Why did Finnish and Sami noun-final A and I flip over?

Question

I noticed a weird sound correspondence between Finnish and Northern Sami, and that is a list of words which pairwise end in -a or -ä in Finnish (this is the same archephoneme), and end in -i in Northern Sami.

• päivä, beaivi. A day. Or, a sun.
• aika, áigi. Time.
• kala, guolli. A fish.

Then there's a list of words that do exactly the opposite:

• kieli, giella. A language.
• neiti, nieida. A girl.

I can only think of one example that doesn't fit into this list, (this one can maybe be explained away by differing morphology because it's a different part of speech) and that is

• neljä, njeallje. Four.

It looks like in all cases, Eastern Saamic languages like Kildin, Skolt and Ter, together with Estonian and Hungarian for some reason, have lost this final vowel.

Now, I don't know much Sámi, and even less Finnish/Karelian, so this small sample size might be misleading me, but it looks like -a/-ä and -i swapped places here. How can that have happened?

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Edit: Oh yeah, how could I forget these:

• yksi, okta. One.
• kaksi, guokta. Two.
• kolme, golbma. Three.

So the sound change applies to "one" and "two", but not to "three" or "four"? Now this is getting bizarre.

Answer 1

I recommend Pekka Sammallahti's historical analysis (collectively, and I think most extensively in The Saami languages). He does does not go straight from proto-FS to North Saami or base his analysis on direct Finnish-NS comparisons, and in his work there are intermediate reconstructed stages. In the case of "language", NS <giella> is from Proto-Saami [kiel̀e̮] which in turn is from PFS [kēli]. In "fish", PFS [kala] becomes Proto-Saami [kuol̀ē], then NS <guolli>, which he treats phonemically as /kuollii/ (I don't entirely agree with that choice but it has its merits). Analogously PFS [äjmä] 'needle' becomes Proto-Saami [āj̀mē] → NS <áibmi> = /aajˈpmii/.

His Appendix C (p. 181-189) traces the vowel developments in great detail. One thing to note is that vowels have to be considered in pairs, because of mutual influences. The stages of development for "needle" are [äjmä] → [äjma] → [äj̀ma] → [āj̀mā] → [āj̀mā] → [āj̀mɛ̄] → [āj̀mē] (Proto-NS) then finally <áibmi> in the modern language. I don't know if you are familiar with the UPA. For some reason he does not give a complete tracing of "language", but the parts that he does give and the analogous examples indicate that the final vowel of PFS [kēli] was not lengthened – the "reason" for the divergence relates to lengthening of final low vowels.

As far as numerals are concerned, his reconstructions are e̮k̀te̮, kuok̀tē, kol̀me̮, ńeal̀jē and his NS forms are <okta, guokte, golbma, njeallje>, which the Sámi-Dáru Sátnegirji agrees with. Diphthongs [ui,ie,ea,oa] before mid vowels are highly anomalous in the language, which combined with number paradigm pressure (a common complication in historical linguistics) nudges the final vowel to [a]. I don't know anything about the distribution of guokte ~ guokta; I know that Kárášjohka speakers often have [guekta].

BTW Álgu-tietokanta is a useful tool with numerous data citations, though it doesn't shed light on the final [e] problem for numerals.