From the Clan Milne website: "According to Scots Kith and Kin, 
Clan Milne (Miln, Milnes) was in Aberdeenshire in the 14th Century. 
It is a sept of Clan Gordon."

According to the Gordon Newsletter #4, "The first Highland Games that we would 
recognise as Highland Games in Scotland took place in St Fillan's in 
Perthshire in 1818. In that very same year, a bunch of fur traders in 
Glengarry County, Ontario, set up a Highland Society to promote Highland 
Games there. There was no connection between the two, but there was a 
parallel development in the way these games evolved on both sides of the 
Atlantic. This was true of many things: piping; costumes and song, among 
others. At many Scottish events songs and poems were made up for the 
occasion - the hills of hame, thinking o' the auld folk - so that many 
of the songs we think of as Scottish were written overseas and exported 
back "hame" to Scotland (Cock's Crow, Fall 1997, p 2)."

From a Milne Family homepage, it says "The name Milne (Miln, Milnes) 
is recorded in Aberdeenshire, Scotland in 1380 and means "at or near 
a corn-mill" The clan Milne is a sept of the Clan Gordon." 

Other interesting links:
How The Milne Name Originated and How They Came To Exist In Aberdeenshire; A Theory
Electric Scotland.com's info on Clan Gordon
Gordon History
Origin of Clan Badges
Gordon Crest Badge
The House of Gordon
A history of CLAN GORDON
History of the Gordon Clan
Gordon 2000
My Milne Roots