Scientific pitch notation

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 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♭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 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 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′′′′ 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 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 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♭₋₅₃) or 3.235 fHz).

The notation is sometimes used in the context of meantone temperament, and does not always assume equal 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 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: standard concert pitch and twelve-tone equal temperament. When a piano is tuned to just 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 112-key piano, light gray.

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

Scientific pitch versus scientific pitch notation

Scientific pitch is an absolute pitch standard, first proposed in 1713 by French physicist Joseph Sauveur. It was defined so that all Cs are integer powers of 2, with middle C (C₄) at 256 hertz. 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 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 and the widespread adoption of A440 as a musical standard, new scientific frequency tables were published by the Acoustical Society of America in 1939, and adopted by the International 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.