The Recording Academy has worked to reshape its voting pool, but the triumph of “Cowboy Carter” as album of the year can’t be traced to any one factor.

Every time someone presented one of the show’s major prizes — album of the year, record of the year, song of the year, best new artist — he or she rattled off the line before revealing the winner. It was a small but telling detail that demonstrated how the academy wants to be perceived after years of being portrayed as a shadowy record-industry cabal.