orthography - Are there rules for when 'e' becomes 'a' in compound words?

For example:

• て＋つな＝たづな（手綱）


• め＋ふた＝まぶた（瞼・目蓋）


• かね＋つち＝かなづち（金槌）

The only thing I can see for sure is that the second word becomes voiced, but that's more of an after-the-fact thing than a rule that dictates when the sound actually changes from e to a.

Is there a rule or pattern to it?

Answer

e does not become a. Rather, it is the other way around: a becomes e. More specifically, there are two forms of e: e₁ and e₂. (See 上代特殊仮名遣) The rule is a + i > e₂. Both e₁ and e₂ merge into e after Nara period.

For reference, these pairs are termed 被覆形 and 露出形. The form without the -i suffix is 被覆形 while the -i suffixed form is 露出形.