Again some of these songs still rhyme in modern varieties of Chinese, but many do not. This was attributed to lax rhyming practice until the late-Ming dynasty scholar Chen Di argued that a former consistency had been obscured by sound change. The systematic study of Old Chinese rhymes began in the 17th century, when Gu Yanwu divided the rhyming words of the "Shijing" into ten rhyme groups ("yùnbù" ). These groups were subsequently refined by other scholars, culminating in a standard set of 31 in the 1930s. One of these scholars, Duan Yucai, stated the important principle that characters in the same phonetic series would be in the same rhyme group, making it possible to assign almost all words to rhyme groups. Assuming that rhyming syllables had the same main vowel, Li Fang-Kuei proposed a system of four vowels , , and . He also included three diphthongs , and to account for syllables that were placed in rhyme groups reconstructed with or but were distinguished in Middle Chinese. In the late 1980s, Zhengzhang Shangfang, Sergei Starostin and William Baxter (following Nicholas Bodman) independently argued that these rhyme groups should be split, refining the 31 traditional rhyme groups into more than 50 groups corresponding to a six-vowel system. Baxter supported this thesis with a statistical analysis of the rhymes of the "Shijing", though there were too few rhymes with codas , and to produce statistically significant results. The following table illustrates these analyses, listing the names of the 31 traditional rhyme groups with their Middle Chinese reflexes and their postulated Old Chinese vowels in the systems of Li and Baxter. Following the traditional analysis, the rhyme groups are organized into three parallel sets, depending on the corresponding type of coda in Middle Chinese. For simplicity, only Middle Chinese finals of divisions I and IV are listed, as the complex vocalism of divisions II and III is believed to reflect the influence of Old Chinese medials and (see previous section). There has been much controversy over the relationship between final consonants and tones, and indeed whether Old Chinese lacked the tones characteristic of later periods, as first suggested by the Ming dynasty scholar Chen Di. The four tones of Middle Chinese were first described by Shen Yue around AD 500. They were the "level" ( "píng"), "rising" ( "shǎng"), "departing" ( "qù"), and "entering" ( "rù") tones, with the last category consisting of the syllables ending in stops ("-p", "-t" or "-k").