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The dagesh (דגש) is a diacritic used in the Hebrew alphabet. It is related to the nikud or vowel points and seems to have been added to Hebrew orthography at the same time. The dagesh is also known as Mapiq.

The dagesh is a dot which is drawn inside a Hebrew letter to modify its sound.
Though it's possible to add a dagesh to any letter, contemporary Hebrew only seems to use it for the letters bet ב, kaf כ & ך, and pe פ & ף.
The effect of the dagesh on the above letters is to turn a fricative sound into its equivelant plosive:

The dagesh is completely optional in modern, Israeli Hebrew and is usually not used. This might help explain why the names of the letters reflect the sound with the dagesh even though there is no dagesh present!

In computer typography there are two ways to use a dagesh with Hebrew text. Here are Unicode examples:

Combining characters

bet + dagesh: בּ בּ
kaf + dagesh: כּ כּ
pe  + dagesh: פּ פּ

Precomposed characters

bet with dagesh: בּ בּ
kaf with dagesh: כּ כּ
pe  with dagesh: פּ פּ

Some fonts, character sets, encodingss, and OSeses may support neither, one, or both methods.

This article currently only concerns the use of the dagesh in modern, Israeli Hebrew. Gritchka has sent me many notes on the use of the dagesh in Biblical Hebrew which I hope to incorporate.

Lonely Planet Hebrew Phrasebook
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