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# Diaeresis

In linguistics, a diaeresis or dieresis (AE) (from Greek diairein, "to divide") is the modification of a syllable by distinctly pronouncing one of its vowels. The diacritic mark composed of two small dots ( ¨ ) placed over a vowel to indicate this modification is also called a diaeresis. (In the case of an "i", it replaces the original dot.)

ä ë ï ö ü ÿ
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## Usage

In French, Greek, and Dutch, and in English borrowings from them, this is often done to indicate that the second of a pair of vowels is to be pronounced as a separate vowel rather than being treated as silent or as part of a diphthong, as in the word naïve or the names Chloë and Zoë. Welsh also uses the accent for this purpose, with the diaeresis usually indicating the stressed vowel. French also uses the diaeresis to indicate syllabification in, for example, Gaëlle and païen. It is called trema or deelteken in Dutch, tréma in French.

The diaeresis is also occasionally used on native English words for the above purposes (as in "coöperate", "reënact", and the surname "Brontë"), but this usage has become very rare since the 1940s. The New Yorker magazine is noted as one of the few publications that still spells "coöperate" with a diaeresis.

In Spanish and Portuguese, it is used over the vowel u to indicate that it is pronounced in places where that vowel would normally be silent. In particular, the u is silent in the letter combinations gue and gui, but in words such as vergüenza ("shame") or pingüino ("penguin"), the u is pronounced, forming a diphthong with the following vowel ([we] and [wi] respectively). Only Brazilian Portuguese uses the diaeresis like Spanish and when the "u" is not silent in the letter combinations "que" and "qui", in words such "cinqüenta" ("fifty") and "qüinqüênio" (a five-year period). The diaeresis doesn't exist in the Portuguese of Portugal and its other former colonies.

In Catalan, diaereses serve two different purposes. Similarly to Spanish, they are used in the groups güe, güi, qüe, and qüi to indicate that the u is in fact pronounced forming a diphthong with the following vowel ([we] and [wi] respectively). For example, aigües ("waters"), qüestió ("matter"). Also, similarly to French, diaereses are used over i or u to indicate that they do not form a diphthong with a preceding vowel. For example, veïna [[email protected]'[email protected]] ("neighbour", feminine), diürn [di'urn] ("diurnal").

Ÿ can also be used in transcribed Greek: there it represents the non-diphthong αυ (alpha upsilon), e.g. in the Persian name Artaÿctes at the very end of Herodotus. Ÿ is also rarely found in French in certain proper nouns (for instance, the name of the Parisian suburb of l'Haÿ-les-Roses ).

## Similar looks, different functions

### Umlaut

The same diacritic mark is used for a different purpose in German: in this language it marks a variation in the pronunciation of vowels known as umlaut. Although sometimes rendered as two vertical or oblique bars above the letter, in most typescripts it is almost indistinguishable from diaeresis — the only difference being that in well-designed typographical fonts umlaut dots will be very close to the letter's body, while diaeresis dots will be a bit farther up with a bit more of white space between the letter and the dots. In computer screen fonts the difference is usually not noticeable.

The mark evolved from the ligatures æ and œ to a small Sütterlin 'e' written above the letter, which would appear as small bars or dots; the umlauts, when needed, can be substituted by 'ae', 'oe' and 'ue'; they should not be substituted by the bare vowels 'a', 'o', and 'u'.

The need to distinguish between Umlaut and Trema in Unicode has led to the following recommendation by ISO/IEC JTC 1/SC 2/WG 2, for use only in cases where a need to distinguish between umlaut and trema is present:

• To represent Trema use Combining Grapheme Joiner (CGJ, 034F) + Combining Diaeresis (0308)
• To represent Umlaut use Combining Diaeresis (0308)

### Other evolved ligatures

In Finnish, Hungarian, Turkish and North Germanic languages (i.e., Danish, Icelandic, Norwegian and Swedish) there are characters that appear similar to German umlauts (ü, ä, and ö), and represent sounds similar to the corresponding sounds in German. Despite this, they are in fact considered as letters in their own right, as is å. This is the reason why, unlike in German, it is not correct to replace them with 'ae' or 'oe'. The umlaut, particularly on the letter u, is also used in the transcription of languages that do not use the Roman alphabet, such as Chinese. For example, 女 (meaning female) is transcribed as .

