～けむ

The auxiliary verb (助動詞) ～けむ is probably a combination of the mizenkei of the perfect aspect marker ～き and dubitative auxiliary verb ～む. As such, it is governed by the ren’youkei. Though it is often grouped with ～らむ, it lacks the evidentiality that ～らむ has. It conjugates as a defective yodan verb lacking the mizenkei, ren’youkei, and meireikei.

The conjunctive particle ～ば cannot attach to the izenkei. ～けむ is also not to be confused with the old mizekei of adjectives (～け) and dubitative ～む (which would subsequently mean “is probably <adj>”). ～けむ has two uses:

• 過去疑義 Past Dubitative Mood

This is very simply expressing doubt or stating very general hearsay (this frequently being the rentaikei) about a past event. The translation would be ～ただろう、～たとかいう、～たようだ.

いにしへにありけむ人も （遠い昔にいたという人も) The people who are said to have lived in the distant past also…

This use may appear paraphrastically to indirectly state a past that is actually known.

• 過去の事情の推量 Past Inferential Mood of Cirumstance

Often (but not always) appearing with an interrogative word or adverb, this use expresses a conjecture or reflection about a past event with reference to cause, reason, degree, time, place, method, or person(s) involved. The resulting sentence can be interrogative (i.e. How nice must it have been?) or declarative (i.e. How nice it must have been!) in nature. It is more common that the above usage.

これをいみじと思へばこそ、記しとどめて世にも伝えけめ (これを素晴らしいと思ったからこそ、本に書き記して後世にも伝えたのだろう。) I wonder if they wrote it down and conveyed it to their posterity for the very reason that they thought it was wonderful.) [reason – explicit]

妻別れ悲しくありけむ (妻と別れてなんて悲しかっただろう。) How sad it must have been to be separated from his wife! [degree-unexpressed]

君や来し我や行きけむ (あなたが来たか、私が行ったか。) Did you come to me, or did I go to you I wonder? [people involved – explicit]

～き

The auxiliary verb （助動詞）～き is added to the ren’youkei verbs, true adjectives, pseudo-adjectives, and some auxiliary verbs. Like ～けり, it conveys the past tense. Unlike ～けり however, ～き denotes a past tense that was experienced first hand by the subject. Therefore, we’ll translate ～き as ～た.

The conjugation of ～き is completely irregular and unpredictable. Furthermore, it’s use with the verbs 来 and す is very sporadic. Instead of attempting to explain the usage in words, I think it is easier to put everything in one conjugation table.

* せ is used only in conjunction with the verbal particle ば. This creates a what’s called the counterfactual provisional mood （反実仮想）. That is, it’s the same as the regular provisional mood （～えば）except the condition is the opposite of what the known reality is. For this reason, it’s often used in complaints or indirect desiderative statements that use words like ものを, まし, and とも.

Ex) 風が止みせば、暖かくあらまし。（風が止んだならば、暖かくなるはずなのに。。）(If they wind would stop, it would be warm but… [ the reality is that it isn’t stopping].)

酒ありせば、飲まましものを。（酒があったならば、飲むのに。。）(If there were sake, I would drink it but… [the reality is that there is none].)

～き does not occur in the ren’youkei nor the meireikei.  From the chart, you can see that it takes different stems for す and 来 depending on its own form. The forms in parentheses are possible but less common alternatives. Lastly, ～き does not occur in the shuushikei with 来.

Ex)  昨日買ひし書読まむ。（昨日買った本を読むつもりだ。）(I intend to read the book I bought yesterday.)