What were the four Divisions of Middle Chinese ?

The text presented here is the final result of a series of versions of our research on the four divisions (or grades) of ancient Chinese (Middle Chinese) :1. (1998) Du chinois archaïque au chinois ancien : monosyllabisation et formation des syllabes tendu/lâche (Nouvelle théorie sur la phonétique historique du chinois), The 31st International Conference on Sino-Tibetan Languages and Linguistics, University of Lund, Swiden, Sept. 30th – Oct. 4th (22 pages). (Available: https://halshs.archives-ouvertes.fr/halshs-00927220)2. (2006) What were the four divisions (děng) of Middle Chinese ?, The 39th International Conference on Sino-Tibetan Languages and Linguistics, University of Washington, Seattle, September 15-17 (12 pages).3. (2009) What were the four Divisions of Middle Chinese ? Diachronica 26(2): 184 213.4. (2014) 中古汉语四等的来龙去脉 Zhōnggǔ Hànyǔ sìděng de láilóngqùmài [Origin and development of the Four Divisions of Middle Chinese / Le pourquoi et le comment des quatre divisions du chinois ancien]. 语言学论从 Yǔyánxué Lùncōng [Bulletin of Linguistics] 49: 312-349. 北京大学 [Beijing University]. This is translation of the third version, enlarged with new paragraphs.5. The present text is the enlarged version that was translated into Chinese.International audienceDetermining the nature of the four Divisions of the Qièyùn is a fundamental problem in the study of the phonetic history of Chinese. Analyses by Baxter and Pulleyblank make it possible to bring out two major changes from Old Chinese to Middle Chinese: a two-way split of the vowel system, and later the lenition of medial -r-. The use of models drawn from Mon-Khmer voice type register languages made it possible to reconstruct the phonetic bases of the four divisions. Div. I consists of tense rimes, Div. II consists of tense, velarized rimes resulting from medial -r-, Div. III consists of lax/breathy rimes. As for Div. IV, it consists of (non velarized) rimes with the diphthong ie