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# Helmholtz pitch notation

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### Helmholtz pitch notation

The naming of individual 'C's using the Helmholtz system

Helmholtz pitch notation is a system for naming musical notes of the Western chromatic scale. Developed by the German scientist Hermann von Helmholtz, it uses a combination of upper and lower case letters (A to G),[1] and the sub- and super-prime symbols ( ͵  ′ ) to describe each individual note of the scale. It is one of two formal systems for naming notes in a particular octave, the other being scientific pitch notation.[2]

## History

Helmholtz developed this system, inspired by the practice of German organ makers for labelling their pipes, in order to accurately define pitches in his classical work on acoustics Die Lehre von den Tonempfindungen als physiologische Grundlage für die Theorie der Musik (1863) translated into English by A. J. Ellis as On the Sensations of Tone (1875).[3] The system is widely used by musicians across Europe and is the one used in the New Grove Dictionary. Once also widely used by scientists and doctors when discussing the scientific and medical aspects of sound in relation to the auditory system, it has now largely been replaced in American scientific and medical contexts by scientific pitch notation.[4]

## Usage

The Helmholtz scale always starts on the note C and ends at B (C, D, E, F, G, A, B). The note C is shown in different octaves by using upper-case letters for low notes, and lower-case letters for high notes, and adding sub-primes and primes in the following sequence: C͵͵ C c c′ c″ c″′ (or ͵͵C ͵C C c c′ c″ c″′) and so on.

Middle C is designated c′, therefore the octave upwards from middle C is c'-b'.

Each octave may also be given a name based on the "German method" (see below). For example, the octave from c′b′ is called the one-line octave.[2]

### Variations

• The English multiple C notation uses repeated Cs in place of the sub-prime symbol. Therefore is rendered as CC.[4]
• The German method replaces the "prime" with a horizontal bar above the letter.[4]
• Primes in subscript (resp. superscript) may be replaced with digits in subscript (resp. superscript) indicating the number of primes (see Article and references on German WP): for example ,,C or C2 or 2C, c'' or c2 (but not 2c).
• A system of pitch designation using uppercase and lowercase letters, commas and apostrophes in a way similar to the Helmholtz pitch notation is used in the ABC music notation system, currently used mainly for Western folk music.
• Scientific pitch notation is a similar system that replaces primes and sub-primes with integers. Hence C4 in scientific notation is c′ (middle C).

## Staff representation

This diagram gives examples of the lowest and highest note in each octave, giving their name in the Helmholtz system, and the "German method" of octave nomenclature. (The octave below the contra octave is known as the sub-contra octave).