When you first start playing the ocarina, it is important to develop a diverse musical repertoire. Here you can find a wide assortment of music that works fantastically on the ocarina.
Jack Campin's 9 note tunebook is a collection of more than 600 folk melodies from many cultures around the world. And all of this music works great on the ocarina.
The book is available for free in two formats:
This music fits into a range of just 9 notes - with a few sharps / flats, suiting an ocarina in C at notated pitch, and can be played on ocarinas in other keys if transposed.
I have compiled a tune book with a wide assortment of Irish tunes that suit a single chambered ocarina, which includes some guidance on playing style:
If you have a multichamber ocarina like the Pure Double alto D, the entire repertoire of Irish music is open to you.
Take a look at thesession.org, an archive of thousands of Irish and other folk tunes, all completely free. Under the 'tunes' menu, on that website, you can find a list of popular Irish tunes.
Bagpipes and ocarinas both have a limited range, and thus a lot of bagpipe music is easily adapted to the ocarina.
It is worth noting that bagpipes are not limited to the highland bagpipe, many different kinds exist, with sounds ranging from loud and strident, to soft.
While not strictly idiomatic (the ocarina is a 19th century instrument), a lot of medieval and early music can be easily adapted to play on the ocarina.
The living history tune books are a good reference, for example:
Emiliano Bernagozzi, an italian ocarina player, has published a number of arrangements for ocarina Ensemble, available from: