Are you using the same .WAV file for each line of code? You will need to divide the .WAV file into multiple .WAV files with different song names to make sure it is different.

This doesn't work. But if I put an empty sound file in the mus_roundstart<number>_intro, it works until round 6, then the music from The Giant plays after the music I put in mus_roundstart_first_intro, even if I have a mus_roundstart6_intro.
By the way, this does fix the looping issue.
Also, which of the numbers is the volume? It's pretty quiet for me.

1. Go to /Programs (x86)\Steam\steamapps\common\Call of Duty Black Ops III\sound_assets on your computer.
2a. Make a folder to put your songs into (Name can be anything your little heart desires).
2b. Name your songs so you can tell which is which REMINDER YOU CAN ONLY USE .WAV FILES!(again can be anything you want.
3. Open new 'File Explorer' and go to \Programs (x86)\Steam\steamapps\common\Call of Duty Black Ops III\share\raw\sound\aliases and open up user_aliases.csv in a Text Editor (Sublime Text is recommended!!)
4. Copy and paste these under test_sound

//ROUNDS
mus_roundend1_intro,,,folder_name/songname.wav,,,UIN_MOD,,,,,BUS_MUSIC,,,,,,100,100,,,,,,,,2,oldest,,,1,1,,,,,,2d,,,NONLOOPING,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
mus_roundstart_first_intro,,,folder_name/songname.wav,,,UIN_MOD,,,,,BUS_MUSIC,,,,,,100,100,,,,,,,,2,oldest,,,1,1,,,,,,2d,,,NONLOOPING,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
mus_roundstart1_intro,,,folder_name/songname.wav,,,UIN_MOD,,,,,BUS_MUSIC,,,,,,100,100,,,,,,,,2,oldest,,,1,1,,,,,,2d,,,NONLOOPING,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
mus_roundstart2_intro,,,folder_name/songname.wav,,,UIN_MOD,,,,,BUS_MUSIC,,,,,,100,100,,,,,,,,2,oldest,,,1,1,,,,,,2d,,,NONLOOPING,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
mus_roundstart3_intro,,,folder_name/songname.wav,,,UIN_MOD,,,,,BUS_MUSIC,,,,,,100,100,,,,,,,,2,oldest,,,1,1,,,,,,2d,,,NONLOOPING,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
mus_roundstart4_intro,,,folder_name/songname.wav,,,UIN_MOD,,,,,BUS_MUSIC,,,,,,100,100,,,,,,,,2,oldest,,,1,1,,,,,,2d,,,NONLOOPING,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
mus_dogend1_intro,,,folder_name\songname.wav,,,UIN_MOD,,,,,BUS_MUSIC,,,,,,100,100,,,,,,,,2,oldest,,,1,1,,,,,,2d,,,NONLOOPING,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
mus_dogstart1_intro,,,folder_name\songname.wav,,,UIN_MOD,,,,,BUS_MUSIC,,,,,,100,100,,,,,,,,2,oldest,,,1,1,,,,,,2d,,,NONLOOPING,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,

//GAMEOVER
mus_gameover_intro,,,folder_name\songname.wav,,,UIN_MOD,,,,,BUS_MUSIC,,,,,,100,100,,,,,,,,2,oldest,,,1,1,,,,,,2d,,,NONLOOPING,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,

Now just link your map and run and it should load up your custom music

Note: If your perk jingles and other sounds disappear after doing this then please visit this tutorial by CraftDAnimations.
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When I use this, the first round start sound is played twice in a row, and whenever a new round starts the round start sound is played three times in a row. How do I fix this?