VGFacts

https://www.youtube.com/watch?v=wGX4obVl64w - SMB1 classic level music
https://www.youtube.com/watch?v=LI_mwl3QcYA - SMB3 World 1 music.
https://www.youtube.com/watch?v=fB2bZM19YPk - Mario's Pad music
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https://www.youtube.com/watch?v=D2S3oyL5VRw - Gaz playing with geno music
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https://www.youtube.com/watch?v=Lw049q22-hY - SMB1 classic starman
https://www.youtube.com/watch?v=DncwPB_xY1Q - SMRPG's Starman theme
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https://www.youtube.com/watch?v=c0SuIMUoShI - SMB1 Underground music
https://www.youtube.com/watch?v=pxAcZmbm1hY - SMRPG underground music
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https://www.youtube.com/watch?v=LI_mwl3QcYA - SMB3 World 1 music.
https://youtu.be/DFkNUboHvD0?t=6s - Super Mario RPG's opening cutscene. Speed up the footage to x1.25-x1.5 to compare.
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https://www.youtube.com/watch?v=h-xih93YIwk - SMB3 Bowser battle theme
https://www.youtube.com/watch?v=_tFWZYTzh_Y - SMRPG Bowser's Battle theme
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https://www.youtube.com/watch?v=se-sEfV95wg - SMB3 Bonus Stage music
https://www.youtube.com/watch?v=tS9v8iEAo7U - Grate Guy's Casino music

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Some of the music in the game is actually remixed from older Mario games. The ones that are easy to tell are;

• Mario's Pad music is a mix of the classic level music from the first [[Super Mario Bros.]] and the overworld music to Grass Land in [[Super Mario Bros. 3]].
  
• The music that plays when gaz plays with his Geno doll is obviously the classic [[Super Mario Bros.]] theme
  
• The Starman theme is a remix from the classic Starman theme, albeit a bit harder to hear than the original.
  
• The underground music is remixed from the classic [[Super Mario Bros.]] underground music.
  

The ones that are harder to tell are:

• The music to the opening cutscene of Princess Toadstool in the garden is actually a slowed down and shortened remix of the overworld music in World 1 - Grass Land, from the game [[Super Mario Bros. 3]].
  
• Parts of Bowser's Battle theme from the beginning of the game are remixed from the music of Bowser's Fight music in [[Super Mario Bros. 3]].
  
• The music in Grate Guy's Casino is remixed from the Bonus Stage music in [[Super Mario Bros. 3]].