It is believed that the Song of Resonance can only be obtained by purchasing it by a specific NPC known as Treasure Hunter Igran Lost Ark Gold. He's located on Deck Ship from Pleccia island in the Sea of Gienah. It's to the west of Anikka.
After arriving, walk to the southeast to the Deck Ship and talk to the Treasure Hunter Igran. The Treasure Hunter Igran will offer you items in exchange for Pirate coins, like an item called the Song of Resonance.
It's going to cost you 16,500 Pirate coins, so you might need to do some work before you can get it. If you don't have enough of them make sure you check your inventory for Coin Chests. Opening those gives you an opportunity to earn different kinds of Coins that you can convert into Pirate Coins. It is as simple as talking to Traveling merchants that are located in ports. If not, you can utilize the standard methods to earn more, including quests and dailies.
When you're there, go to the southeast towards your Deck Ship and talk to the Treasure Hunter Igran Buy Lost Ark Gold. He'll give you items to purchase in exchange for Pirate coins, including the Song of Resonance.