How usual is it for languages to have multiple contrasting "neutral" vowels?

Question

First of all, I used scare quotes on "neutral" because I can't think of a better word. I was going to say "central vowels" but that would cover some "a"-like vowels whereas I am only thinking of "schwa"-like vowels. Anyway, on with the question...

• In English we have /ə/ in words like "the" (mid-central unrounded).
• In Bulgarian there is ъ → /ɤ/ (close-mid back unrounded) or /ɐ/ (near-open central).
• (Hebrew has ְ, the source of the English word "schwa", but it probably doesn't fit my idea of "neutral vowel").
• (In Japanese "i" becomes "neutral" after "sh" and "u" becomes neutral after "s", but I don't know whether they're the same or different.)
• In Korean there is ㅡ → /ɯ/ (close back unrounded).
• In Russian there is ы → /ɨ/ (close central unrounded).
• In Turkish there is ı → /ɯ/ (close back unrounded).

Of course many languages have no such vowels at all, such as Georgian, Italian, and Spanish.

But

• In Romanian there are two contrasting sounds, each with their own letter(s): ă → /ə/ (mid-central unrounded) and â/î → /ɨ/ (close central unrounded).
• Also Azeri has two letters, ə and ı but I couldn't find good info on the vowel phonology if they represent the same sounds as in English and Turkish.

So how unique is the case of Romanian in having two of these "neutral" or "schwa-like" vowels? Is Azeri another example? Are there other well known languages? Little known languages?

Answer 1

It seems there are two questions here: central unrounded vs. reduced ones.

Vowel reduction usually co-occurs with centralization and loss of roundness. It make sense because when spoken in a natural speed, there's no time to articulate it properly.

In Russian, unstressed vowels may reduce significantly, but it applies to any vowel, not only ы:

молоко [mə lɐ 'ko] (milk)
невозможно [nʲe vɐz 'moʐ nɐ] (impossible)
жалеть [ʐɨ ˈlʲetʲ] (to be sorry)

The vowels in first syllables are retracted to almost nothing, depending on a local dialect.

---

Maybe a good example is Thai. As many languages, it has an effect of epenthesis, an insertion of a vowel.
Usually, it is [a]:
ขนม [kʰà - nǒm] (dessert) - note that no vowels are written, but the 2nd one is phonetically much longer;

But it can be [ɔ]:
บริการ [bɔ̀ - rí - kaːn] (service)

See this article, sections III.b and IV.a

Answer 2

Vietnamese has four “central” vowels, orthographic â, ă, ư, ơ. There are at present two conflicting analyses. One group of scholars says that â, ă are a higher and a lower central vowel, and ư , ơ are a higher and a lower back unrounded vowel, but others say that â, ă are short central vowels and ư , ơ are long central vowels. Both theories have their strengths and their weaknesses.

There is a rather detailed discussion here: http://forum.wordreference.com/showthread.php?t=2727474