Signaries and Statistics

It is obvious that the more complexity of the possible syllables of a language interacts with their numbers. A language such as Fijian that permits only open syllables is bound to have a fewer syllables than one that permits syllables with complex initial and final margins of the type of English strength. Also it would appear that a language whose basic lexical stratum is monosyllabic needs more syllable types than one that has a basic stratum of polysyllabic lexemes. A writing system that targets the syllable as the key function unit thus means different things for different languages. (...)

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The Chinese Script Reform Committee says that there are more than 1,200 syllables in Mandarin, this total number of possible syllables is much smaller than that in English. (...)

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Syllable Structure: The Limits of Variation
By San Duanmu

The total number of possible syllables, therefore, should be the number of possible onsets times the number of VX rhymes times the number of choices for the extra final C.

Possible monosyllables in English. Total = Onsets x VX x C = 59 x 298 x 10 = 170,510

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Clearly, this is an order of magnitude that makes syllabaries unmanageable. In practice there are no, and never have been any, complete syllabaries in the above sense, which confirms the more general truth that no writing system encodes every distinction relevant in its language. Various strategies were developed for syllabic writing to get by with signaries such smaller that the number of speech syllables. An inevitable consequence of this is a certain degree of syntagmatic complexity in combining graphic symbols unambiguously to denote speech syllables.

Where syllabic writing evolved, the number of symbols was gradually reduced. (...)

Much has been made of the economic advantage of syllabic writing over word writing, which stems from the fact that the number of the speech syllables of a language is closed while that of words is open. Gelb (1963) in particular considered the economizing on the inventory of signs was the driving force in the development of writing. This is the cornerstone of his theory. To be sure, the structural unit of writing has an effect on the size of a writing system's signary.