Hitler Waltz is one of the four songs that are included in Wolfenstein 3D (DOS), but never played. It's timing and sound implies that it was meant to be used for background music for a mission.
John Romero said that there wasn't a particular reason why this song was excluded from the game. However, if you look how the music is utilized, each background song is used four times--only the secret levels don't follow this pattern. This track could have been written to fill one of the secret levels that used repeated music, but was just never assigned.
The song, naturally, is in the 3/4 time signature, fitting the waltz theme. It is in the key of A minor and plays at 88 beats per minute. The lead instrument is a type of low-range string instrument (possibly a viola, cello, or even contrabass). It is accompanied by harmonizing clarinets every second and third eighth-notes of each bar. A bassoon also accompanies throughout the song, usually playing in dotted half-notes, but sometimes plays faster notes. There are no drums or percussion. While the song starts out in the key of A minor, it shifts up to D minor at approximately the 0:16 mark. At about 0:32, the song goes back to the beginning, but this time with slightly different riffs. Also, during the second portion, at the 0:57 point, the chord shifts to E major, F major, back down to E major, and finally back to A minor.
The song sounds a little similar to another Prince song, Nobody Told Me About id.
Wolfenstein 3D (DOS)
Hitler Waltz is track #6 in the game's data files, and the IMF meta tag title is "HITLWLTZ". It's not included in demo release.
Spear of Destiny (DOS)
The song would eventually find a home in this game, where it is played at the initial copy protection questions.
In Spear of Destiny, it is track #20 and has the IMF tag "COPYRO", however, it is not included in the demo release of the game.
Wolfenstein II: The New Colossus (W64)
This song makes an appeareance in the arcade game "Wolfstone 3D", which parodizes Wolfenstein 3D and can be found during the actual gameplay of the "New Colossus". It is heard on the title screen, replacing Horst-Wessel-Lied.
This track was just rendered from AdLib MS-DOS original version, so the only difference is the PCM output.