How many phonemic vowels are there in Middle Chinese? I'm interested in this question because Shanghainese has 16 phonological vowel/12 phonemic vowels, and was wondering if it had innovated more distinctions or not. Middle Chinese has 8 tonal distinctions but Cantonese innovated 2 more distinctions between high level - high falling and mid level - changed tone.
It seems that OP wants to know the relationship between Shanghainese and Middle Chinese. I recommend reading the book 上海市区方言志 published by 上海教育出版社 in 1988, which has a whole chapter devoted to exactly that. Because there is too much content I'll just post part of the table of contents here:
If OP wants to know more about Middle Chinese, you can read 音韻學概論 by 麥耘. (There are many controversies around the reconstruction of Middle Chinese. Use this book just as an introduction.) According to this book, the main vowels are as follows (allophones are in the brackets):
Note that vowels in Chinese are not treated in isolation. 韵母, which is 介音 + vowel + 韵尾, is usually a unit. In Shanghainese many 韵尾s are dropped or merged with the main vowel. So you can't directly compare the number of vowels and conclude on whether there is innovation.