Pitch

The tilde was firstly used in the polytonic orthography of Ancient Greek, as a variant of the circumflex, representing a rise in pitch followed by a return to standard pitch.

Abbreviation

Carta marina showing Finnish economy, with the captions Hic fabricantur naves and Hic fabricantur bombarde abbreviated

Later, it was used to make abbreviations in medieval Latin documents. When an ⟨n⟩ or ⟨m⟩ followed a vowel, it was often omitted, and a tilde (physically, a small ⟨N⟩) was placed over the preceding vowel to indicate the missing letter; this is the origin of the use of tilde to indicate nasalization (compare the development of the umlaut as an abbreviation of ⟨e⟩.) The practice of using the tilde over a vowel to indicate omission of an ⟨n⟩ or ⟨m⟩ continued in printed books in French as a means of reducing text length until the 17th century. It was also used in Portuguese and Spanish.

The tilde was also used occasionally to make other abbreviations, such as over the letter ⟨q⟩, making q̃, to signify the word que ("that").

Nasalization

It is also as a small ⟨n⟩ that the tilde originated when written above other letters, marking a Latin ⟨n⟩ which had been elided in old Galician-Portuguese. In modern Portuguese it indicates nasalization of the base vowel: mão "hand", from Lat. manu-; razões "reasons", from Lat. rationes. This usage has been adopted in the orthographies of several native languages of South America, such as Guarani and Nheengatu, as well as in the International Phonetic Alphabet (IPA) and many other phonetic alphabets. For example, [ljɔ̃] is the IPA transcription of the pronunciation of the French place-name Lyon.

In Breton, the symbol ⟨ñ⟩ after a vowel means that the letter ⟨n⟩ serves only to give the vowel a nasalised pronunciation, without being itself pronounced, as it normally is. For example, ⟨an⟩ gives the pronunciation [ãn] whereas ⟨añ⟩ gives [ã].

In the DMG romanization of Tunisian Arabic, the tilde is used for nasal vowels õ and ṏ.

Palatal n

The tilded ⟨n⟩ (⟨ñ⟩, ⟨Ñ⟩) developed from the digraph ⟨nn⟩ in Spanish. In this language, ⟨ñ⟩ is considered a separate letter called eñe (IPA: [ˈeɲe]), rather than a letter-diacritic combination; it is placed in Spanish dictionaries between the letters ⟨n⟩ and ⟨o⟩. In Spanish, the word tilde actually refers to diacritics in general, e.g. the acute accent in José,^[21] while the diacritic in ⟨ñ⟩ is called "virgulilla" (IPA: [birɣuˈliʝa]) (yeísta) or (IPA: [birɣuˈliʎa]) (non-yeísta). ^[22] Current languages in which the tilded ⟨n⟩ (⟨ñ⟩) is used for the palatal nasal consonant /ɲ/ include

Tone

In Vietnamese, a tilde over a vowel represents a creaky rising tone (ngã). Letters with the tilde are not considered separate letters of the Vietnamese alphabet.

International Phonetic Alphabet

In phonetics, a tilde is used as a diacritic that is placed above a letter, below it or superimposed onto the middle of it:

• A tilde above a letter indicates nasalization, e.g. [ã], [ṽ].
• A tilde superimposed onto the middle of a letter indicates velarization or pharyngealization, e.g. [ɫ], [z̴]. If no precomposed Unicode character exists, the Unicode character U+0334 ◌̴ COMBINING TILDE OVERLAY can be used to generate one.
• A tilde below a letter indicates laryngealisation, e.g. [d̰]. If no precomposed Unicode character exists, the Unicode character U+0330 ◌̰ COMBINING TILDE BELOW can be used to generate one.

Letter extension

In Estonian, the symbol ⟨õ⟩ stands for the close-mid back unrounded vowel, and it is considered an independent letter.

