Yes, The Legend of Zelda: A Link Between Worlds is a sequel to A Link to the Past. That being said, don’t worry if you haven’t played the SNES game. The Link Between Worlds OST can definitely stand on its own.
A Link Between Worlds is loyal in its resurrection of songs from A Link to the Past. It’s not Pokémon: HeartGold, with its different styles and interpretations of Pokémon: Gold tracks. The Link Between Worlds OST uses almost identical scores as the songs in A Link to the Past; the most notable difference is updated instruments. A Link to the Past fans will no doubt appreciate the richer sounds, and new players will be able to enjoy the OST as if they were encountering the 24-year-old original for the first time.
All the new characters and settings in A Link Between Worlds warrant their own songs. The villain Yuga, the merchant Ravio, the parallel universe princess Hilda, the witch Irene, and the magical octopus Maimai all have their own personal themes. The new Milk Bar song is catchy (though not as catchy as the one in Majora’s Mask…), and the Octoball Derby song is all-around adorable. But composer Ryo Nagamatsu shows off his creativity the most in the second half of the game, in the dungeons of Lorule (the Dark World of A Link Between Worlds). Desert Palace, Swamp Palace, Ice Ruins, Turtle Rock, and Skull Woods all share the same theme, adapted to the different settings. The same melody blends as easily to its surroundings as Link blends into the walls.
At the end of both discs of the OST are a collection of songs played by the Bard, the musical duo in the Milk Bar. Their role in the game is minimal: pay them ten rupees and listen to their music (and receive no reward). But these songs have a strong presence on the OST, especially considering that they are the only tracks recorded live. They sound similar to the countless ocarina/guitar covers of Zelda songs on YouTube and may in fact be a response to them. What better way to reward a loyal fanbase than to put them in the next game?
The Legend of Zelda series has evolved well alongside the gaming community, from the NES to the 3DS. Just the same, the world and story of A Link to the Past have evolved nicely into A Link Between Worlds. Best of all for music lovers, A Link Between Worlds has a charming soundtrack, enjoyable by both old and new fans.