Vowel Harmony Q

Hi,

There are not a small number of vowel systems that have just four vowels,
where the four vowels are /a/, /e/, /i/ and /o/.   I was wondering: Would a vowel
harmony system be possible where the relationship was a Z relationship?
(That is, put those vowels into the places they'd fall into on the vowel space,
and connect them with a Z.)   What that would entail is, first, abandoning the
current thinking for vowel harmony, and then going back to underspecified
vowels.   To be more concrete...

Vowel 1: I

/I/ > [i] / V[-back]_
/I/ > [o] / V[+back]_

Vowel 2: E

/E/ > [e] / V[-back]_
/E/ > [o] / V[+back]_

Vowel 3: A

/A/ > [e] / V[-back]_
/A/ > [a] / V[+back]_

In actuality, you'd have four underspecified vowels, but two would behave
identically: O and E.   For the others, when the high vowel wants to show up as
front, it goes to its closest counterpart, which is [i].   When it wants to
show up as back, it has a choice of [o] and [a], since those are the sounds
available.   The higher of the two is [o], so it shows up as [o].   With the mid
vowels, they're on the same level, so they behave as expected.   The low vowel
behaves like the high, but in reverse: When it's back, it shows up as the
lowest back vowel possible, which is [a].   When it's front, it shows up as the
lowest front vowel possible, which is [e].   What this would lead to is a very
strange looking system, such as the following:

tan = bird
lis = dog

-tAs = ben.

tantas = "for the bird"
listes = "for the dog"

-kEl = dat.

taNkol = "to the bird"
liskel = "to the dog"

-pIr = enessive (on)

tampor = "on the bird"
lispir = "on the dog"

Is such a system feasible?   Do any four-vowel languages like the above even
have a vowel harmony system?   Or how about three vowel languages?   For some
reason it doesn't seem likely.

-David

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