While the game may never have been, there are a few confirmed music pieces for EarthBound 64. The first two pieces come from this page of EarthBound creator Shigesato Itoi's website.
News:
Overview:
Confirmed Music:
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Battle
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This is one of the songs that would be used in battle. It ended up being reused for the final GBA version of the game.
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Tatsumairi Village
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This was intended to be the theme of the main core location of the game, Tatsumairi Village. This song did not make it over to the final version.
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Pigmask Theme (Music from EB64 Trailer)
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The song here was taken directly from IGN's Spaceworld trailer and does contain the sound effects from the game. The song was in the GBA version of Mother 3, but this version was solely unique to the 64 title.
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Bon Voyage, Amigo
While there's no music clip available, in an issue of Dengeki 64, it was confirmed the song, Bon Voyage, Amigo, would be present in the game. Whether it would be the same as it was in the GBA version is unknown.