An article I wrote a little while back for DZone about native Tizen development has just been published, in it I work through the creation of an application to identify music (similar in principle to Eyrie, although greatly simplified). It involves a brief look at the native user interface builder, use of the native sound capture and HTTP APIs, a small amount of audio processing and instructions on how to incorporate a general 3rd party GNU/Linux library into a Tizen project.
The full article can be read on DZone: http://css.dzone.com/articles/native-app-development-tizen