Diatonic intervals for ocarina
It is important to learn the fingerings and pressure changes needed to move between notes cleanly. While you can learn to do so by playing tunes, they can be practised more systematically. If you learn the fingerings and breath change for every interval, you'll find it much easier to play new music.
A good place to start with this is to learn your ocarina's diatonic intervals, the intervals within its key. The simplest diatonic interval is the second, the step between any two notes in the scale. It is easiest to begin from the middle of the scale as the higher notes are less sensitive to pressure changes.
Once you have the hang of it starting mid-range, try doing the same starting on the low C. As you work through these, pay attention to both your fingering and intonation.
The same thing can be done with other intervals. Here is every diatonic third possible on an 11 hole alto C:
Following are the remaining intervals of C Major. You may find it easier to practise the fingering of these exercises without blowing at first. If you find them boring, see 'Finding interest in technical exercises'.