Music for the ocarina
When it comes to music for the ocarina, most of the time you will be adapting music that was originally written for other instruments, or the human voice.
There is a very small amount of music that was written for the ocarina, which is mostly music for the Italian ocarina ensemble tradition, and can be found online by searching.
But with regards to adapting music to the ocarina, it always comes down to the fact that ocarina is a limited range instrument. Ocarinas can also be made to sound with quite a range of different timbres, which is set when the instrument is made and cannot be changed.
Ocarinas do not work like other mainstream instruments where one can play everything using one instrument. Rather you will need multiple ocarinas, depending on the range of notes, and timbre that you require.
In music, approximately 7 octaves are used, and an ocarina is a 'window' into a part of this range. You can change the range that you have by using an ocarina tuned to a different key or pitch range. See Ocarina keys and pitch ranges.Alto C ocarinas play from about C5 to F6: While bass C ocarinas play from about C4 to F5: And an ocarina can also overlap multiple ranges if it is tuned in a different key, for example an alto G:
You choose an ocarina range and key to provide the range of notes that you require, and then use fingerings to play in the correct sounded pitch.
Multichamber ocarinas can provide more range from a single instrument, but they are not a panacea as splitting the range across multiple chambers, as well as fingering complexity in certain keys, make some expressive possibilities practically infeasible. There is still considerable value in having an ocarina with a tuning that well suits the music.
Matching ocarina range to music range
Its really useful to learn to identify what key of ocarina you'd need to play a given piece of music at it's written pitch.
How music for the ocarina is notated
Music for the ocarina is usually written using standard music notation.
Being a limited range instrument, with less than two octaves, the notes are referred to as just 'high' and 'low', for example 'high C' and 'Low C', not using an octave number.
The low C on the staff is usually considered to be 'low C' on the instrument, regardless of the pitch range of the ocarina. Thus an alto C sounds an octave higher than written, and a soprano C sounds 2 octaves higher.
Is the ocarina a transposing instrument?
It depends on the situation.
Ensemble music is commonly notated with all parts transposed into C. Thus if an ocarina is tuned in G, the low G would be written as low C on the staff. To play it, you use C fingerings even though you are playing on a G ocarina. I've only ever come across this in ocarina ensemble music at the Budrio ocarina festival.
However, given that music for the ocarina is so rare, being able to sight read onto ocarinas in different keys at written pitch, as well as transpose music at sight are very useful skills to develop. It allows you to play arbitrary music you encounter without needing to first transpose it into C. Its great for playing music meant for the voice, or other instruments.
I find reading at pitch to be a vastly more useful skill as I mostly play Irish folk music, and everything in this tradition is written at sounding pitch. If you wish to play music from these traditions, you will also need to learn to read at written pitch on ocarinas in different keys.
The same applies to bagpipe music, which is another great source of music for the ocarina.