Clue: Duke's number 501, absorbed by what cow says to dog (4,6)
Answer: MOOD INDIGO
Explanation: Definition: Duke's number
An envelope ('absorbed by') of DI ('501', Roman numeral) in MOO ('what cow says') plus DINGO ('dog') – or perhaps, whimsically, "MOO, DINGO" as a phrase; for the jazz song composed by Duke Ellington, on a theme provided by Barney Bigard.