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Musical notation system to describe pitch and relative frequency

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 name (with accidental if needed) and a number identifying the pitch's octave. Although scientific pitch notation was originally designed as a companion to scientific pitch (see below), the two are not synonymous. Scientific pitch is a pitch standard—a system that defines the specific frequencies 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.

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 conventions 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 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 two octaves 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, c′′′′ from 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 or higher than E 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 million years was described by NASA as corresponding to the B fifty seven octaves below middle C (B or 3.235 fHz).

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 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), forcing the musician to treat samples at any other pitch as transposing instruments when using them in songs. Alternately, both Yamaha and the software MaxMSP define middle C as C3. Apple'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 semitones, 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 1/100 semitone or 1/1200 octave. This measure of pitch allows the expression of microtones not found on standard piano keyboards.

The French–Belgian system defines the note C placed two ledger lines below the bass staff as Do1 and middle C as Do3. As in the scientific pitch notation, the index of a Do is shared with all notes above it until the next Do. However, no octave receives the index zero, the octave right below 1 receiving the index −1. Therefore while C4 in SPN equates to Do3 in the French–Belgian system, C1 in SPN equates to Do−1.