Final answer:
The forgotten mod with unique music is the Tremor Mod, which was discontinued by its developers and is not as active as other mods like the Spirit Mod or Terraria Overhaul.
Step-by-step explanation:
The mod from Terraria that is typically noted for being forgotten and having unique music is the Tremor Mod. This mod adds a substantial amount of content to the game, including new items, enemies, bosses, and a notable soundtrack. However, due to various reasons including developer discontinuation, the Tremor Mod isn't as actively discussed or maintained compared to others like the Spirit Mod or Terraria Overhaul.