That's a pretty nice playlist and they seem to be mixing it up well throughout the day. Do they play anything modern?
Ocassionally. However, they do have this every Saturday night (included is last weeks playlist):
Modern Masterpieces with Alan Chapman
Alan invites you to explore the great musical works of the past three-quarters of a century and share the unique emotional power that only music of our time can offer. 10:01 pm Leos Janacek: String Quartet #1 "The Kreutzer Sonata"
Brodsky Quartet
Brodsky 3503
10:20 pm Karol Szymanowski: Symphony #3 "Song of the Night" Op 27
City of Birmingham Symphony Orchestra / Simon Rattle
CBSO Chorus
Jon Garrison, tenor
EMI 55121
10:45 pm Igor Stravinsky: Octet
London Sinfonietta / Riccardo Chailly
London 417114
11:01 pm George Antheil: Airplane Sonata
Marthanne Verbit, piano
Troy 146
11:07 pm Kurt Weill: Concerto for Violin & Wind Orchestra Op 12
London Sinfonietta / David Atherton
Nona Liddell, violin
Deutsche Grammophon 423255
11:35 pm Paul Hindemith: Nobilissima Visione
Philadelphia Orchestra / Wolfgang Sawallisch
EMI 55230