This answer cites some numbers for the count of distinct syllables of a couple of languages.
And I read on brilliant.org that more distinct syllables mean more knowledge transfered per second.
Is there a count of distinct syllables for Arabic?
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Arabic is a macro-language and the facts differ substantially across dialects. The main variables are whether onsets can have two (vs. only one) consonants, or two (vs. only one) coda. There is also variation in the number of consonants (e.g. whether θ, ð have become t, d). The number of vowels also varies, for example some dialects have just long and short /i u a/ and some have mid vowels and schwa. Finally, some consonants only appear in roots (e.g. /θ, ħ, ʕ/, and /ʃ/ in some dialects (depends on whether they have the negative suffix /-ʃ/), but there are limits on what consonants can appear in adjacent root positions (for example, /td/, /χʁ/ are not possible root sequences), which affects the possibility of a syllable [χiʁ]. Lastly, there are in some Saudi dialects syllable-positional restrictions of gutturals.
All that said, there are generally not the kinds of specific sequencing restrictions that you find in English, so the possible syllables is generally "anything allowed given the CV canon of the dialect, plus the segmental inventory".
The exact number of distinct syllables in Arabic, like in many other languages, can vary based on the dialect, and it isn't straightforward to calculate due to the complexity of the language's morphology.
Arabic has 28 consonantal phonemes and 6 vowel phonemes (3 short vowels and 3 corresponding long vowels). The syllable structure of Arabic is typically CV (Consonant-Vowel) or CVC, and there are also instances of CVCC or CCVC.
If we were to simply multiply the number of consonants by the number of vowels, we'd get a basic estimate. However, this does not account for all the possible combinations or the rules of Arabic phonology and morphology.
Moreover, Arabic is a morphologically rich language, which means that the number of actual syllable combinations used in words can be quite large due to the inflections and derivations possible in the language.
Regarding your point about "more distinct syllables mean more knowledge transfered per second," it's important to note that this is an oversimplification. The rate of information transfer in a language depends on many factors, including the rate of speech, the complexity of the vocabulary and grammar, and the context in which the language is used.
So, while it's hard to give a specific number, it’s clear that Arabic, like all languages, has a rich syllabic structure that enables a wide range of expression. For a more precise count, linguistic research focusing specifically on Arabic syllable structure would be necessary.