It's hard to overstate the intellectual puzzle this is! Classical Chinese scholarship had a developed body of proto-linguistics, including rime spelling, a sys

It's hard to overstate the intellectual puzzle this is! Classical Chinese scholarship had a developed body of proto-linguistics, including rime spelling, a system for phonetic transcription and analysis, which transcribed sounds using Chinese characters purely phonetically. It was used to indicate the pronunciation of characters, as well as foreign words in bilingual dictionaries and so on: https://en.wikipedia.org/wiki/Fanqie https://en.wikipedia.org/wiki/Fanqie The problem is, it's mostly self-referential. As the Wikipedia example gives, we don't precisely know how 東 was pronounced in 1000 AD from a fanqie dictionary entry. It would tell us something like that 東 (dong1 in Mandarin or dung1 in Cantonese today) was pronounced in the author's time like the initial consonant in 德 (de2, dak) with a closing syllable pronounced like 紅 (hong2, hung4). And of course, a dictionary from a thousand years before that, or even just from a speaker on the other side of China, might give a different entry... If you collect all the known fanqie pronunciations given in all the eras from all the probable sister languages, and especially when you start comparing with our knowledge of other languages (Japanese, Sanskrit, etc.) you can start to piece together the puzzle and get a rather good understanding of Chinese historical sound change. Chinese scholars back then were aware, on some level, of sound change, especially later in the Ming and Qing dynasties, but there was no general theory to address it, and the apparent contradictions in the ancient poetry and the old rime dictionaries were a source of a lot of perplexity.