One of the things that's difficult about Finnish is that it is a language with vowel harmony -- your vowels have to match up (Finnish has eight vowels in two overlapping groups). There are rules governing how this works, and they aren't at all complicated or difficult (if you have ä or ö, you have to continue with ä or ö, for instance). But the problem is that it's not the sort of thing you actually should be doing by rule at all, even by simple and easy rule. The rule identifies what is correct, but if you are speaking, you shouldn't be stopping to check the rule; you should just automatically be harmonizing your vowels as you go. And that's a bit tricky.
However, for the second half of the summer I am taking a Turkish course, and we had our first class tonight. (My last Urdu class is later this week.) And Turkish is also a language with vowel harmony, which I hadn't known. So, for instance, Bizim means 'our', and there are suffixes you do to match that grammatically just as you would in a Romance language. But if your suffix has vowels, they need (usually) to match the last vowel of the word to which you are adding it. Let's take s℩n℩f, which means 'class'. (℩ is to first approximation like the English 'ih'; 'i' in Turkish is always more like the English 'ee'.) If I want to say 'my class' and 'our class', I get:
benim s℩n℩f℩m : my class
bizim s℩n℩f℩m℩z : our class
But if we pick a different word with different vowels, like gül ('rose', the vowels have to change to correspond (ü is a strong 'oo' sound, like the 'u' in 'duke'):
benim gülüm : my rose
bizim gülümüz : our rose
And as with Finnish it works mostly according to rules and the rules themselves are relatively simple -- for instance, Turkish has eight vowels that fall into two groups, hard and soft, and hard has to go with hard and soft has to go with soft.
But I had an epiphany while we were going over this in class. Essentially, the appropriate suffix to add when saying 'our' is always a -*m*z suffix; it reflects the pronoun you use, or would use if you drop the pronoun -- -*m*z is a sort of reflection onto the noun of the pronoun bizim. But the vowels are carrying through the prior sound in the words to which the suffix belongs.
To call it 'vowel harmony', then, is potentially misleading. That makes it sound like I have a vowel and then I have to select another vowel that fits with it. But really that's not what's going on; what's going on is that the vowel sound is continuing across the consonant, sometimes directly and sometimes with modification, but it is a vowel continuation -- in essence, how you are framing the vowel in your mouth just continues on through the suffix. If I say adlar℩ (their name), the second 'a' shape continues through the generic -a/e and -℩/-i sounds of the suffix, and that gives us the ℩. With a word like defterleri (their notebook), the second 'e' shape continues on through the same generic sounds to give us e and i. It's exactly the same suffix; you just don't reshape your mouth for it, so that modifies the sound.
This is true in Finnish as well. If you look at a Finnish grammar, it always looks like Finnish has a jillion times a jillion suffixes; in reality it only has a jillion suffixes, because the variants for vowel harmony are actually just the same suffix while carrying over the framing of the vowel from previously in the word. In English, and generally in Romance languages, we start over with each syllable; but in vowel harmony languages, the vowel-sounds in a sense flow through the word rather than existing entirely as discrete units.
And this is exactly why there are relatively nice rules for them that are pretty much completely useless for conversation and of only limited value for writing. If you do it right, you'll fit the rule, but if you are using the rule, you will have difficulty doing it right. Because, although in some sense your vowels have to match, you don't get that effect easily and consistently by matching your vowels; you get the effect by learning how not to unmatch them, by just letting them continue on through into the next syllable or syllables.
Incidentally, this seems to me to be something of an analogy for the difference between a deontological and a virtue-ethical approach to rules in ethics; in deontology, you apply rules, while in virtue ethics, you try to learn how to harmonize, to carry the relevant moral quality through, and, lo, there's a rule that shows that you did it right even though you weren't applying the rule. That's why phronesis, prudence, is so important in Aristotelian ethics: it is the virtue of harmonizing your actions to the moral qualities of the circumstances.