Well my theory is..pythagorean....

The 3rd is sharp in tempered tuniing, thus we horn players are supposed to know when to use the 3rd valve if we are playing a 3rd I think it is 14 cents flatter than 1 and 2 unless you naturally lip it down to compensate. A third on a tempered tuning will beat, unlike playing the root fifth which is close to beatless.....

Now perhaps in a perfect world someone had an ear and went, wow, that combo strikes a chord....

John Conley
Musica est vita