3 Octave Major Scale on Guitar

Starting in the root position of the Ionian mode (for example: in F major)...you would play typically with the first finger on the first fret of the 6th string and play your 2 octave scale in position.  However, if you wish to make a 3 octave scale on F major, you will have to travel across the fretboard.

One good piece of philosophy when trying this out is to remember that in order to stretch out and keep playing on F major and ending up in the 4th F above the lowest one on the guitar, you will need to go across until you make it to the 10th position or the Aeolian mode in the same key.

That is pretty simple, however, a good piece of info for when you're improvising and flying across the neck!  You can typically run all your modes from the lowest one you choose and then add 5 more to that.  So if you started on F as your Ionian mode, then you will end up in your 6th mode across and have achieved the 3 octaves.  Now, what you do in the middle could be structured or could not :)