イ音便 | Japanese with Anime

In Japanese, i-onbin イ音便 is a change in pronunciation often seen in conjugations where a kana 仮名 of the word gets pronounced as i い instead.

For example: the past form of sagasu 探す is sagashi-ta 探した, but the past form of kaku 書く, isn't kaki-ta 書きた, it's kaita 書いた, with an i い.

Explanation

Like all other changes in pronunciation, i-onbin exists because of the following process:

You make a word out of two morphemes, like kaki 書き and ta た.
Logically, the outcome is the sum of the morphemes, kaki-ta 書きた, and that's how you're supposed to pronounce it.
In practice, people pronounce it ~~wrong~~ differently, kaita 書いた, because the way it's "supposed" to be is too difficult to pronounce naturally.
The official orthography of the word changes to match its usage in real life, and a linguist comes up with a term for the phenomenon: i-onbin. Not necessarily in this order

連用形

The i-onbin affects the ren'youkei form of godan verbs ending in ku く and gu ぐ, but only under certain circumstances.

In general, the ren'youkei form is derived by changing the vowel of the ending of the verb to ~i. If the case of ~ku ～く, that's ~ki ～き, and for ~gu ～ぐ, that's ~gi ～ぎ.

sagasu
探す
To search.
sagashi
探し
The search.

kaku
書く
To write.
kaki
書き
The writing.

oyogu
泳ぐ
To swim.
oyogi
泳ぎ
The swimming.

There are many auxiliaries that attach to the ren'youkei above.

For example, the jodoushi 助動詞 ~masu ～ます:

sagashimasu
探します
To search. (polite.)
kakimasu
書きます
To write. (polite.)
oyogimasu
泳ぎます
To swim. (polite.)

And the auxiliary adjective ~yasui ～やすい:

sagashi-yasui
探しやすい
Easy to search.
kaki-yasui
書きやすい
Easy to write.
oyogi-yasui
泳ぎやすい
Easy to swim.

The i-onbin only manifests when the jodoushi ta た or te て are suffixed to the ren'youkei.

The ~ta ～た jodoushi creates the past form:

sagashita
探した
Searched.

*kakita
~~書きた~~
(wrong.)
kaita
書いた
Wrote.

*oyogita
~~泳ぎた~~
(wrong.)
*oyoita
~~泳いた~~
(also wrong, since ~gu ～ぐ has dakuten 濁点, ~ta ～た gets dakuten, too.)
oyoida
泳いだ
Swam.
- The ~da ～だ thing is a separate phenomenon called renjoudaku 連声濁.

While ~te ～て has various functions, like asking people to do things, or connecting to actions together.

sagashite
探して
Search [it for me].
Search, and.
kaite
書いて
Write [it for me].
Write, and.
oyoide
泳いで
Swim [for me].
Swim, and.

Note that i-onbin applies to derived forms of the ta た and te て jodoushi.

For example, the conditional ~tara ～たら jodoushi is derived from ~ta ～た, so i-onbin applies to it, too.

kaitara
書いたら
If wrote.
oyoidara
泳いだら
If swam.

On the other hand, the desiderative ~tai ～たい jodoushi has nothing to do with ~ta ～た, and gets attached to the ren'youkei without i-onbin.

kakitai
書きたい
Want to write.
oyogitai
泳ぎたい
Want to swim.

います

There are a few words that don't fit in the usual rule above, but that normally receive i-onbin when attached to ~masu.

degozaru
でござる
To be.
degozari
でござり
(ren'youkei.)
degozaimasu
でございます
(same meaning, polite.)

ossharu
おっしゃる
To say.
osshari
おっしゃり
(ren'youkei.)
osshaimasu
おっしゃいます
(same meaning, polite.)

According to the dictionary, i-onbin only affects the syllables ~ki ～き, ~gi ～ぎ, ~shi ～し, and ~ri り.

Consequently, the phrase suimasen すいません, "[I'm] sorry," isn't i-onbin, but merely a relaxed pronunciation of sumimasen すみません.

連体形

The i-onbin also seems to have affected the rentaikei 連体形, attributive form, of ku-adjectives and shiku-adjectives, which are kind of archaic, but I'm including them here anyway.

Such attributive form would end in ~ki, like atsuki 熱き, and utsukushiki 美しき, but end up becoming atsui 熱い, "hot," and utsukushii 美しい, "beautiful," instead.

Maybe ku-adjectives and shiku-adjectives are the origin of the modern i-adjective? I don't know for sure, but they seem somehow related.