A sentence of a tonal language presents critical lexical information in the tones whereas a nontonal language such as English does not. What might be a way of developing useful statistics that measure and show this difference? In other words, how much of the information content is in the tones?
- E.G. let us say English is 100% nontonal and Mandarin can be shown to be 60% nontonal and 40% tonal [I do not really know what the statistics would be].
you could adapt the Functional Load measure first introduced by Hocket (1955; see wikipedia link for references including generalizations by Surendran&Nyiogi). For your purpose you could quantify the functional load of tone FL(t) e.g. the following way:
FL(t) = (H(L) - H(L_nt)) / H(L)
H(L) is the entropy of a collection of phonetic transcriptions derived from a pronunciation dictionary or by transcribed word n-grams. H(L_nt) is the entropy resulting from neutralizing the tones in the transcriptions. For English H(L)=H(L_nt), since the transcriptions for L and L_nt are the same, thus FL(t)=0. For Mandarin H(L) >H(L_nt), since L_nt contains more homophones. FL(t)>0 quantifies this information loss.
The Surendran&Levow speech prosody paper (see link) might quite well match your needs.
http://www.isca-speech.org/archive_open/sp2004/sp04_099.pdf
https://en.wikipedia.org/wiki/Functional_load
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