It seems to be generally understood that transitive/intransitive verb pairs, when they are not a 四段活用 and a 二段活用 that share the same 終止形, were created by taking a base verb, whether transitive or intransitive, and adding an Old Japanese auxiliary - す for transitivity, and る or ゆ for intransitivity - to the 未然形 to form the verb of opposite transitivity. For example, [減]{へ}る (intransitive) + す = [減]{へ}らす (transitive).
But something confuses me - since auxiliaries like す、る、ゆ、ふ、etc. only attach to the 未然形, what is the deal with 二段活用 verbs? For example, [覚]{さ}む is a 下二段活用 intransitive verb, and [覚]{さ}ます is its transitive variant.
Where does this -a stem in [覚]{さ}ます come from? The 未然形 of [覚]{さ}む is [覚]{さ}め, not [覚]{さ}ま like if it were a 四段活用. Would it not logically be [覚]{さ}めす instead? [上]{あ}ぐ becomes [上]{あ}がる, [満]{み}つ becomes [満]{み}たす - all of these are 二段活用 verbs, which do not feature an -a stem in their 未然形, yet the opposite transitivity uses an -a stem. What is the reason for this?
This also seems to appear for カ行変格活用 verbs as well, as [出]{で}[来]{き}る -> [出]{で}[来]{か}す instead of でこす.
According to the Wiktionary etymology of あぢさはふ:
The initial adi is likely from the 䳑鴨 (ajigamo, “Baikal teal”),[1] while the derivation of sapapu is unknown.
One theory states from 障ふ (sapu), basis for modern 障える (saeru, “to hinder, interrupt”, transtitive) and 障わる (sawaru, “to disturb, harm”, intransitive). This is problematic as sapu is a 下二段活用 (shimo nidan katsuyō, “lower bigrade conjugation”) verb and not a 四段活用 (yodan katsuyō, “quadrigrade conjugation”) verb required for a 未然形 (mizenkei, “irrealis form”) ending in -a.
This seems to suggest that 二段活用 verbs cannot simply swap to an -a stem when an auxiliary is added (here being ふ).
There are also some verb pairs where both the intransitive and transitive verbs have auxiliaries on a non-verbal-未然形 root, like [外]{はづ}す and [外]{はづ}る, and there are also some curiosities like [消]{け}す and [消]{き}ゆ where the roots are not the same vowel. What is the reason for this as well?
