
Sennheiser
HD 560S
Budget gaming king with clear sound, but tight fit.
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Most headphones are tuned 'warm' so if you felt the 559 was too muddy/boomy you're probably the (semi-rare) person who prefers a 'cold' (bright) sound, something with bright treble. Someone already suggested the Grado GW100 and I'll second that based on the info you've provided here. On-ear headphones aren't for everyone though, but that's the only one I can think of off the top of my head that is both bright and wireless and in budget. In fact, it's the only one I can think of that is both bright and wireless period.
The HD 559 are really lightweight and comfortable to wear for hours. This would probably be my choice.
1. Audio is very subjective... listen to them in store to compare 2. Getting a separate headphones and microphone is in the end better value for your money. 3. Wireless vs. Wired.... I'd go wired any day of the week with the standard 3.5mm jack as that means I can basically connect it to anything, if you need it to be USB you can even get a cheap 5 dollar USB soundstick... Wireless usually is more expensive and usually has more delay. 4. Over-ear, on-ear or IED, that's all up to you, over ear has better sound isolation 5. Open- vs Closed back, open has a wider soundstage making it so that it's easier to pinpoint the sound but has sound bleeding to the outside. Closed-back has less/no sound bleed but a narrower soundstage. just my 2 cents. (I bought myself a Sennheiser HD559 and am using my webcams microphone, which was slightly more expensive than your budget but sounds very good to my ears)
**Budget and location** - Canada; budget is 250 to 500 usd (350 to 700 cad). I can stretch it a bit. But not too much. **Source/Amp** - USB or colourful hole thing? Willing to adjust if I can buy a dongle. **How the gear will be used** - Always at my home office where no one else is really around. I work in sales (lots of calls and meetings where I talk a lot while typing) but I want a wireless headset with a mic. My current setup (Snowball mic + Seinnheiser HD 559) makes my desk too "busy" and would rather avoid cables and the giant ball on my desk. Open back is fine; better even for classical music imho. **Preferred tonal balance** - Accurate acoustic / good treble / Balanced for my purpose. **Preferred music genres** - Classical is the genre I am having issues with. I looked into the Sony XM4 or 6 but honestly, it felt less than ideal with this type of music. Otherwise, psychedelic rock (Jefferson airplane, Pink Floyd, etc.) or EDM. **Past gear experience** - Sennheiser HD 559. Feels muddy and boomy. Not the quality I am looking for. I don't take it out of the office or anything. Open back is usually in my experience better for classical music but I am not some professional guy neither; just what I enjoy. Wireless is a must; mic too but any suggestions like a wireless ModMic I am willing to consider if people think they are good choices. I have considered the Sony XM4-5-6, Momentum 4 and uh, that's about it. A lot of good recommendations came up in my search but everything seems tuned for bass or genre of music that in my experience aren't well-tuned when I switch to classical. Thanks a lot for the help on this!
I haven't used a gaming headset in about 15 years. Went from Sennheiser HD298s to Sennheiser HD558s, to my current cans, Sennheiser HD6XXs with defenestrated sheepskin velour cups. They're incredibly comfortable and despite daily use for about 5 years and a total of 5 house moves, they're still holding up with zero damage. I've paired all three sets with Antlion Modmics and have never been let down. I goddamn love this setup. Congrats on the killer set of cans, OP (phrasing)
Also the hd550 is on sale which is basically the same as 560s except a lil warmer, and a tiny bit more bass
It's more of a technical side grade than an upgrade imo. But depending on the person and the ears some people prefer the 560s and others say that's shite and prefer the 550. This is where comparing frequency graphs can come in handy.

Sennheiser
HD 560S
Budget gaming king with clear sound, but tight fit.

Sony
WH-1000XM4
ANC king, durable, but unreliable mic and touch controls.

Sennheiser
HD 6XX
Legendary mids, durable, but narrow soundstage and weak bass.

Sennheiser
HD 490 PRO
Super comfortable, wide soundstage for gaming, versatile pads.

Sennheiser
HD 599
Super comfortable, easy to drive, wide soundstage, open-back.

Ranked #1
Sennheiser - HD 6XX

Ranked #1
FiiO - FT1 Closed-back Headphones

Ranked #1
Sennheiser - HD 560S

Ranked #1
Sony - MDR-7506

Ranked #1
Sony - WH-1000XM4

Ranked #1
Sennheiser - HD 560S