上代特殊仮名遣い【じょうだいとくしゅかなづかい】 is a Nara-period practice in which two distinct versions of certain syllables (called 甲類【こうるい】 and 乙類【おつるい】, and denoted by subscript 1 and 2 in Latin script) were consistently denoted using different manyogana. For example, the word we now write as 上【かみ】 is /kami1/, which could be rendered with the second syllable as 美, while 神【かみ】 is /kami2/, which could be rendered with the second syllable as 尾.
The Wikipedia article states that "the phonetic difference [between the two types] is unclear", so it looks like this isn't a solved problem. Even so, I would like to know what we do know about the phonetic differences between the 甲類 and 乙類 syllables (if we know anything at all).