Here are some numbers, culled from several collections, of tunes beginning in the 2nd whistle octave (ignoring pick-ups):
Mally's 100 Essential: 27/100 = 27%
Mally's 100 Enduring: 23/100 = 23%
Norbeck Reels: 201/822 = 25%
Norbeck Jigs: 103/386 = 27%
Norbeck Hornpipes: 16/105 = 15%
By these counts, that's roughly 25%, or 1 out of 4 tunes.
Here's another perspective. The basic range of ITM tunes (with fiddle tunes included) is 17 diatonic notes from G below the the treble staff to b above the staff. Of those, the whistle's 2nd octave comprises 6 [defgab] of those notes, or 6/17 = 35%.
So, in a random distribution you might expect that 35% of the tunes would begin in the second octave. The fact that it's actually 25% means that the tunes are only slightly weighted (by 10%) toward the 1st octave or below.
In any case, look through any general ITM tune collection and you'll find that 25%. If the tunes you know are all 1st octave starters, it just means that your repertoire isn't completely representative.
Tunes that begin on high g or above are rarer still - around 5% by my count. But there are a few well-known ones, including (some already mentioned):
The Blackthorn Stick
Tom Billy's Jig
The Coolea Jig
Maid on the Green
Gillian's Apples
Boys of the Town
Larry O'Gaff
The High Reel
Connemara Stocking
Dublin Reel
Reel of Mullinavat
The Skylark
Swinging on a Gate
The Primrose Lass
Fox on the Town
The Mason's Apron
Stack of Barley
Belfast (Sweep's) Hornpipe
FWIW, I think that the starting note isn't a very useful measure of a tune's character. The tensions created by the rise and fall of the melodic contour are more subtle than that. It's more entire phrases that go or stay high or low, or sweep dramatically between the two, that can give a tune its personality.
But sometimes it's fun to look at statistics like this anyway.
![smile :-)](./images/smilies/icon_smile_144.gif)