Edit: in the interests of attribution, much of this was from this page by an unknown author, Wikipedia, or Bricka's page on vowel systems.
I am stealing a classification system I found on one of those pages. It is as follows:
T indicates a triangular vowel system, by far the most common.
S indicates a square vowel system.
V indicates a vertical vowel system.
C indicates a "cubic" vowel system.
This is followed by the number of vowels, and:
C indicates that the system mostly has central vowels as its "extras".
R indicates that the system mostly has front rounded vowels as its "extras".
U indicates that the system mostly has back unrounded vowels as its "extras".
F means it has extra front unrounded vowels as its "extras".
B means it has extra back rounded vowels as its "extras."
L means it has extra laxed vowels as its "extras".
This is by no means hard and fast, but it is useful.
For the sake of easy analysis, I'll not analyze pure length, tone or nasalization, just vowel quality. I will also not include diphthongs.
One Vowel
There are no modern languages with just one vowel, with the very, very possible exception of Nuxalk (see below). One or two restructions of Proto-Indo-European have just /e/, but this is somewhat untenable, given that all of its daughters have at least three vowels (I think), many of its daughters have at least four or five, and you'd be hard-pressed to explain ablaut that way.
You could write the phonemic status of a conlang with just one vowel as probably just about anything you want, although it would probably have a most common vowel of a centralized vowel like [ə].
1
Code: Select all
ə
1a
Code: Select all
a
This too is rare. Some other reconstructions of PIE have given it two vowels, /e o/:
S2
Code: Select all
e o
V2
Code: Select all
ə
a
There are also several analyses of Mandarin Chinese that analyze it as having a V2 system, with the extra vowel phones coming from sequences of vowel and approximant. The Australian language Arrernte also has a V2 system, and the Ndu languages of New Guinea are rumored to have a V2 system as well. (The Ndu claim is particularly suspect; although they can all theoretically be analyzed as having a V2 system, at least one linguist has analyzed the Ndu language Iatmül as having twelve phonemic vowels. This is par for the course with strange little vowel systems.)
Because the only thing differentiating the two phonemes in a V2 system is height, they tend to have very wide ranges of allophones. In Arrernte, for example, /ə/ has the range [ɪ ~ e ~ ə ~ ʊ], with little regard for context.
Three Vowels
This is where we really get started; almost all languages have at least three vowels. Usually, this is the T3 system, as seen in Quechua, Inuktitut, Classical Arabic, most Australian languages, and Aleut:
T3
Code: Select all
i u
a
T3b
Code: Select all
e o
a
T3c
Code: Select all
i
o
a
Beyond this, there is the system V3, which is found in the Sepik family (of which Ndu is a subfamily) of New Guinea:
V3
Code: Select all
ɨ
ə
a
Code: Select all
ɪ~ʊ
ɛ~ɔ
a
V3F
Code: Select all
i
ɛ
a
Four Vowels
Here, we start to see that a language can have a triangular system, or a square one. The triangular-central-square analysis starts to lose its accuracy after about six vowels, but it's still useful for classificatory purposes.
Most languages with four vowels have some variant of T4, of course, since most languages have triangular systems. Usually this is T3 with some sort of addition:
Central Alaskan Yup'ik (in the short vowels only) and the Taiwanese language Rukai have T4C, which we'll refer to as just T4:
T4
Code: Select all
i u
ə
a
There is also the vowel system /i e a u/, which can be analyzed as being the square S4:
S4
Code: Select all
i u
e a
Code: Select all
i u
e
a
T4Fb
Code: Select all
i
e o
a
Finally, there is the V4 system, found only in the bizarre Marshallese language of Micronesia:
V4
Code: Select all
ɨ
ɘ
ɜ
a
V4 is basically the largest vertical vowel system that you'd ever see in nature. Past this point, the square-vertical-triangular split begins to become less and less useful.
Five Vowels
Here we find the most common vowel system, T5, found in Classical Latin, Modern Greek, Spanish, Hebrew, Japanese, Swahili, the Polynesian languages, and Basque:
T5
Code: Select all
i u
e o
a
T5C
Code: Select all
i ɨ u
e
a
T5B
Code: Select all
i ɨ u
o
a
S5
Code: Select all
i u
ə
e a
Most of the systems I could find were just T5 with an extra vowel.
