Ocarinas are great, however they have one big downside, the range of notes available is very limited. People try to solve this in two ways, adding more holes to a single chamber, and adding additional chambers. But for someone playing the ocarina as a serious instrument, which approach is better?
Answering this question isn't difficult, as I can say that in almost all cases, a multichamber is going to sound better, and be easer to play than extended range single chambers, such as the 12 hole ocarina.
Ocarinas function on lossy physics. They work by blowing air into an enclosed chamber, creating a pressure differential between the chamber and external environment. Opening holes raises the pitch as there is less resistance to air movement. But allowing air to escape also makes the instrument less efficient, and more airy.
Multichamber ocarinas work with the instrument's limitations, as each chamber can be tuned to play in the range it sounds best. A multichamber has considerably more scope for increasing sounding range, than adding holes to a single chamber ever can. As holes are added, it it becomes exponentially harder to attain good sound over the whole range.
I feel that it's worth mentioning that the same benefits found in the individual chambers of multichamber ocarinas are also present in single chambered ocarinas with fewer holes. That is, 10 and 11 hole ocarinas. Many players today have probably never tried one, as the 12 hole ideal is so common.
There have been considerable design innovations that have arisen from improving the sound of 12 hole ocarinas, but few people have thought to apply these to 10 or 11 hole ocarinas. The ocarina is a lossy instrument, and as such, these innovations work even better when applied to an instrument with fewer holes.
When applied to a 10 or 11 hole ocarina, you can achieve an instrument that has an exceptionally balanced timbre and volume over it's sounding range, and a very flat breath pressure curve. Such an instrument has notable musical benefit, as it will be easier to play agilely and more easily blend with other instruments.
I also feel that the absolute range of an ocarina is less of a problem than many people think:
Another thing that I'd say, is that playing a multichamber ocarina in a lower key can give you the 'subhole' notes of a 12 hole ocarina without the compromises.
From having been involved with the ocarina making community for about 8 years, it seems to me that many makers don't make multichamber ocarinas because they are afraid of them. They look more complex, but in reality that couldn't be further from the truth.
In my experience Making a multichamber ocarina is easier than making an 11 hole single chamber, and considerably easier than making a 12 hole. As the individual chambers produce a smaller part of the total range, multichambers do not require such a high degree of precision with voicing and chamber size in order to sound good.
I'd love to see more innovation in multichamber ocarinas as the existing designs are not perfect. Designs can be improved to make chamber switching, and fingerings easier for players. The Pacchioni system, as well as other designs which have come onto the market recently demonstrate that there is a lot of scope for improvement.
If you are a new maker, your effort will be far more fruitful spent developing a better multichamber, than a better 12 hole. 12 holes ocarinas exist on the limits of the instrument's physics, and are well into law of diminishing returns. Whereas multichambers have vast scope for improvement.
I think it's important that when we consider a musical instrument, we do so with it's limitations in mind, and try to work in ways that align with these limitations in a positive way, instead of fighting with them.
As we have explored, multichamber ocarinas work with the limitations of the physics and have notable advantages. Even single chambers with fewer holes have benefits that aren't often considered.