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In linguistics, a diaeresis or (American English only) dieresis (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 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 name Zoë. It is called trema in Dutch, tréma in French.
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 usually silent in the letter combinations gue and gui, but in word like vergüenza ("shame") or pingüino ("penguin") the u is in fact pronounced forming a diphthong with the following vowel ([we] and [wi] respectivelly).
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] respectivelly). 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 [b@'in@] ("neighbour", feminine), diürn [di'urn] ("diurnal").
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 an umlaut. Strictly speaking an umlaut is two bars above the letter rather than two dots, but in most typescripts it is represented by two dots and is undistinguishable from diaeresis. Since these bars derive from a small 'e' written above the letter it is considered correct usage to use a following 'e' instead of the umlaut.
In Finnish, Hungarian and North Germanic languages (i.e., Danish, Icelandic, Norwegian and Swedish) characters looking similar to German umlauts (ü, ä, and ö), and representing sounds similar to the corresponding sounds in German. Despite this, they are in fact considered as letters of their own merits, as is å. As it is not a case of marking grammatical variation, i.e. of tempus or modus, nor of syllable modification, it is in fact neither a case of umlaut nor of diacritical marking. Hence it ought to be improper to call these characters umlauts; however, no better name is known in English. Note that these letters ought to be written with two dots above always: unlike in German it is not correct to replace them with a following 'e'.
Using the ISO-8859-1 character encoding, one can type the letters ä, ë, ï, ö, ü, and ÿ. Dozens more letters with the diaeresis are available in Unicode. Unicode also provides the diaeresis as a combining character.