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{{short description|System for naming musical notes}}
[[Image:Helmholtz pitch notation c.svg|thumb|right|300px|The naming of individual '''C'''s using the Helmholtz system]]
'''Helmholtz pitch notation''' is a system for naming [[musical note]]s of the [[Classical music|Western]] [[chromatic scale]]. Fully described and normalized by the German scientist [[Hermann von Helmholtz]], it uses a combination of [[upper case|upper]] and [[lower case]] letters (A to G),{{efn|In German musical text, the letter '''B''' is used to designate a standard '''B'''{{music|flat}}, whereas '''H''' is used for '''B'''{{music|natural}}.}} and the sub- and super-[[prime (symbol)|prime]] symbols (''' ͵'''  {{prime}}   or  {{sub|⸜}} {{sup|⸝}}) to denote 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]].<ref name="Schmidt-Jones">{{cite web |last=Schmidt-Jones |first=Catherine |title=Octaves and the major-minor tonal system |website=cnx.com |url=http://cnx.org/content/m10862/latest/ |access-date=3 August 2007}}</ref>{{unreliable source?|date=June 2020}}{{efn|name=Scientific-pitch-description|[[Scientific pitch notation]] is a similar system that replaces primes and sub-primes with integers. Hence in [[Scientific pitch notation|scientific notation]], [[Middle C|middle&nbsp;'''C''']] (Helmholtz '''c{{prime}}''') is either  '''C<sub>4</sub>''' or '''C4'''.}}

==History==
Helmholtz proposed this system 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 [[Alexander John Ellis|A.J. Ellis]] as ''[[On the Sensations of Tone]]'' (1875).<ref name=Grove-2007-Helmholtz>{{cite encyclopedia |encyclopedia=The Concise Grove Dictionary of Music |title=Hermann von Helmholtz |publisher=Oxford University Press |year=1994 |url=http://www.answers.com/topic/hermann-von-helmholtz |access-date=3 August 2007}}</ref><ref name=Helmholtz-Ellis-1885>{{cite book |last=von&nbsp;Helmholtz |first=Herman |date=1885 |orig-year=1863 |title=On the Sensations of Tone |edition=2nd English |translator=[[Alexander John Ellis|Ellis, A.J.]] |language=en |page=15 |publisher=Cosimo |isbn=9781602066397 |url=https://books.google.com/books?id=2CiqYQXZjIYC&pg=PA15 |via=Google Books}}</ref>{{efn|name=Helmholtz-Ellis-remarks|In the German edition of the book, [[Hermann von Helmholtz|Helmholtz]] wrote:
:"German musicians denote the pitches of the higher octaves by accents (''strichelungen'')".<ref name=Helmholtz-Ellis-1885/>
[[Alexander John Ellis|Ellis]] noted that
:"English works use strokes above and below the letters, which are typographically inconvenient. Hence the German notation is retained."<ref name=Helmholtz-Ellis-1885/>}}

Helmholtz based his notation on the practice of German organ builders for labelling their pipes, itself derived from the old German [[organ tablature]] in use from late medieval times until the early 18th&nbsp;century. His system is widely used by musicians across Europe and is the one used in the ''New Grove Dictionary''.<ref name=Grove-2007-Helmholtz/> 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 been replaced in the US in scientific and medical contexts by [[scientific pitch notation]].<ref name="Dolmetsch">{{cite web |last=Blood |first=Brian |title=Helmholtz |series=Staffs, clefs & pitch notation |website=Dolmetsch Online |url=http://www.dolmetsch.com/musictheory1.htm#helmholtz |access-date=2 August 2007}}</ref>{{unreliable source?|date=June 2020}}

==Use==
The accenting of the scale in Helmholtz notation always starts on the note  '''C'''  and ends at '''B''' (e.g. '''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{{prime}}'''  '''c{{pprime}}'''  '''c‴'''  (or  ''',,C'''  ''',C'''  '''C'''  '''c'''  '''c{{prime}}'''  '''c{{pprime}}'''  '''c‴'''  or  '''C{{sub|⸜⸜}}'''  '''C{{sub|⸜}}'''  '''C'''  '''c'''  '''c{{sup|⸝}}'''  '''c{{sup|⸝⸝}}'''  '''c{{sup|⸝⸝⸝}}''') and so on.

[[Middle C|Middle&nbsp;'''C''']] is designated '''c{{prime}}''', therefore the [[octave]] from [[Middle C|middle&nbsp;'''C''']] upwards is '''c{{prime}}'''–'''b{{prime}}'''.

