The ocarina's breath curve and tuning
For an ocarina to produce a strong tone, the voicing has to push air into the chamber faster than it can escape through the finger holes. Because of this, the low notes require little air to sound. As higher notes are played, there are more holes for air to escape, so you have to blow harder or the tone becomes more and more airy. How the pressure requirement changes over an ocarina's range is called the breath curve.
Makers have a great deal of freedom to craft the shape of the breath curve when making an ocarina. Some require only a small pressure change, whereas others ramp up hugely towards the high notes. These differences are sometimes called 'type 1' and 'type 2' ocarinas—type 1 referring to a constant pressure between the high and low notes, and type 2 referring to a breath curve where pressure increases towards the high notes. See the following diagram.
In reality, this strict distinction does not exist. Ocarinas can be made to play anywhere between the two extremes. The exact shape of this breath curve depends on quite a lot of factors including chamber volume, the size of the sound hole, the distance to the labium, how restricted the windway is, and how the ocarina was tuned.
When an ocarina is blown at different pressures, its pitch and timbre (tone colour) change. If too little pressure is used, the instrument produces a very weak, airy sound. As pressure is raised further, this starts to sound cleaner, and continuing further makes the sound more harsh and eventually produces squeaking. Ocarinas are tuned such that the desired notes play in tune within a pressure range that sounds good.
The ocarina's natural pressure curve is approximately exponential. An ocarina made to play at a low pressure (curve A) will have a flatter breath curve as less energy is needed to drive the chamber. Designing an ocarina to be louder, with a higher tuning pressure results in larger finger holes, so requires a steeper breath curve to maintain the high notes (curves B and C). You can make a guess where an ocarina falls in this range by looking at the hole size, as tuning with a steeper breath curve results in larger holes.
Another big influence on the breath curve is how many holes the ocarina has. As the breath curve is exponential, every additional hole significantly increases the pressure required to sound the high note. This in turn increases the pressure difference between the low and high end. Consequently, a 10 hole ocarina may be tuned with a flatter breath curve than a 12 hole, if both follow the same design. Multichambers may also have a flatter breath curve, as each chamber produces a smaller part of the total range.
The shape of an ocarina's breath curve has a big impact on how it plays and sounds. Ocarinas are naturally louder on their high notes, and steeper breath curves exaggerate this effect. Steeper breath curves also demand more from the player, and can make the instrument difficult to play quickly due to the big pressure changes between notes. Flatter breath curves have the opposite characteristic: their volume is more balanced over the range, and such instruments are typically easier to play quickly.
Which of these factors is desirable varies depending on what you are trying to do with the ocarina. A steep breath curve can be useful if you are playing outside or without amplification. My preference leans towards lower pressure instruments. Ocarinas are naturally loud on their high end, and a steep pressure curve often pushes that to an extreme. Amplification, on the other hand, can provide you extra volume without the downsides of a steeper breath curve.
Measuring the breath curve
Measuring an ocarina's breath curve is a good way of judging the quality of the instrument. The pressure should ramp up gradually between notes, with no sudden and arbitrary changes. The two following graphs exemplify a well tuned breath curve and an (exaggerated) poor one.
Directly measuring an ocarina's breath curve requires specialist equipment as the pressures involved are so low. However, it can be judged indirectly by measuring the tuning of adjacent notes. To do this, blow a lower note and, without changing your pressure, raise the finger for the next note in sequence. The higher note will fall flat and you can measure this change using a chromatic tuner. Begin at your ocarina's lowest note and check each note sequentially, writing down the note and how flat it falls.
When you have this list, the changes should be fairly regular. Their magnitude will be larger on high pressure ocarinas, and you may notice that they may increase or decrease gradually between sequential notes. You should not see any large irregular changes though, such as a sudden pressure increase followed by a decrease. If so, you have probably found a tuning error.
Whether or not an error is actually a problem depends on how bad it is: 5 to 10 cents is usually tolerable, but 40 or more will be difficult to compensate for when playing at a moderate tempo. I advise double checking your result as it can be difficult to hold the breath perfectly constant at first. I also recommend taking a few measurements and averaging them.
Do be aware that the exact magnitude of the changes between notes will vary with temperature. That is covered on the page 'How air temperature affects an ocarina's pitch'.
Blowing technique and the impact of tuners
Two different things make measuring the breath curve accurately a lot easier, the first being to use a good blowing technique, and the second is related to the chromatic tuner that you are using.
With regards to breathing, the human body can do so in two different ways, called shallow breathing and diaphragmatic breathing. To get the best possible control you really need to use diaphragmatic breathing, and how to do this is explained on the page 'Blowing an ocarina correctly'.
Secondly, a poor chromatic tuner can make this task much more difficult. Tuners frequently have a feature called needle damping, which averages pitch over time. This is done to hide small fluctuations in pitch, but for measuring breath curves it causes problems. What you are trying to measure is the pitch change at the exact instant you lift your finger. Needle damping creates an error as it smears this change out over a longer time.
Also, chromatic tuners do not measure the pitch that you are playing continually, but sample it periodically. A tuner with a slow sample rate will not be able to keep up with the slight fluctuations in your breath, and thus won't show what is actually happening. Taken together, these two issues make reading pitch accurately very hard, and cause the tuner to display confusing results that vary every time.
Using a tuner with high sampling rate, low latency, and without needle damping will make your job far easier. The only tuners I know that meet these requirements are software tuners such as APTuner. Most of these have needle damping, but most have an option to it off.
As an additional recommendation, look for a software tuner with a numeric display showing cents in addition to, or instead of, a needle based readout. They are much easier to read quickly.