T6C, with /ə/ added, is found in Nepali and Armenian, as well as Southern Welsh (in a pinch):
T6C
Code: Select all
i u
e ə o
a
T6Cb
Code: Select all
i ɨ u
e o
a
S6
Code: Select all
i u
e o
æ a
Common among conlangers, I think, is T6R:
T6R
Code: Select all
i y u
e o
a
S6R
Code: Select all
i ɨ
ø o
ɛ a
T6Rc
Code: Select all
i y
e ø o
a
Almost all systems past this point will be using T5 as a base.
In plain T7L, usually, /ɛ ɔ/ is added. This is the vowel system of Vulgar Latin, Italian, Bengali, Brazilian Portuguese, and Yoruba:
T7L
Code: Select all
i u
e o
ɛ ɔ
a
T7R
Code: Select all
i y u
e ø o
a
T7C
Code: Select all
i ɨ u
e ə o
a
T7Rc was found in Occitan, after a chain shift of VL ɔ -> o -> u -> y:
T7Rc
Code: Select all
i y u
e o
ɛ
a
Finally, there is T7Cb, found in Amharic:
T7Cb
Code: Select all
i u
e o
ɛ ə
a
Many of these are extended versions of T7L.
In T8C, found in Javanese, Catalan, São Tomean Creole, Lo-Toga (with fronting of /u/ to /ʉ/) and Slovene, /ə/ is added:
T8C
Code: Select all
i u
e o
ɛ ə ɔ
a
Here is T8F, found in Finnish:
T8F
Code: Select all
i y u
e ø o
æ ɑ
T8B
Code: Select all
i y u
e ø o
ɔ
a
T8R is the usual analysis- er, or a more usual analysis- of Mandarin:
T8R
Code: Select all
i y u
ɪ
e ə o
a
C8
Code: Select all
i u
ɪ ʊ
e o
a ɔ
Turkish has another system, C8R:
C8R
Code: Select all
i y ɯ u
e ø a o
My own dialect of American English would probably be S8L:
S8L
Code: Select all
i u
ɪ ʊ
ɛ ʌ
æ ɑ
By now we're well past the usual number of vowels for natural languages. The systems will start getting increasingly more baroque, but also much less common.
T9L is found in Maasai; it's T7L with lax variants of /i u/:
T9L
Code: Select all
i u
ɪ ʊ
e o
ɛ ɔ
a
S9C
Code: Select all
i ɨ u
e ə o
ɛ ɔ
a
S9R is- in a pinch- standard French (kudos to Legion):
S9R
Code: Select all
i y u
e ø o
ɛ ɔ
a
S9Rb
Code: Select all
i y ɨ ʉ u
e o
ɛ ɑ
S9L
Code: Select all
i u
ɪ ʊ
ɛ ʌ ɔ
æ ɑ
T9F
Code: Select all
i y u
e ø ɤ o
æ ɑ
T9Fb
Code: Select all
i y ʉ u
e ø o
ɛ ɑ
T9Fb
Code: Select all
i ɯ u
e ø o
ɛ ʌ
a
Ten Vowels
T10L is found in Hindi and Panjabi, and I believe several African languages with vowel harmony, where /ɪ ʊ ɛ ɔ a/ alternate with /i u e o ə/:
T10L
Code: Select all
i u
ɪ ʊ
e o
ɛ ə ɔ
a
T10R
Code: Select all
i y u
e ø o
ɛ œ ɔ
a
S10C
Code: Select all
i ɨ u
e o
ɛ ə ɔ
a ɑ
S10R
Code: Select all
i u
e ɘ o
ɛ ɐ ɔ
a ɑ
Past this point, almost everything you'll see is from Northwest Europe.
