The split hole pendant ocarina is a modification to the standard 4 hole pendant ocarina suggested to me by Kristina Lago.
The standard pendant ocarina fingering system is limited as there are not enough holes for all of the diatonic notes to be well tuned, and some of the chromatic notes are impossible without part covering holes.
It is possible to correct this with blowing pressure, but doing so creates imbalances in timbre and volume in relation to the surrounding notes.
The split hole pendant ocarina solves all of these problems, and varies only slightly from the standard pendant fingering system:
The best tuned fingerings from my testing are as follows:
Note that this system would normally have two thumb holes as well, adding 4 additional chromatic notes to the high end. I omitted them here as they are irrelevant in the context of this modified fingering system.
The split hole pendant has the following advantages over the standard system:
I think that the tuning issues of the pendant system have gone largely unnoticed as they are rarely played as serious musical instruments. The 10 hole linier fingering system also solves the tuning limitations, and is generally preferred by serious players.
The 4 hole ocarina fingering system does have advantages though. Having fewer holes allows the whole instrument to be made considerably smaller than a transverse can be. The minimum size of a transverse is limited by the player's hands, as each hand must cover 4 holes, which defines a minimum chamber length.
Being able to make a smaller, yet equally well tuned ocarina allows higher pitched instruments to be made, which will fit the hands of more players. That allows for the possibility of higher pitched notes in an ocarina ensemble.
Kristina also considers the pendant ocarina an 'instrument of the soul' as they can be made small enough to be worn as jewellery, allowing someone to always have an instrument on them. This fingering system carries the same advantage, while allowing instrument quality to be improved, and opening doors like spontaneous playing with other musicians.
There are other modified pendant ocarina designs, but all of them have limitations compared to the split hole pendant described above.
This design takes the standard pendant fingering system and adds a small hole to the right thumb, called an intonation hole, which allows the low C sharp and D sharp to be played. It is more limited than the split hole design:
I have seen pendant ocarinas where the right middle finger hole is a split hole, with no other split holes or subholes. This fixes the tuning of the low C sharp, but D sharp and notes mentioned above will be off.
There are pendant ocarinas with a subhole on the index finger, which can also be used to play the low C sharp. However using it to play D sharp would require curling a finger to cover only the subhole. It also has the same tuning issues noted above.