Here's the tab for the Legend of Zelda Main Theme/Overworld Theme.  I'm pretty sure this is 100% correct - it sounds fine to me when I play it.

G|---------------------------1-3---3-3-1---1-----|
D|-------------0-1-3---3-3-4-------------4---4-3-|
A|-1-----1-1-4-----------------------------------|
E|---1-------------------------------------------|

G|-------------------------------------0-----------------|
D|-3-1-1-3-4---3-1---1-3---1-----0-2-----3---------------|
A|-----------------4---------4-3-------------------------|
E|-----------------------------------------111-111-111-1-|

The E|111-111-111-1 can be played any way you want; but it happens really quickly.  I use the triplets method because that's how it sounds ingame.

BIG thank-you goes out to Nintendo for making the Zelda games.