===Variations===

{|class="wikitable"
! Octave !! Helmholtz !! Helmholtz<br>(English) !! Helmholtz<br>(numbered) !! ABC !! Lilypond !! [[Scientific pitch notation|SPN]]
|- 
|style="background-color:white"| <score>{ \clef bass   \ottava #-1 c,,,1 }</score>
| C͵͵ ''or'' ͵͵C || CCC    || C₂ ''or'' ₂C || {{code|C,,,,}} || {{code|c,,,}}   || C₀
|-
|style="background-color:white"| <score>{ \clef bass   c,,1  }</score>
| C͵ ''or'' ͵C   || CC     || C₁ ''or'' ₁C || {{code|C,,,}}  || {{code|c,,}}    || C₁
|-
|style="background-color:white"| <score>{ \clef bass   c,1   }</score>
| C              || C      || C            || {{code|C,,}}   || {{code|c,}}     || C₂
|-
|style="background-color:white"| <score>{ \clef bass   c1    }</score>
| c              || c      || c            || {{code|C,}}    || {{code|c}}      || C₃
|-
|style="background-color:white"| <score>{ \clef treble c'1   }</score>
| c′             || c′     || c¹           || {{code|C}}     || {{code|c'}}     || C₄
|-
|style="background-color:white"| <score>{ \clef treble c''1  }</score>
| c′′            || c′′    || c²           || {{code|c}}     || {{code|c''}}    || C₅
|-
|style="background-color:white"| <score>{ \clef treble c'''1 }</score>
| c′′′           || c′′′   || c³           || {{code|c'}}    || {{code|c'''}}   || C₆
|-
|style="background-color:white"| <score>{ \clef treble c''''1 }</score>
| c′′′′          || c′′′′  || c⁴           || {{code|c''}}   || {{code|c''''}}  || C₇
|-
|style="background-color:white"| <score>{ \clef treble \ottava #1 c'''''1 }</score>
| c′′′′′         || c′′′′′ || c⁵           || {{code|c'''}}  || {{code|c'''''}} || C₈
|}


* The ''English multiple-letter notation'' uses repeated ''C''s in place of the sub-prime symbol. Therefore  '''C͵'''  is rendered as  '''CC'''  ;  '''C͵͵''' as '''CCC'''  ; etc.<ref name="Dolmetsch"/> This has notation has appeared in some part names for contrabass instruments, for example, the "[[Contrabass tuba|CC Contrabass Tuba]]" or the "[[Contrabass clarinet|BB♭ Contrabass Clarinet]]".
* The ''English strokes notation'' replaces subscript-primes with underlines and superscript primes with overlines:  '''C͵͵'''  is rendered as  '''C͇'''  ;  '''C͵'''  as  '''{{underline|C}}''' ; '''c{{prime}}'''  as  '''c̄'''  and  '''c{{pprime}}'''  as  '''c̿'''  ;  etc. Because the typesetting is difficult this notation has fallen out of use.{{efn|name=Helmholtz-Ellis-remarks}}
* Primes in subscript and superscript may be replaced with digits, indicating the number of primes.{{efn|See article ''[[:de:Tonsymbol|Tonsymbol]]'' and references in the German Wikipedia.}} For example, '''͵͵C''' can be written as '''C<sub>2</sub>''' or '''<sub>2</sub>C''', and '''c{{pprime}}''' written as '''c<sup>2</sup>''' (but ''not'' '''<sup>2</sup>c''').{{efn|The variant Helmholtz notation with number-subscripts is problematic, since it is easily confused with [[scientific pitch notation]].{{efn|name=Scientific-pitch-description}}}}
* A system of pitch designation using uppercase and lowercase letters, commas and apostrophes, formally identical to Helmholtz pitch notation but shifted by two octaves, is used for [[ABC notation]].{{efn|The [[ABC notation|ABC music notation system]] is used mainly for documenting Western folk music as plain text files, and as a musical notation exchange format.}} In ABC, the notes <code>C,</code> and <code>C</code> (middle C) and <code>c</code> represent Helmholtz '''c''' and '''{{prime|c}}''' and '''{{pprime|c}}''' respectively.
* [[LilyPond]] music publishing software uses an all-lowercase variant, also with commas and apostrophes, where pitches that would be uppercase in Helmholtz notation are written in lowercase with an additional sub-prime. Thus, <code>c,,,</code> and <code>c,,</code> and <code>c,</code> represent Helmholtz '''C͵͵''' and '''C͵''' and '''C''' respectively.<ref>{{cite web |url=http://lilypond.org/doc/v2.18/Documentation/notation/writing-pitches |work=LilyPond Notation Reference |edition=2.18.2 |title=1.1.1 Writing pitches |access-date= 2017-11-08}}</ref>

==Octave and staff representation==
Whole octaves may also be given a name based on "English strokes notation". For example, the octave from '''c{{prime}}'''–'''b{{prime}}''' is called the ''one-line octave''<ref name="Schmidt-Jones"/> or (less common) ''once-accented octave''.<ref>{{cite dictionary |title=Once–accented octave |dictionary=Merriam-Webster Dictionary of the English Language |url=https://www.merriam-webster.com/dictionary/once%E2%80%93accented%20octave |access-date=2017-07-19}}</ref> Correspondingly, the notes in the octave may be called ''one-lined'' '''C''' (for '''c{{prime}}'''), etc.

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.)
[[Image:Helmholtz pitch notation.svg|center|800px]]

==See also==
* [[Scientific pitch notation]]

==Notes==
{{notelist}}

==References==
{{reflist|25em}}

==External links==
* {{cite web |url=http://www.dolmetsch.com/musictheory1.htm#helmholtz |website=Dolmetsch Music theory online |title=Staffs, clefs & pitch notation}}
* {{cite web |url=http://cnx.org/content/m10862/latest/ |title=Octaves and the major-minor tonal system |website=cnx.org}}

{{Musical notation}}
{{Pitch (music)}}

{{DEFAULTSORT:Helmholtz Pitch Notation}}
[[Category:Musical notation]]
[[Category:Pitch (music)]]
[[Category:Hermann von Helmholtz]]