Blowing an ocarina correctly
It is important to blow an ocarina correctly to create a clean sound and this begins with your breathing. The human body has two patterns of breathing, shallow (clavicular) breathing where the shoulders raise/lower and belly (diaphragmatic) breathing where the belly moves in and out. You must use belly breathing while playing the ocarina. It allows you to play longer between breaths and improves your breath control.
Try taking a few full belly breaths without your ocarina. Open your mouth and place your hand on your belly. Inhale steadily through the mouth so that your hand moves out while the shoulders don't raise. Then exhale steadily through the mouth. Repeat this for a number of breaths until you become comfortable with it. To further enhance your breath control, engage your abdominal muscles, a cue being 'draw the belly button towards the spine'. This creates pressure in the abdominal cavity and pushes up on the diaphragm. It gives the muscle something to work against.
As sitting can negatively affect your posture, I advise playing while standing, useing an eye level music stand if playing from sheet music. A slouched posture reduces the volume of the chest and limits how much air you can inhale. Consequently, it limits how long you can play between breaths. To check your posture, you can stand with your back to a wall, preferably one with no baseboard. Your heels, bottom, shoulders and the back of your head should all touch the wall.
If you cannot do this, your body is out of alignment. This can be improved by lying flat on a hard floor. In this position, gravity will move your body into alignment. You may feel tension in the chest muscles as it is common for them to become tight. If you do this for several minutes a day for a few weeks, the muscles will start to loosen.
Controlling your breath
When playing a wind instrument, you need to start and stop your breath to separate notes. The intuitive way to do this is to 'puff', as if blowing out a candle. This isn't a good idea. Puffing causes the pitch to ramp up, peak and roll off. While it can work as an effect, it is poor general technique. The result sounds uncertain, as the note has no duration at a single pitch. The breath has to start and finish abruptly to create a good sound. Listen to the sound samples below.
To start and stop your airflow crisply, you have to use the tongue. While you are exhaling, you can touch the tip of the tongue to the top of your mouth, blocking the airflow as if making a consonant like 't', 'l', or 'd'. Try this for yourself: with your mouth partly open, take a deep belly breath, exhale steadily, then block the flow with the tongue. Let some short pulses of air out by quickly lowering and raising your tongue. It is best to practise this without your ocarina.
To begin a note cleanly you touch the tip of the tongue to the roof of the mouth, attempt to exhale creating pressure then lower the tongue to release this stored pressure. This is similar to 'th', but you continue to exhale. The closest syllable analogy I can think of is 'Thhhhhh...'. To stop a note the inverse is done, raising the tongue quickly to block the airflow, like '...hhhhhhT'.
While thinking of syllables can be a useful guide to get started, you should not get too attached to this analogy. Syllables carry other mouth postures; for example, while pronouncing 'ta', I notice that I raise the back of my tongue. This secondary action is not desirable while playing the ocarina, as it creates turbulence which creates a noisy tone, particularly on the high notes. The back of the tongue should always be at the base of the mouth.
Realise that what you are doing is using the tongue as a valve to control the air. Unlike a syllable, the tongue can stop the air for a long time—as long as you could normally hold your breath. As the diaphragm is still engaged, the area behind the tongue is pressurised. Lowering the tongue releases this stored pressure all at once, causing the note to begin cleanly. To create a longer articulation, leave the tongue raised for longer. To create a shorter articulation, just touch the roof of the mouth briefly.
The initial pulse of air pressure gives an 'attack', a moment when the sound quality is different from what you get with steady blowing—nearly all instruments do this, in many different ways. Where you position your tongue changes how the notes attack sounds; closer to the teeth as in 't' creates a distinct and airy attack, while placing the tongue further back along the roof of the mouth creates a softer attack.
The ocarina's embouchure
You may think that, because ocarinas have a windway, they don't need a special embouchure. This is not the case as they are sensitive to turbulent airflow. You have to position your lips and tongue to create a smooth air passage or the tone will be noisy.
Firstly, part your teeth. Roll your lips in slightly so they are flat with the teeth (arrows). Position the tongue level with the bottom lip covering the lower teeth.
Form a small oval-shaped aperture between your lips. This should be of moderate size as it will create a noisy tone if too restricted. LIGHTLY touch the mouthpiece of the ocarina against the aperture using just enough pressure to create a seal. When playing the mouthpiece should not be fully in the mouth and should never touch the teeth. To get the best sound, angle the ocarina so you are blowing directly down the windway. Tilting it sharply up or down kinks the air passage and results in a noisy tone.
The lip aperture isn't critical for playing single chambers; you can get away with having more of the mouthpiece in your mouth. However, when it comes to playing multichambers, this is required, the lip aperture being used to direct the air into the correct windway. Putting too much of the mouthpiece of a multichamber in your mouth also creates a lot of friction and makes chamber switching excessively difficult.
Make sure that you hold tension in your cheeks while playing, so that they do not puff out. This achieves nothing, and may limit your ability to control the instrument.
Playing long tones on your ocarina
Above, I mentioned the importance of being able to start notes cleanly and hold them stable over their duration. It is good to practise this regularly using the long tone exercise.
Finger a note in the middle of the range. If you are playing an ocarina in C, the note G is good. Stop the air with your tongue, engage your chest muscles and start to exhale, building pressure in your mouth. Release this pressure by lowering the tongue and the note will start crisply. As you are about to run out of air, don't strain; finish the note cleanly with the tongue.
As the ocarina's pitch depends on your blowing pressure, it is a good idea to check the note you are actually playing using a chromatic tuner. Beginners frequently use too much or too little pressure: while fingering a G, you could be sounding anything from a F♯ to A.
Using a tuner, raise or lower your breath pressure to get the note in tune. You may find that you have to use a great deal less or more pressure than what feels right. Resist any temptation to change it; it will start to feel natural after a few days.
Final notes on tone clarity
As has been explored, an ocarina's tone is influenced by your mouth posture. While you practice, take note of how the position of your tongue affects the tone. Notice that if you raise the back of your tongue, you will get a more noisy tone. Similarly, positioning the tip of the tongue too close to the teeth results in a noisy tone. You can use this for effect in your playing by varying where you place the tip of your tongue. Experiment to find a position which gives you the cleanest sound, then vary as appropriate.
In addition to the tongue, there is another valve in your throat called the glottis. This is what allows you to hold your breath with your mouth open. You can feel it move if you put your hand on your throat while holding and releasing your breath. On other wind instruments, the glottis is sometimes used to create articulation. Doing this on the ocarina can be an extreme effect as the glottis responds much slower than the tongue. Creating a fast articulation with it requires holding it almost closed as a resting position. This creates turbulence, which results in a noisy tone. It also restricts the airflow, which may be a problem as the high notes require a large volume of air.