Zhyler Vowel Harmony
Vowel harmony is what keeps the planets revolving around the sun. What it does (in the context of Zhyler) is that it requires vowels in suffixes added onto words to change depending on the vowel which directly precedes it. If that explanating was a bit confusing, I promise you, it will only get more confusing from here on in (unless, of course, it in fact gets less confusing, in which case the preceding would be totally untrue). Anyway, I will now do my best to explain the Zhyler vowel harmony system.
Where Does Vowel Harmony Apply?
Excellent question. In Zhyler, vowel harmony applies only to suffixes. Let's start off with a nice example.
Say you have the bare stem pet, which means nothing, and you want to turn it into a class five noun (see the section on noun classes). This would require adding the class five suffix, which begins with a d (but, which, according to the voicing rules, becomes a t), and then has a vowel that follows it. Unfortunately, this vowel is not fixed. By that I mean the vowel varies depending on the last vowel in the stem (in this case, e).
So, once you know the vowel in the stem, and know the suffix, you're set to learn what the vowel in the suffix should be. With this particular suffix, you can have one of four variants: -ti, -tü, -tÿ, or -tu. To decide which variant is to be used, you should refer to the vowel chart on the phonology page, and pay special attention to the following pairs: front vs. back; high vs. low; round vs. unround. What you're looking for is which suffixes vowel matches with the stem vowel in terms of classification.
So, look at the vowel e; the stem vowel. According to the three pairs, the vowel e is: (1) front, (2) low, and (3) unround. Now, look at the suffix vowels. If you examine how they're classified via the three pairs, you'll notice that ever single vowel is high. This means that the height distinction is unimportant for this suffix (since, no matter what vowel you choose, they'll all be high). The remaining two, then, determine which vowel will be used. (Oh, and a quick note: All suffixes will use only one or two of the three pairs to make their match; none use all three. If all three were used, the result would be reduplication.)
So, then, what we need is a vowel that's both front and unround. By narrowing your scope to front vowels, the back vowels and u and are eliminated, so half your work is done. Next, you eliminate the round vowel, that being , and you're left with your winner: i!
Now that that's been determined, you choose your suffix, -ti, and add it to your stem, pet, to get the word petti: king, queen or ruler. And presto; you're done! Simple, huh?
Now, to address the still lingering question, "Where does vowel harmony apply?", I'll repeat: It applies exclusively to suffixes. What types of suffixes are there? The most common are the noun class suffixes, and the noun case suffixes. That's where most of this war will be waged.
The Big Picture
Truth be told, most vowel harmony systems are unstable (i.e., they have lots of exceptions, and most known systems are degenerating). This one, however, is not, because, well, I invented it, and while it could be made unstable, I choose not to. It's my choice, and I'm sticking with it. That said, if one were to grow up speaking Zhyler, such a one would operate within the framework of the vowel harmony system effortlessly. Since that is not the case, however, a large chart is needed. And, rather than listing all the possible variants of every suffix in the Zhyler language (or any language with vowel harmony), linguists (and I) have found it useful to introduce the idea of an underspecified vowel. (I couldn't find a web reference, so I'll do my best to explain.) What an underspecified vowel is is a capital letter (usually a vowel; not always in Zhyler), such as I, which then stands for a set of vowels chosen via the method I showed you above. The particular underspecified vowel I chose stands for the vowel set we saw above--namely, i, ü, ÿ, and u. That said, rather than listing all four variants of the above suffix, you might, instead, simply write -dI (or, in the case above, -tI), which would stand for: -di, -dü, -dÿ, or -du.
Now then. A language like Turkish has two underspecified vowels, which is well and good for Turkish. Zhyler needed more, though, which is why it has fourteen. That's a lot (and, incidentally, that's why I had to use consonants as well as vowels to represent the underspecified vowels--English just doesn't have fourteen orthographic vowels), but, once you get the hang of it, by no means unmanageable.
Underspecified Vowel Chart
Below, are all fourteen underspecified vowels. First is listed their symbol. In the next column are its two to four variants. To the right of that column are its classifications, via the pairs dicussed above (unimportant distinctions are left out). To the right of that will be a list of the vowels it occurs after. Below this chart I have reproduced the vowel chart from the phonology section for easy reference, but this time with the orthographic versions of the vowels, and not the transcribed versions. (Oh, by the way: The underspecified vowels are listed in order of frequency. In other words, you'll see the first one a lot; the second one also a lot, but not as much as the first, etc.)