My understanding of a song cycle is that it is a collection of songs on a single theme, but it does not necessarily tell a story nor does it necessarily require a dramatic production.

Vaughan Williams setting of A E Houseman's poems "A Shropshire lad" is an example.

This has been done here in N. Yorks using Graeme Miles's songs of the Cleveland (UK) iron industry. Them group who do it call themselves the Ironopolis Singers and they tell the story of the rise and fall of the iron industry on Teesside.