The US military thought a lot about how to entertain its soldiers because there was a lot of downtime during a war and most of them were draftees who didn't necessarily want to be there, Another thing they did was publish pocket paperback editions of books back when paperbacks were less common.
Interesting that they don't seem to have had much cultural impact. I've never heard of these, never seen them in war films. You don't hear songs wistfully using a wartime ocarina or referring to them.
That explains the Joey's ocarina in the movie Stalag 17.
Back in the day in elementary school we were each issued a tonette
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It came with some sheet music that shows each note as a box with four dots in it that can be shown as either open or closed:
https://ocarinasongbook.com/fingering-charts/four-hole/
It sounds unusually sophisticated — perhaps even better after forty-plus years -- and it's actually a relatively new design. The ocarina is ancient but the four hole chromatic design dates from the 1960s, so it's newer than those Gretsch ocarinas in the article.
You can get them in all sorts of shapes and sizes -- Thomann sell hand-painted clay 4H ocarinas in the shapes of strawberries and clownfish.
I wish we'd been taught to play these in school instead of with those Aulos descant recorders that everyone in British schools, particularly teachers I imagine, grew to hate.