Conductor Mariss Jansons This week, listeners can see for themselves how the area’s hometown orchestras, all featured below, measure up against the orchestra considered by many to be the finest in the world. Also, a months-long festival of American music — with lots of free concerts to hear — kicks off this weekend. BATTLE OF THE ORCHESTRAS: >> Amsterdam’s Royal Concertgebouw Orchestra often appears at or near the top of lists of the world’s…

Pianist Emanuel Ax (photo courtesy Boston Symphony Orchestra) The National Symphony Orchestra has been in a sort of leadership vacuum this season, with a carousel of guest conductors filling time until Christoph Eschenbach takes the helm next season. While the results have been varied, the month of January is shaping up to be, as expected, one of the best in recent memory for the hometown band. After a lovely performance of Elgar’s violin concerto…