation every 10 million years was described byNASA as corresponding to the B♭ fifty-seven octaves below middle C (B♭₋₅₃) or 3.235 fHz).^[4]

The notation is sometimes used in the context ofmeantone temperament, and does not always assumeequal temperament 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^[5] 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.^[a]

The table below gives notation for pitches based on standardpiano key frequencies:standard concert pitch andtwelve-tone equal temperament. When a piano is tuned tojust intonation, C₄ refers to the same key on the keyboard, but a slightly different frequency. Notes not produced by any piano are highlighted in medium gray, and those produced only by an extended 108-key piano, light gray.

Mathematically, given the numbern of semitones above middle C, the fundamental frequency in hertz is given by${\displaystyle 440\cdot 2^{(n-9)/12}}$ (seetwelfth root of two). Given the MIDI NoteOn numberm, the frequency of the note is normally${\displaystyle 440\cdot 2^{(m-69)/12}}$ Hz, using standard tuning.

Scientific pitch is an absolute pitchstandard, first proposed in 1713 by French physicistJoseph Sauveur. It was defined so that allCs are integer powers of 2, withmiddle C (C₄) at 256 hertz. As already noted, it is not dependent upon, nor a part of scientific pitchnotation 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, andA440 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).^[6]

With changes inconcert pitch and the widespread adoption of A440 as a musical standard, new scientific frequency tables were published by theAcoustical Society of America in 1939, and adopted by theInternational Organization for Standardization in 1955. C₀, which was exactly 16 Hz under the scientific pitch standard, is now 16.35160 Hz under the current international standard system.^[5]

• Music and mathematics
• Helmholtz pitch notation
• MIDI
• MIDI tuning standard
• Piano key frequencies
• Keyboard tablature
• Letter notation

• 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.

• Musical notation
• Pitch (music)

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