Other uses

Some languages and alphabets use the tilde for other purposes, such as:

• Arabic script: A symbol resembling the tilde (U+0653 ـٓ ARABIC MADDAH ABOVE) is used over the letter ⟨ا⟩ (/a/) to become ⟨آ⟩, denoting a long /ʔaː/ sound.
• Guaraní: The tilded ⟨G̃⟩ (note that ⟨G/g⟩ with tilde is not available as a precomposed glyph in Unicode) stands for the velar nasal consonant. Also, the tilded ⟨y⟩ (⟨Ỹ⟩) stands for the nasalized upper central rounded vowel [ɨ̃]. Munduruku, Parintintín, and two older spellings of Filipino words also use ⟨g̃⟩.
• Syriac script: A tilde (~) under the letter Kaph represents a [t͡ʃ] sound, transliterated as ch or č.^[23]
• Estonian and Võro use the tilde above the letter o (õ) to indicate the vowel [ɤ], a rare sound among languages.
• Unicode has a combining vertical tilde character: U+033E ◌̾ COMBINING VERTICAL TILDE. It is used to indicate middle tone in linguistic transcription of certain dialects of the Lithuanian language.^[24]

Range

In some languages (though not generally in English), a tilde or a tilde-like wave dash (Unicode: U+301C 〜 WAVE DASH) may be used as a punctuation mark (instead of an unspaced hyphen, en dash or em dash) between two numbers, to indicate a range. Doing so avoids the risk of confusion with subtraction or a hyphenated number (such as a part number or model number). For example, "12~15" means "12 to 15", "~3" means "up to three", and "100~" means "100 and greater". East Asian languages almost always use this convention, but it is sometimes done for clarity in some other languages as well. Chinese uses the wave dash and full-width em dash interchangeably for this purpose. In English, the tilde is often used to express ranges and model numbers in electronics, but rarely in formal grammar or in type-set documents, as a wavy dash preceding a number sometimes represents an approximation (see below).

Approximation

Before a number the tilde can mean 'approximately'; '~42' means 'approximately 42'.^[25] When used with currency symbols that precede the number (national conventions differ), the tilde precedes the symbol, thus for example '~$10' means 'about ten dollars'.^[26]

The symbols ≈ (almost equal to) and ≅ (approximately equal to) are among the other symbols used to express approximation.

Japanese

The wave dash (波ダッシュ, nami dasshu) is used for various purposes in Japanese, including to denote ranges of numbers (e.g., 5〜10 means between 5 and 10) in place of dashes or brackets, and to indicate origin. The wave dash is also used to separate a title and a subtitle in the same line, as a colon is used in English.

When used in conversations via email or instant messenger it may be used as a sarcasm mark.

The sign is used as a replacement for the chōon, katakana character, in Japanese, extending the final syllable.

Unicode and Shift JIS encoding of wave dash

Correct JIS wave dash, current in Unicode

Previous Unicode wave dash (incorrect)

In practice the full-width tilde (全角チルダ, zenkaku chiruda) (Unicode U+FF5E ～ FULLWIDTH TILDE), is often used instead of the wave dash (波ダッシュ, nami dasshu) (Unicode U+301C 〜 WAVE DASH), because the Shift JIS code for the wave dash, 0x8160, which should be mapped to U+301C,^[27][28] is instead mapped to U+FF5E^[29] in Windows code page 932 (Microsoft's code page for Japanese), a widely used extension of Shift JIS.

This decision avoided a shape definition error in the original (6.2) Unicode code charts:^[30] the wave dash reference glyph in JIS / Shift JIS^[31][32] matches the Unicode reference glyph for U+FF5E FULLWIDTH TILDE,^[33] while the original reference glyph for U+301C^[30] was reflected, incorrectly,^[34] when Unicode imported the JIS wave dash. In other platforms such as the classic Mac OS and macOS, 0x8160 is correctly mapped to U+301C. It is generally difficult, if not impossible, for users of Japanese Windows to type U+301C, especially in legacy, non-Unicode applications.

