In a footnote to my previous post I passingly speculated that Finnic *ä-backing: *ä-ä > *a-ə (> late Proto-Finnic *a-i : *a-ë-) should perhaps be split in two phases: stem vowel reduction leading to a split from *ä-ə as an earlier stage, completion of the 1st-syllable vowel backing as a later stage.
I have already gathered some other evidence for this particular chronology, from the analysis of some forthcoming examples. But if I were to suppose for early Finnic an intermediate vowel *ȧ in these words, how should the situation be analyzed phonetically (or for that matter, phonologically)?
My initial thought was to posit a central vowel *ȧ (IPA [ä]). But this would have contrasted with both front *ä (IPA [æ]) and back *a (IPA [ɑ]); e.g. *särkə ‘roach’ : *sȧrńə (< *särńä) ‘ash tree’ : *śarwə ‘horn’. Such a crowded low vowel inventory is highly rare in the world’s languages.
But since I was also speculating that this *ȧ still induced front vowel harmony, perhaps a better alternative will be to reconstruct this as a fully open front vowel (IPA [a]). Contrasts between this and near-open [æ] are also rare, but this situation seems to be well salvageable by replacing the latter with an open-mid vowel *ɛ instead.
PU *ä in fact shows mid reflexes in most Uralic languages:
- In Samic, *ä-ə yields *ē-ë (though *ä-ä still yields *ā-ē).
- Erzya merges *ä with Proto-Mordvinic *e (from PU *i, *e) as /e/.
- I’ve seen [ɛ] rather than [æ] reported for some dialects of Moksha, though I don’t have a clear picture on the exact distribution of this.
- Mari reflects *ä as *e, which normally remains /e/ in all varieties.
- Permic reflects *ä most often as a vowel that has been reconstructed as Proto-Permic *ɛ, which in turn yields Komi /ɤ/, Udmurt /o ~ e/. PP *e > Komi /e/, Udm. /o ~ e/ is also common.  Some cases show Proto-Permic *a > Udm., Komi /a/, but they’re rarer and tend to involve messier data. I suspect this last vowel was in origin a rare conditional allophone at best, later strongly reinforced by loanwords from various sources.
- Hungarian reflects *ä as /ɛ/ ~ /eː/, the latter from Old Hungarian *ɛː.
- Far Eastern, Southern and Northern Khanty reflect *ä as tense /e/ (conventional Proto-Khanty *ee).
- All Samoyedic languages show a change *ä > *e. This looks like it would have to be dated as later than *e > *i (which does not apply to Nganasan), but the resulting “Late Samoyedic” *e is generally indeed realized closer to /ɛ/ than /e/.
Aside from Finnic, the only languages uniformly in favor of an open value are Mansi (*ä > *ää) and Surgut Khanty (*ä > reduced /ä̆/). The idea of an original open *ä thus rather starts looking as yet another Finno-centricism of Proto-Uralic reconstruction.
Suppose we consider Finnic and Ob-Ugric outvoted, and adjust the PU vowel system ever so slightly by reconstructing original *i *e *ɛ rather than *i *e *ä. This vowel-height inventory is well attestable from the world’s languages, and can also be encoded phonologically identically, with *ɛ as simply a [+open] vowel.
After the initial stage of *ä-backing in early Finnic, the inventory would be extended to four heights *i *e *ɛ *ȧ: a rarer setup, but again still quite well attestable (e.g. in English). To get from here to the attested Finnic setup, a counterclockwise mini-chain shift is required: *ȧ > *a [ɑ], *ɛ > *ä [æ]. The phonological makeup of this four-height system looks a bit more precarious, and may require assuming a feature like [+tense] making a fleeting appearence.
This all also has some unexpected synergy with the development of back open vowels in Western Uralic. I have already a good while ago outlined a defense of the following model:
- Proto-Uralic had labial *å [ɒ] in the first syllable, illabial *a [ɑ] in the 2nd syllable.
- In Proto-West Uralic, illabial *a in the first syllable arose thru three innovations:
- *ë > *a in all positions (*sënə > *sanə ‘sinew’, *mëksa > *maksa ‘liver’)
- *å-a > *a-a (*kåla > *kala ‘fish’)
- in palatal environments, *å > *a (*wåjə > *wajə ‘butter’)
- Remaining cases of *å later merged with *o in Samic and Mordvinic, with *a in Finnic (*śårwə > pre-S and pre-Mo *śorwa, pre-F *śarwə ‘horn’).
Assume now that the first point holds mutatis mutandis also in the case of front vowels: the PU vowel structure I mark as *ä-ä was not phonetically a fully harmonic setup either, but instead phonetically *[ɛ]-[a].  This provides a great motivation for height assimilation to *[a]-[a]. Such a change could perhaps be assumed to have been common to pre-Finnic and pre-Samic, and also substantially demystifies the phonetic motivation for Finnic *ä-backing. (Regardless, it will still have to remain unclear why, on the Finnic side, the stem vowel was concurrently reduced to *ə; much like it remains unclear why *å-ə in Samic and Mordvinic yields *o-a rather than *o-ə.)
Some further similarities:
- *ɛ-ȧ > *ȧ-ȧ is exactly parallel to *å-a > *a-a: a kind of sub-phonemic a-umlaut.
- The Finnic shift *ɛ(-ə) > *ä(-ə) is closely parallel to *å(-ə) > *a(-ə): both constitute a shift of non-cardinal vowels towards more cardinal values (though the former change is sub-phonemic, the latter an actual merger).
- The Samic shift *ɛ(-ə) > *e(-ə) is also closely parallel to *å(-ə) > *o(-a): both constitute a reduction of openness contrasts through raising. The former will have to be later than the merger of *e-ə with *i-ə — but as this change is shared with Mordvinic, dating it as quite early does not seem problematic to me. It may have begun e.g. as a push chain in early Samic, with the second merger then spreading to Mordvinic. (Indeed, perhaps also to Mari, where *e and *i seem to have identical reflexes across the line.)
Finally, one further interesting corollary of this model is probably that the split of *ä-ə and *ä-ä in Samic will end up being earlier than the a-umlaut of *e and *o to eventual ea and oa. This chronology will go quite well together with some other hypotheses of mine under work as well.
 As the two have seemingly identical outcomes in Udmurt, I suspect that their split might even be post-Proto-Permic.
 It would be also possible to reconstruct non-vowel-harmonic *ä-a = *[ɛ]-[ä], *å-a = *[ɒ]-[ä]. Despite vowel harmony being clearly reconstructible for both Proto-Finnic and Proto-Samoyedic, and at least probable for many of the branches in-between, I do not currently have a firm opinion on if vowel harmony existed in PU. There seem to be a number of indications that it could be late Turkic influence in at least (Hill?) Mari, Hungarian and Southern Mansi — but, on the other hand, all three have clearly been subject to reduction and loss of unstressed syllables, which could have already early on eliminated inherited vowel harmony (as also has happened e.g. in Livonian, standard Estonian, and dialects of Veps).