Over at his excellent weblog Rénhírek, László Fejes has written several concise introductions to the vowel harmony of various Uralic languages. I’ve translated below his Nganasan description.
The Nganasan vowel inventory
We the following vowels in Nganasan: i, y, ü, u, e, ə, o, a. The majority of these can be compared to the similarly written Hungarian vowels, with the exception of the following: y (really i with a diacritic, but here y for typographical reasons) is similar to i, but but slightly further back (cf. Romanian â/î, Polish y, Russian ы); ə is similar to e, but further back (so it is not a ‘mumbled’ schwa, like in Mari, Khanty or Mansi; cf. Romanian ă, Estonian õ); a is similar to Hungarian á. These can appear as long vowels as well, in which case they are written double: ii, aa etc. Besides these there are also two diphthongs: ia and ua.
Nganasan vowel harmony
There is no tendency in Nganasan that requires that only palatal or velar vowels appear only in roots. Vowel harmony appears only in suffixes, and there it only relates to high vowels. In certain suffixes i/y or ü/u are involved in variation: these only appear if i or ü is present in the preceding syllable. However, this does not occur in all suffixes, but only thosse in which there is always i, y, ü or u.
Nganasan earlier had a different harmony as well. Traces of this are found only in two types of roots: each takes different variants of various suffixes. The rule applies in the U and Y root classes: from the vowels which are now present in them, one cannot tell which words belong to which root class. According to the root class the following pairs of alterations can be observed in the suffix vocalism: u/y, ü/i, a/y, a/i, a/ia. In the first two pairs the suffixes occasionally alternate according to roundedness, and in the remaining three according to height, that is, there is a difference according to height and front-back quality. There are suffixes where root alteration is combined with vowel harmony, so four suffix vowels are possible: i/y/ü/u.
According to scholars, the U and Y root classes leave traces of an earlier palatal-velar harmony. As for the relationship between the current active palatal-velar harmony and the earlier one, is still not clear.