An abjad, also called a consonantary, is a writing system wherein the only signs are consonants, and vowels are left unwritten. (Sometimes vowels that are sometimes consonants, like y and w, are written also.)

The name "abjad" comes from two letters of the Arabic abjad.

Semitic languages, so I understand, are well suited for abjads, because their morphology is based on the manipulation of consonantal roots. Hebrew, Aramaic, and Egyptian also use or used abjads.

Some of these writing systems use diacritics called matres lectionis ("mothers of reading") to indicate vowel sounds when teaching the language, or when otherwise important (for example, in sacred writings).

One correction to the above is that the name abjad is derived from four Arabic letters. They are the first four letters of the Hebrew alphabet/abjad. Huh?

The Semitic alphabets came from a common ancestor, and the letters had a certain order, and the Greeks and the Romans took over that order, modifying only in some cases the pronunciation. So the common Semitic ancestor gave rise to, among others,

Arabic script however, as is well known, is not separate letters but a very flowing fusion. In the course of its evolution many letters became extremely similar, and a system of dots above and below them had to be devised to distinguish one from another. For example, the letters B, T, and TH are identical in Arabic apart from their dots.

The identical letters were moved up together into the topmost slot for that shape. So the order of the Arabic alphabet became A, B, T, TH, J, ...

However, in several ways they still retain the memory of the old Semitic order. The name abjad, A-B-J-D, is one.

Another is in using them as numbers. As we use (a) (b) (c) to list things, the same can be done in Greek and Hebrew. (The superstition of gematria or numerology also uses this.) In Arabic they number in the old order, alif-ba-jim-dal, not in the current order of the alphabet.

The name Abjad is also specifically used to refer to the Arabic script, when talking about languages such as Malay or Hausa that were formerly written in it.

The letters of the Arabic abjad/alphabet in the modern order are: alif, ba, ta, tha, jim, ha, kha, dal, dhal, ra, za, sin, shin, sad, dad, ta, za, ain, ghain, fa, qaf, kaf, lam, mim, ha, waw, ya. Because of the limitations of HTML, I have had to use the same romanization of different letters: ha, ta, and za each represent two different letters and sounds.

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