A similar situation exists regarding the Korean KS X 1001 character set, in which Microsoft maps the EUC-KR or UHC code for the wave dash (0xA1AD) to U+223C ∼ TILDE OPERATOR,^[35][36] while IBM and Apple map it to U+301C.^[37][38][39] Microsoft also uses U+FF5E to map the KS X 1001 raised tilde (0xA2A6),^[36] while Apple uses U+02DC ˜ SMALL TILDE.^[39]

The current Unicode reference glyph for U+301C has been corrected^[34] to match the JIS standard^[40] in response to a 2014 proposal, which noted that while the existing Unicode reference glyph had been matched by fonts from the discontinued Windows XP, all other major platforms including later versions of Microsoft Windows shipped with fonts matching the JIS reference glyph for U+301C.^[41]

The JIS / Shift JIS wave dash is still formally mapped to U+301C as of JIS X 0213,^[42] whereas the WHATWG Encoding Standard used by HTML5 follows Microsoft in mapping 0x8160 to U+FF5E.^[43] These two code points have a similar or identical glyph in several fonts, reducing the confusion and incompatibility.

As a unary operator

A tilde in front of a single quantity can mean "approximately", "about"^[14] or "of the same order of magnitude as."

In written mathematical logic, the tilde represents negation: "~p" means "not p", where "p" is a proposition. Modern use often replaces the tilde with the negation symbol (¬) for this purpose, to avoid confusion with equivalence relations.

As a relational operator

In mathematics, the tilde operator (which can be represented by a tilde or the dedicated character U+223C ∼ TILDE OPERATOR), sometimes called "twiddle", is often used to denote an equivalence relation between two objects. Thus "x ~ y" means "x is equivalent to y". It is a weaker statement than stating that x equals y. The expression "x ~ y" is sometimes read aloud as "x twiddles y", perhaps as an analogue to the verbal expression of "x = y".^[44]

The tilde can indicate approximate equality in a variety of ways. It can be used to denote the asymptotic equality of two functions. For example, f (x) ~ g(x) means that ${\displaystyle \lim _{x\to \infty }{\frac {f(x)}{g(x)}}=1}$.^[13]

A tilde is also used to indicate "approximately equal to" (e.g. 1.902 ~= 2). This usage probably developed as a typed alternative to the libra symbol used for the same purpose in written mathematics, which is an equal sign with the upper bar replaced by a bar with an upward hump, bump, or loop in the middle (︍︍♎︎) or, sometimes, a tilde (≃). The symbol "≈" is also used for this purpose.

In physics and astronomy, a tilde can be used between two expressions (e.g. h ~ 10⁻³⁴ J s) to state that the two are of the same order of magnitude.^[13]

In statistics and probability theory, the tilde means "is distributed as";^[13] see random variable(e.g. X ~ B(n,p) for a binomial distribution).

A tilde can also be used to represent geometric similarity (e.g. ∆ABC ~ ∆DEF, meaning triangle ABC is similar to DEF). A triple tilde (≋) is often used to show congruence, an equivalence relation in geometry.

In graph theory, the tilde can be used to represent adjacency between vertices. The edge ${\displaystyle (x,y)}$ connects vertices ${\displaystyle x}$ and ${\displaystyle y}$ which can be said to be adjacent, and this adjacency can be denoted ${\displaystyle x\sim y}$.

As a diacritic

The symbol "${\displaystyle {\tilde {f}}}$" is pronounced as "eff tilde" or, informally, as "eff twiddle".^[45][46] This can be used to denote the Fourier transform of f, or a lift of f, and can have a variety of other meanings depending on the context.

A tilde placed below a letter in mathematics can represent a vector quantity (e.g. ${\displaystyle (x_{1},x_{2},x_{3},\ldots ,x_{n})={\underset {^{\sim }}{\mathbf {x} }}}$).

In statistics and probability theory, a tilde placed on top of a variable is sometimes used to represent the median of that variable; thus ${\displaystyle {\tilde {\mathbf {y} }}}$ would indicate the median of the variable ${\displaystyle \mathbf {y} }$. A tilde over the letter n (${\displaystyle {\tilde {n}}}$) is sometimes used to indicate the harmonic mean.

