Prelude: Yes, I'm back-to-back posting about arcane Chinese language trivia. But with the week off for Chinese New Year, I've been spending a lot of time studying and thinking about these issues.
Shortly after posting earlier today on unique pinyin combinations, I discovered a terrific and related post about the pinyin chart on a site called Laowai Chinese. The comments section is recommended reading in addition to the post.
Albert from Laowai Chinese reckons there are 409 possible pinyin sound combinations. However, the actual number of syllables is somewhat debatable, because different pinyin charts and dictionaries list different possible combinations. Here is a chart that I created that includes 412 combinations:
The three extra combinations that I included that Albert didn't are tei 忒, kei 剋, and rua 挼.
On the other hand, here's a list that includes 416 possible sounds. Although that list omits dia, rua, and tei, it includes these that I don't: diang, shong, yai, nia, sei, lün, and lüan. But I'm not so sure these are valid, since I can't find any characters for these combinations.
Ok, last comment on this today. Here's a pretty cool online pinyin chart that includes audio pronunciation. This chart includes certain obscure combinations like tei, kei, den, eng, dia, rua, and chua, but still omits others like lo, yo, and ei.