In Lëtzebuergesch, the native language of Luxembourg, the two dots over the first 'e' represent a stressed schwa. Since the language uses the mark to show stress, it cannot be used to modify the 'u' which therefore has to be 'ue'.

As such uses do not mark grammatical variation, i.e. of tense or mood, nor syllable modification, they are not properly cases of umlaut. Hence it is improper to call these characters umlauts.

The letter IJ is sometimes written Ÿ/ÿ, but this is not a standard use. IJ/ij should be used for these character; Ĳ/ĳ is a poorly supported and discouraged alternative. Ÿ is used because the "Dutch Y" represents a single letter in all cases, for example IJsselmeer. Note that in Afrikaans (a language derived from Dutch) the 'y' does correspond to and is pronounced the same as the Dutch 'ij'.

Other evolved ligatures include the letters W ("double U"), æ, and the German ß.

## Diaeresis in Cyrillic

Cyrillic letters А, О, У with diaeresis are used in Altay, Mari and Keräşen Tatar alphabets for sounds ä, ö, ü since the 19th century. The early Cyrillic alphabet, used to write Old Church Slavonic, also employed diaeresis. In Udmurt language diaeresis is also used with consonat letters З,Ж.

## How to produce the characters on computers

The ISO 8859-1 character encoding includes the letters ä, ë, ï, ö, ü, and their respective capital forms, as well as ÿ in lower case only (Ÿ was added in the revised edition, ISO 8859-15). Dozens of more letters with the diaeresis are available in Unicode. Unicode also provides the diaeresis as a combining character U+0308. Unicode treats the umlaut as the same diacritic mark as diaeresis, and does not encode seperate characters for the same letter with umlaut and with diaeresis. In those cases where umlauts must be distinguished from diaeresis, the special character U+034F COMBINING GRAPHEME JOINER (CGJ) can be used:

For diaeresis: X + CGJ + COMBINING DIAERESIS (e.g. a͏̈)
For umlauts: X + COMBINING DIAERESIS (e.g. ä)

It is then up to the user agent and typeface being used to provide meaningful distinction between the two characters.

The HTML entities for these characters all end in uml; e.g. &auml; = ä. These entities however use the Unicode diaeresis codepoints when rendered.

TeX also allows double dots to be placed over letters in math mode, using "\ddot{}", or outside of math mode, with the \" control sequence:

$\mathrm{\ddot{a}\ddot{b}\ddot{c}\ddot{d}\ddot{e}\ddot{A}\ddot{B}\ddot{C}\ddot{D}\ddot{E}}$

However this will give the diaeresis-style dots that are too far above the letter's body for good typographical umlauts. TeX's "german" package should be used if possible: it adds the " control sequence (without backslash) which gives nice umlauts.

On the Apple Macintosh, the diaeresis is produced with the keystroke Option+U, followed by the character to receive the diaeresis.

Using Microsoft Word, the diaeresis is produced by pressing Ctrl+Shift+:, then the letter.

## Time derivatives in mathematics

The derivative with respect to time is often represented as a dot above a variable. Two dots represents the second derivative.

${\dot{a}} = {\mathrm{d} \over \mathrm{d}t} a$
${\ddot{a}} = {\mathrm{d} ^2 \over \mathrm{d} t ^2} a$

This may be contrasted with the more common notation for a derivative using a prime:

$f'(x) = {\mathrm{d} \over \mathrm{d}x} f(x)$
$f''(x) = {\mathrm{d}^2 \over \mathrm{d}x^2} f(x)$