In machine learning, a tilde may represent a candidate value for a cell state in GRUs or LSTM units. (e.g. c̃)

Directories and URLs

On Unix-like operating systems (including AIX, BSD, Linux and macOS), tilde normally indicates the current user's home directory. For example, if the current user's home directory is /home/user, then the command cd ~ is equivalent to cd /home/user, cd $HOME, or cd. This convention derives from the Lear-Siegler ADM-3A terminal in common use during the 1970s, which happened to have the tilde symbol and the word "Home" (for moving the cursor to the upper left) on the same key. When prepended to a particular username, the tilde indicates that user's home directory (e.g., ~janedoe for the home directory of user janedoe, such as /home/janedoe).^[52]

Used in URLs on the World Wide Web, it often denotes a personal website on a Unix-based server. For example, http://www.example.com/~johndoe/ might be the personal website of John Doe. This mimics the Unix shell usage of the tilde. However, when accessed from the web, file access is usually directed to a subdirectory in the user's home directory, such as /home/username/public_html or /home/username/www.^[53]

In URLs, the characters %7E (or %7e) may substitute for a tilde if an input device lacks a tilde key.^[54] Thus, http://www.example.com/~johndoe/ and http://www.example.com/%7Ejohndoe/ will behave in the same manner.

Computer languages

The tilde is used in the AWK programming language as part of the pattern match operators for regular expressions:

• variable ~ /regex/ returns true if the variable is matched.
• variable !~ /regex/ returns false if the variable is matched.

A variant of this, with the plain tilde replaced with =~, was adopted in Perl, and this semi-standardization has led to the use of these operators in other programming languages, such as Ruby or the SQL variant of the database PostgreSQL.

In APL and MATLAB, tilde represents the monadic logical function NOT, and in APL it additionally represents the dyadic multiset function without (set difference).

In C the tilde character is used as bitwise NOT unary operator, following the notation in logic (an ! causes a logical NOT, instead). This is also used by most languages based on or influenced by C, such as C++, D and C#. The MySQL database also use tilde as bitwise invert^[55] as does Microsoft's SQL Server Transact-SQL (T-SQL) language. JavaScript also uses tilde as bitwise NOT, and because JavaScript internally uses floats and the bitwise complement only works on integers, numbers are stripped of their decimal part before applying the operation. This has also given rise to using two tildes ~~x as a short syntax for a cast to integer (numbers are stripped of their decimal part and changed into their complement, and then back).

In C++ and C#, the tilde is also used as the first character in a class's method name (where the rest of the name must be the same name as the class) to indicate a destructor – a special method which is called at the end of the object's life.

In ASP.NET application tilde ('~') is used as a shortcut to the root of the application's virtual directory.

In the CSS stylesheet language, the tilde is used for the indirect adjacent combinator as part of a selector.

In the D programming language, the tilde is used as an array concatenation operator, as well as to indicate an object destructor and bitwise not operator. Tilde operator can be overloaded for user types, and binary tilde operator is mostly used to merging two objects, or adding some objects to set of objects. It was introduced because plus operator can have different meaning in many situations. For example, what to do with "120" + "14" ? Is this a string "134" (addition of two numbers), or "12014" (concatenation of strings) or something else? D disallows + operator for arrays (and strings), and provides separate operator for concatenation (similarly PHP programming language solved this problem by using dot operator for concatenation, and + for number addition, which will also work on strings containing numbers).

In Eiffel, the tilde is used for object comparison. If a and b denote objects, the boolean expression a ~ b has value true if and only if these objects are equal, as defined by the applicable version of the library routine is_equal, which by default denotes field-by-field object equality but can be redefined in any class to support a specific notion of equality. If a and b are references, the object equality expression a ~ b is to be contrasted with a = b which denotes reference equality. Unlike the call a.is_equal (b), the expression a ~ b is type-safe even in the presence of covariance.

In the Apache Groovy programming language the tilde character is used as an operator mapped to the bitwiseNegate() method.^[56] Given a String the method will produce a java.util.regex.Pattern. Given an integer it will negate the integer bitwise like in C. =~ and ==~ can in Groovy be used to match a regular expression.^[57][58]

In Haskell, the tilde is used in type constraints to indicate type equality.^[59] Also, in pattern-matching, the tilde is used to indicate a lazy pattern match.^[60]

In the Inform programming language, the tilde is used to indicate a quotation mark inside a quoted string.

