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There are a few significant songs that don't get recorded automatically when discovered.

[edit] The Ghost Mother's Song

The Ghost Mother's Song is necessary to proceed through certain portions of the Abyss and the Body but isn't explicitly given to you as other songs are. Instead it's sung in the background of a particular area. The onus is on the player to interpret and remember what the notes are and play them back at the appropriate time. Given that this song is rather complicated this can be a frustrating task for those of us without a well developed sense of pitch.

[edit] The Whale's Song

This song allows entry into the stomach of the whale that resides in the Abyss, to the left of the transporting sea turtle, past a sun-form door and some steam. The song can be found inscribed on a wall over an image of a whale hidden behind a false wall and a heavy current in the area between Open Waters and The Abyss, just above the Arnassi Ruins.

[edit] The Seahorse's Song

Played to start the race mini-game in the Arnassi Ruins. Unlike the other two these notes are written on the wall in the only place you'd need to use them. Mentioned here only for completion's sake.