Just rename "winmm.dll" to "wav-winmm.dll" in the main folder, which is it's original file name according to file properties/details.
For me it works on Windows 10 and WITH ingame CD-Music. Perhaps try the same on WIndows 11 and/or with Imperialism II.

Before i had the same common problem that Imperialism didn't start at all and intead put 100% CPU-load on one core.

Have fun!

Thanks , Jusch25 for the hint !! But it does not solve the music issue with Imperalism 1. I use Windows 8.1 on my laptop. Already mentioned the issue in a different topic in the forum:
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Hello !! I have nearly the same issue: game starts with music. But after one round of gameplay, there is suddenly no music anymore. Only the unit and industry sounds (ambient sounds) are still playing. Any new ideas how this can be fixed ?? The hint with renaming the winmm.dll-file (from other forum posts) does not solve the issue. There are already several topics in the forum, with the music issue. Help by the GOG team would be appreciated, as this seems a common issue for Imperalism 1. Cheers !!
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i would recommend to make a copy and rename it and keep the originale one with it's original filename just to be sure for other apps