I'll split the audio performance analysis into two parts—gaming and music. Even though the headset produces the same sound regardless of what it's being used for, you won't necessarily look for the same things while annihilating your virtual opponents as you will when listening to your favorite tunes.
Gaming
Even though there's no official confirmation, it's safe to assume that the Sennheiser GSP 670 uses the same dynamic speaker drivers as the GSP 500/550/600. In terms of sound quality, it's closest to the closed-back GSP 600. It's worth mentioning that the built-in electronics don't feel underpowered, which is the case with the GSP 550 as its USB sound card just wasn't able to match the requirements of the headset. In other words, the GSP 670 can get quite loud, and does so without the slightest hint of distortion—sweet!
Overall sound quality of this headset is where you're getting your money's worth. The speaker drivers are tuned to produce a warm, deep, and rich bass, with a very informative and clean mid-range and detailed and surprisingly open highs. As a result, the GSP 670 is pure joy to use when gaming. It sounds exceptionally fun, explosive, and lively and proves extremely versatile: in multiplayer first-person shooters you'll pinpoint the location of your enemies with ease and extreme accuracy, and after you switch to an atmospheric, dialogue-driven single player title, this headset will impress you with the warmth and fullness of the sound it produces.
That's the thing with headsets from Sennheiser's GSP 5XX and 6XX lineup (except for the GSP 550, which limps behind because of its underwhelming sound card): they cost quite a bit, but you most likely won't feel inclined to buy another pair of headphones for non-gaming usage.
Thanks to a great seal the ear cushions make with the ears and the head, passive noise isolation is excellent and definitely contributes to the overall sound quality. Nobody close to you will be able to hear what you're listening to, nor will you hear what's happening around you; unless you activate the microphone sidetone feature, that is.
Music
The warmth, depth, and fullness of the Sennheiser GSP 670's sound transfers beautifully from games and movies to music. The thick yet punchy bass is an instant crowd pleaser in genres like EDM and rap, but that's just the tip of the iceberg. Thanks to the mid-range being very clean and without the bass interfering, both male and female vocals sound great too, and the smooth highs tie everything together wonderfully. This headset is extremely easy to listen to even when playing more demanding genres, like rock, metal, or classical music. I can't point out a single music genre this headset can't handle properly. For a closed-back headset, the soundstage is impressively wide and airy. The stereo imaging works nicely inside the space it's given.
Connecting the Sennheiser GSP 670 to a higher-quality DAC/amp isn't an option as it isn't equipped with a 3.5-mm input.
All in all, in terms of sound quality, this is quite possibly the best wireless headset I ever used. The only one that comes close is the $279/€279 SteelSeries Arctis Pro Wireless. It's hard to say which one is better as their sound is vastly different. The GSP 670 sounds significantly wider and larger—the Arctis Pro Wireless moves everything "closer to the ears" and provides a much more intimate experience. However, its spatial positioning is esports-grade, perhaps even better than that of the GSP 670. Both are comparably clear and detailed. The GSP 670 has a meatier, fuller bass, but the bass on the Arctis Pro Wireless is faster and with a crispier punch. The Arctis Pro Wireless can play louder as well. There are some other differences I'll save for the conclusion.
7.1 Virtual Surround Sound
The Sennheiser GSP 670 supports 7.1 Virtual Surround Sound. Most of my testing of the surround sound performance was done in Battlefield V, a game well-known for its superb audio production, and Apex Legends. The surround sound is toggled on either by pressing the Smart Button on the right ear cup or inside Sennheiser Gaming Suite.
7.1 virtual surround sound is much the same as with the GSP 550. Meaning, the surround sound feature is implemented well enough to be completely usable in a wide variety of titles and genres, but don't expect miracles. I didn't really get that sense of complete sound immersion, of it coming from all sides. Everything did sound wider, with an increased sense of scale, but there's an unmistakable sense of artificiality in that width. I'd never consider using this 7.1 virtual surround sound for multiplayer gaming as it makes spatial awareness more difficult—it is harder to determine the exact location of enemies, especially in terms of distance. For single player gaming, your mileage may vary. Sennheiser managed to preserve the bass and a big part of the sound clarity with virtual surround sound on, so do give it a try—perhaps you'll enjoy it in some titles.