In "text mode" of the LaTeX typesetting language a tilde diacritic can be obtained using, e.g., \~{n}, yielding "ñ". A stand-alone tilde can be obtained by using \textasciitilde or \string~. In "math mode" a tilde diacritic can be written as, e.g., \tilde{x}. For a wider tilde \widetilde can be used. The \sim command produce a tilde-like binary relation symbol that is often used in mathematical expressions, and the double-tilde ≈ is obtained with \approx. The url package also supports entering tildes directly, e.g., \url{http://server/~name}. In both text and math mode, a tilde on its own (~) renders a white space with no line breaking.

In MediaWiki syntax, four tildes are used as a shortcut for a user's signature.

In Common Lisp, the tilde is used as the prefix for format specifiers in format strings.^[61]

In Max/MSP, a tilde is used to denote objects that process at the computer's sampling rate, i.e. mainly those that deal with sound.

In Standard ML, the tilde is used as the prefix for negative numbers and as the unary negation operator.

In OCaml, the tilde is used to specify the label for a labeled parameter.

In R, the tilde operator is used to separate the left- and right-hand sides in a model formula.^[62]

In Object REXX, the twiddle is used as a "message send" symbol. For example, Employee.name~lower() would cause the lower() method to act on the object Employee's name attribute, returning the result of the operation. ~~ returns the object that received the method rather than the result produced. Thus it can be used when the result need not be returned or when cascading methods are to be used. team~~insert("Jane")~~insert("Joe")~~insert("Steve") would send multiple concurrent insert messages, thus invoking the insert method three consecutive times on the team object.

In Raku, ~~ is used instead of =~ for a regular expression. Because the dot operator is used for member access instead of ->, concatenation is done with a single tilde.

my $concatResult = "Hello " ~ "world!";
$concatResult ~~ /<|w><[A..Z]><[a..z]>*<|w>/;

say $/; # outputs "Hello"
# the $/ variable holds the last regex match result

Keyboards

The presence (or absence) of a tilde engraved on the keyboard depends on the territory where it was sold. In either case, computer's system settings determine the keyboard mapping and the default setting will match the engravings on the keys. Even so, it certainly possible to configure a keyboard for a different locale than that supplied by the retailer. On American and British keyboards, the tilde is a standard keytop and pressing it produces a free-standing "ASCII Tilde". To generate a letter with a tilde diacritic requires the US international or UK extended keyboard setting.

• With US-international, the `/~ key is a dead key: pressing the ~ key and then a letter produces the tilde-accented form of that letter. (For example, ~ a produces ã.) With this setting active, an ASCII tilde can be inserted with the dead key followed by the space bar, or alternatively by striking the dead key twice in a row.
• With UK-extended, the key works normally but becomes a 'dead key' when combined with AltGr. Thus AltGr+# followed by a letter produces the accented form of that letter.
• With a Mac either of the Alt/Option keys function similarly.
• With Linux, the compose key facility is used.

Instructions for other national languages and keyboards are beyond the scope of this article.

In the US and European Windows systems, the Alt code for a single tilde is 126.

Backup filenames

The dominant Unix convention for naming backup copies of files is appending a tilde to the original file name. It originated with the Emacs text editor^[63] and was adopted by many other editors and some command-line tools.

Emacs also introduced an elaborate numbered backup scheme, with files named filename.~1~, filename.~2~ and so on. It didn't catch on, as the rise of version control software eliminates the need for this usage.

Microsoft filenames

The tilde was part of Microsoft's filename mangling scheme when it extended the FAT file system standard to support long filenames for Microsoft Windows. Programs written prior to this development could only access filenames in the so-called 8.3 format—the filenames consisted of a maximum of eight characters from a restricted character set (e.g. no spaces), followed by a period, followed by three more characters. In order to permit these legacy programs to access files in the FAT file system, each file had to be given two names—one long, more descriptive one, and one that conformed to the 8.3 format. This was accomplished with a name-mangling scheme in which the first six characters of the filename are followed by a tilde and a digit. For example, "Program Files" might become "PROGRA~1".

The tilde symbol is also often used to prefix hidden temporary files that are created when a document is opened in Windows. For example, when a document "Document1.doc" is opened in Word, a file called "~$cument1.doc" is created in the same directory. This file contains information about which user has the file open, to prevent multiple users from attempting to change a document at the same time.