I don’t know what brands are available in Europe so I can’t recommend a certain brand. I am also not sure what synthetic music is but my guess is that it is music where the musicians create it by using synthesizers rather that traditional instruments and in my experience it is rather a bass centric style. If I am correct you are going to want a very high output sub since you need to reproduce a 40 Hz signal approximately 20 dbspl louder than a 1K signal just to have them sound like they are at the same volume level. I also believe that you will require a driver no smaller than 30 cm and you will want that in a sealed well braced and damped enclosure. One of the biggest issues with subs is to be able to get the driver to stop quick enough and subs that have servo control are better at doing that. Subs with opposing drivers have less cabinet issues.
Having said that, have you tried bi-amping your hrs-130’s? That might give you the extra bass energy you are looking for with-out the drawbacks of a single sub woofer.