How to Make a Sweet Potato Ocarina out of clay, instructions on how to make a ceramic 10 finger hole ocarina...
Finger Holes and Interior Ocarina Volume
Adding finger holes to an ocarina will increase its internal volume by a very small amount. This shouldn't pose any problems for medium to large ocarinas, because the gained interior volume is so little. It will have no discernible impact on lowering the overall pitch of the ocarina, unless you have a very small ocarina, with a very thick wall.
How does this happen?
The picture on the right shows two cutaway side views of an ocarina. In Figure 1, the ocarina has no finger holes. The interior volume is highlighted in blue. In Figure 2, finger holes have been added. Notice how the interior space is expanded to include the finger hole openings. This added volume is highlighted in bright yellow-green. The thicker the wall is made, the deeper the finger holes will be. The column of air that is the finger hole becomes longer when the ocarina wall is made thicker.
What to do?
When tuning an ocarina, many makers cut, trim, and size the finger holes one-at-a-time, starting with the lowest note. Each time a finger hole is added and trimmed, it will add a tiny bit to the interior volume of the ocarina. The last hole tuned will seem to be the most "in tune," having been cut after the "extra volume" was added from the first finger holes. The preceding holes will be slightly flat, because they were tuned before the extra volume (from the later finger holes) was added. The small lowering of pitch most likely would not be detected by the average ear, but your chromatic tuner may register it.
To minimize this effect:
1) Make the ocarina walls as thin as possible. Don't overdo this - if your clay ocarina's walls are too thin, it won't even survive to reach its first firing.
2) Re-tune the ocarina, starting with the lowest note (all finger holes covered). This second tuning is being calibrated with the new, larger volume that resulted from adding all those finger holes in the first place. Any additional under cutting (which would add a minuscule amount to the interior volume) would have little, if any discernible effect on the accuracy of this second tuning.
Another option
Another option for small to medium sized finger holes is to recess them. The finger hole is placed within a depression or "dimple." Doing this shortens the length ("depth") of the finger hole by making the ocarina wall thinner around it. This serves to decrease the amount of volume added to the interior. (Figure 3) Another benefit is that a a recessed finger hole is easier to cover because it can be felt better than a “flat” finger hole. Figure 4 Ocarina with recessed finger holes.