# Scientific pitch notation

### From Wikipedia, the free encyclopedia

**Scientific pitch notation** in Western music is a method of naming the notes of the standard Western chromatic scale by combining a letter-name, accidentals, and an Hindu-Arabic numeral identifying the pitch's octave.

As an example, "A_{4}" refers to the A above middle C (that is, A440, the note that has a frequency of 440.0Hz). Middle C is set as "C_{4}" (261.6Hz).

Scientific pitch notation is an example of a **note-octave notation**, see below.

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 musical 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. The conventional octave naming system, where for example C_{0} is written as ''C, or CCC, or referred to as subcontra C, and C_{4} is written as c' or one-lined C, applies to the written notes that may or may not be transposed. For example, a d' played on a B♭ trumpet is actually a C_{4} in scientific pitch notation.

Three cautions should be observed:

- Several variant systems (perhaps originally in error) use the same symbols as scientific pitch notation, but differ from it in the numbering of the octaves. Some MIDI documentation uses C
_{3}to represent middle C; other writers have used C_{5}. Notation that*appears*to be scientific pitch notation may be one of these variant systems. While they are still*note-octave*systems, when they are called*scientific pitch notation*(as does occur) this is certainly in error.

- The notation is sometimes used in the context of meantone temperament, and does not always assume equal temperament nor the standard concert A of 440 Hz; this is particularly the case in connection with earlier music.

- There is some possible confusion as to assigning the correct octave to C♭. The convention is that the letter name is first combined with the Arabic numeral to determine a specific pitch, which is then altered by applying accidentals. For example, the symbol C♭
_{4}means "the pitch one chromatic step below the pitch C_{4}" and not "the pitch-class C♭ in octave 4", so C♭_{4}is the same pitch as B_{3}, not B_{4}.

The matter is clarified by viewing "♭" and "♯" as denoting a certain fixed amount of cents flat or sharp. In equal temperament, that amount is exacly 100 cents, whereas in 1/4 comma meantone it is precisely 5^{7/4}/2048, or 76.049 cents, taking other values for other meantone tunings. Hence "C♭_{4}" is the same as "C_{4}♭", which in equal temperament is 100 cents below middle C, and equal to B_{3}, and in 1/4 comma meantone is 76 cents below C_{4}, and sharper than B_{3}, which is 117 cents below C_{4}.

This is not a great problem in practice, as in most usages of scientific pitch notation one is notating equal temperament, and neither C♭ nor B♯ need be used at all; rather these notes could be, and usually are, simply named B and C respectively.

## See also

- MIDI
- MIDI Tuning Standard
- Piano key frequencies

## External links

- http://www.dolmetsch.com/musictheory1.htm#uspitch

Category: Musical notation