Whistled Turkish
Some earlier coverage, with pretty much the same content, can be found Peter Kenyon, “In A Turkish Village, A Conversation With Whistles, Not Words”, NPR 9/26/2015. Both articles provide several recorded examples, e.g. this sequence of Turkish phrases translated into whistling, from the NYT article:
Your browser does not support the audio element. The most relevant part is chapter 7, “Phonetics, Phonology and Typology of Whistled Languages”, which I don’t have time this morning to describe in detail — but here’s a hint for the vowels:
See also Julien Meyer, “Whistled Turkish: Statistical Analysis of Vowel Distribution and Consonant Modulations”, ICPhS 2007.
Source: languagelog.ldc.upenn.edu