"The later part of the 20th century" vs. "the latter part of the 20th century"

For the sentence fragment:

"...during the later part of the 20th century"

using "latter" sounds better to me:

"...during the latter part of the 20th century"

But most websites I find have later as the option that deals with time, e.g. http://grammar.about.com/od/words/a/latergloss.htm

Which word is more appropriate in this case?

Solution 1:

"Latter" connotes an informal reckoning... could even start before the half is reached so long as it continues longer into the second half. (From the 40s through the 80s, for example.)

"Later" often implies that it started after the half, and lasted much closer to the end.

Rock and roll, jazz, and techno were music of the latter part of the 20th century. Techno was music of the later part of 20th century.

The distinction is somewhat pedantic, even if useful.