T11R takes T10R and adds a back variant to /a/. It's found in a language of Vanuatu called Sakao:
T11R
Code: Select all
i y u
e ø o
ɛ œ ɔ
a ɑ
T11Rb
Code: Select all
i y u
e ø o
ɛ œ ə ɔ
a
T11C
Code: Select all
i u
ɪ ʊ
e ɘ o
ɛ ɐ ɔ
a
Nothing major here, except for Selkup. At this point categorization starts to become an exercise in extremely iffy pedentry, so I'll stop:
Selkup
Code: Select all
i y ɨ u
ɪ
e ø ɘ o
ɛ ɔ
æ a
Code: Select all
i u
ɪ ʊ
ə
ɛ ɜ ɔ
æ ʌ ɑ ɒ
Everything on this list is a Germanic language.
Dutch
Code: Select all
i y u
ɪ ʏ o
e ø ə ɔ
ɛ
a ɑ
Code: Select all
i y u
e ø ə o
ɛ œ ɐ ɔ
a ɑ
Code: Select all
i y u
ɪ ʏ ʊ
e ø ə o
ɛ œ ɐ ɔ
a
Code: Select all
i y ʉ u
ɪ ʏ ʊ
e ø ɵ o
ɛ œ ɔ
a ɑ
Don't necessarily just copy a vowel system from this list.
You've probably noticed by now that certain patterns tend to recur. In particular, there are a lot of "base" vowel systems (/i a u/ (T3), /i e a o u/ (T5), and /i e ɛ a ɔ o u/ (T7L) in particular) to which languages add one or two "outliers". French and Hungarian, for example, add /y ø/ to T5 and T7L respectively.
Often you'll want to take a vowel system and add an extra dimension to it, like throwing in some central vowels, or a lax set of vowels.
For small vowel systems, most of the possible bases are covered in the overview- there simply aren't very many options. As I noted, vowels are kind of like a gas; they usually spread out to fill the vowel space very well. As a result, having a handful of vowels that are relatively close together is really only an option once you've already filled the space; a vowel system like /a ɑ ə/ is basically impossible, as is /i ɨ u/. (However, if your vowel system is very small, the vowels often will centralize a bit. Modern Quechua, for example, has /i a u/, but before the Spanish arrived it was more like /ɪ æ ʊ/.) Throwing in a random vowel often is justified when you're just one more than a "standard" system- I can't find a language that has /i y e a o u/, for example, but it wouldn't surprise me in the least if there was one, and it's certainly fair game for your conlangs.
"Filling the available space" is generally a good strategy in larger systems as well. E.g. I'd question the realism of a vowel system
Code: Select all
i ɨ ʉ u
e ə ɵ o
a
Code: Select all
i y ɨ u
e ø ə o
a
As your vowel system gets larger, you'll start to run out of places to put your vowels, and will generally want to play with things like roundedness. Germanic languages are so large in part because they have roundedness distinctions in a lot of vowels.
As it gets larger, too, it will get easier to throw in random vowels- there's nothing very symmetrical-looking about English, for example. It will also get a lot more unstable. Diphthongization is a classic way to deal with this; indeed it's one of the reasons English sounds so distinctive- it cleared off several vowels by making them diphthongs. Even so, there are universals that will pretty much be followed at any size: you're not going to have very many more back than front vowels (so /i a u o/ is- probably- a no-no; but then it's just Proto-Uto-Aztecan without /ɨ/, so that's what you get for following universals too heavily); vertical vowel systems aside, vowels generally like to spread out to the margins (so a system like /i ɨ u ə ɐ a/ is very unlikely); a system tends to be higher than it is wide (so a system /i ɨ u e ə o/ is also probably not possible). There are other universals about vowel systems too, I'm sure, but the relevant PDF seems to have 404ed in the mists of time.
You can often create a distinctive-looking vowel system by taking a more boring one and putting in some sound changes. Occitan, for example, underwent a chain shift in the Vulgar Latin back vowels. The English Great Vowel Shift is another example. (Or take a distinctive vowel system and make it boring...Modern Greek's /i e a o u/ is the descendent of /i y e ɛ a ɔ o/.)
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Phew, that's it. That took me a while...hope it's appreciated! Glad I didn't also do a post on consonant systems like I thought, that would be much harder...