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I wish to compare the syllable diversity and length distributiin of different languages. En-Fr to start with, phonetically even more than in writing.
I want to check the theory that short word short phrase languages have a higher phonic diversity. Longer syllables which are more varied require smaller phrases to convey the same information.
Where can i find comparative phonic studies to enumerate syllable range and variability?
I assume you are interested in the number of possible syllables in a given language, and how that might relate to word length. This is not a property that is generally studied and there isn't a definite answer for English, though there is an estimate on the order of 16,000 syllables in this paper. This would be because of the number of segments that we have in English (more than Hawaiian, fewer than Ubykh) and the number of syllable types (more than Hawaiian, fewer than Polish). Length per se is probably irrelevant, since a language where every syllable is of the kind CCVCC is longer than one with (C)(C)V(C)(C) as its template, but the latter has more "syllable diversity".
Shona has about 642 possible syllables (or, twice that many) – it has much simpler syllable structure, limited to (N)C(w)V. Also, Shona words are on average longer than English words (actually, there are no single-syllable words in the standard dialect). The figure 642 comes from knowing the consonants of the language, which ones can be preceded by n or m, then doubling that for consonant-plus-w. I should knock off one from that count because expected [βw] becomes [ɦw]. Then multiply by the number of vowels. This is a theoretical limit, but I don't know whether [vwu] is actually attested anywhere in the language.
I do not know how you can really test "conveying the same information". Texts in Lushootseed seem to be kind of long given their information content, but that's because of style, not the language per se. You might take Bible translations as a standard text, since there was been a concerted effort to convey the same information in all translations. Unfortunately for your interest, you will not get versions transcribed into a uniform and phonologically justified manner, instead you will get spelling with tri- and quadrigraphs for single segments (rather than use fancy IPA letters). So you would have to read up on spelling conventions for the language to know that Hmoob doesn't have a consonant cluster at the beginning and a [b] at the end. It will be difficult to create the kind of data that you are looking for, and much harder to find it already published.
There are other factors that will affect the validity of such a study. Although [vw] is a possible syllable in Shona and 5 syllable long words are hard to avoid on ordinary conversation (nobody has studied corpus frequency to the best of my knowledge), [vw] has a very low frequency of occurrence and probably never appears in a syllable more than 3 from the end. There is really just a C(w)V(N)C core which exploits the full range of segment possibilities, then many prefixes and suffixes of the type (C)V- and -VC- drawing on a dramatically decreased set of consonants and vowels. You might expect there to be about 1.0906242e+14 possible 5-syllable words (20 syllable words are not a problem in this language), but I suspect that you would find that the actually attested or acceptable number of syllable-permutations is many orders of magnitude less that that figure.
While the information content of a syllable can vary considerably between natural languages this fact is largely compensated by speech rate: Languages with simple syllables are spoken at a faster pace than languages with complicated syllables. The net effect is an almost constant information rate for very different natural languages, see this answer and the paper quoted therein.
Actually, I remember an article (Oh et al. 2013) showing that shorter syllables languages (shorter phonetic debit for syllables) needed more syllables to form words (Japanese) ans longer syllables debit languages needed less syllables per word. But eventually, the ratio between these two factors was about the same.
Maybe this SE answer can assist with your analysis. It compares languages by the number of existing syllables.
