How does labial harmony distinguish Eastern Mongolian languages from Western Mongolian languages?

In the study of Mongolian languages, the development of labial (rounding) harmony serves as a key innovation that distinguishes the Eastern group from the Western group.1

In the Eastern Mongolian languages—such as Khalkha—nonhigh vowels undergo rounding when they follow a nonhigh rounded vowel in the immediately preceding syllable. For instance, in Khalkha, the vowel a is rounded to o following o, as seen in the form mor’or ("by horse").12

In contrast, Western Mongolian languages, including Oirat and Kalmyk, generally retain the unrounded a in such suffixes, as demonstrated by the Kalmyk equivalent -ar. While both groups share many linguistic features, this relatively recent innovation in the Eastern group is a primary point of divergence between the two.1