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This is somewhat related to the discussion of classical auxiliary verb ふ, mentioned in the answer to snailboat's question, What is the わ in 忌まわしい and 嘆かわしい?.

Another apparent iterative / repetitive ending that I've bumped into is る, attaching not to the 未然形【みぜんけい】 but instead to the old 終止形【しゅうしけい】. This suffix shows up much less often. Examples that come to mind are まく・まくる and むく・むくる, but I think there may be a few more that escape me at the moment. According to Shogakukan's Kokugo Dai Jiten dictionary, this form appears to have evolved from the classical 連体形【れんたいけい】, formed by adding る onto the 終止形【しゅうしけい】 for 二段{にだん} and 一段{いちだん} verbs (both 下{しも} and 上{かみ}). (I almost listed あく・あくる above, but I realized that あくる here is still restricted to 連体-only usage.)

Does anyone have any information on the process whereby this 連体形 form evolved into an apparent iterative/repetitive? Alternatively, does anyone have any explicit explanation of this formation and its semantic uses?

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Are you aware that "iterative" and "repetitive" are terms for forms of aspect? Is that what you mean? – Thomas Gross May 20 '14 at 19:02
Re: aspect, yes. Have a look at the linked thread, that mentions the repetitive / continuative aspect conveyed by the auxiliary ふ. This る seems similar, but much more limited in use. – Eiríkr Útlendi May 20 '14 at 22:59
As you found out, まくる and むくる are the 連体形 of まく and むく. Their structure is mak-uru and muk-uru, rather than mak-u-ru and muk-u-ru because 終止形 is an inflectional suffix, and aspectual affixes are usually derivational. But it is rare for a derivational suffix to follow an inflectional one. Also note that the first /u/ of the -uru was replaced by /e/ because these verbs are 下二段. There is nothing especially iterative or repetitive about the 連体形 of the above verbs. The property resides in their lexical aspect. – Thomas Gross May 21 '14 at 7:14
@ThomasGross -- 1) まく is a 五段 verb that apparently evolved from a 四段 verb, and as such, the 連体形 would be まく, not まくる. Likewise for むく. Also, although both root verbs apparently had 下二段 variants, these are the intransitive forms, whereas the 四段 forms and the -る forms are transitive. I am left thinking that this -る is not the usual 連体形. 2) Not sure what you mean by aspectual affixes are usually derivational. Could you expand on that? Do you mean similar to how iterative / continuative ふ may have derived from あふ? – Eiríkr Útlendi May 21 '14 at 22:13
It has been known at least since Bybee 1985 that the morphemes after the verb appear in a specific order: valence - voice - aspect - tense, etc. Iterative, progressive, repetitive, etc. express aspect. Note that aspect is closer to the verb than tense. Your assumption reverses that, and thus goes against the grain of established knowledge. Up until and including aspect, morphemes are derivational suffixes, from tense on, they become inflectional suffixes. In Japanese, a derivational suffix cannot follow an inflectional suffix. See the paper by Narrog, (Journal) Morphology 2010 vol20/1. – Thomas Gross May 22 '14 at 9:58

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