a note on the hyperxcloud II.... they received quite alot of negative feedback due to many issues which is why the original hyperxcloud (not II) is recommended over them. for the money it certainly is a good pair of cans however for your budget you can do much much better (though this is your choice of course).
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i am not saying that no headphone is capable of providing both good highs and bass, only that certain designs accentuate certain areas of the spectrum or excel more in certain areas.
now, you will not find a headphone which provides both earth shattering eardrum rupturing bass-head sub-bass levels and still remains articulate and clear on highs, but if you want to keep things in moderation then yes, you have headphones which can do both.
the dt990 for example has great (though sometimes piercing) detailed highs and fairly decent bass for a set of open cans like i said before. it will not generate excessive bass like bass-head cans but certainly enough to be considered enjoyable.
the hd600 is much the same way except it is more neutral and you can really hear the mids shine more than the 990's since this is more of a flat eq profile instead of peaked in the treble/bass like the 990s are.
the ad500/700/900x and many akg cans are all rather bass light and focus more on large soundstaging, positional audio and treble/mids. some people (especially competitive gamers) find this to be great as it gives them an advantage though perhaps not as enjoyable as some other models athough i do know some people do love the bass-light sound (typically people who care about subtle nuances and details in sound).
the hd558 or hd598 bring up the middle of the path. fair all the way around without excelling in one area.
honestly i'd need to know what kind of "sound profile" you are expecting out of them and some of your tastes if you want more than just a few ideas thrown out there. i know nothing about what kind of cans you're looking for right now other than you want to game with them (which is why i'm suggesting all open cans... though perhaps you dont want open?). basically what i mean by sound profile is how you like your sound to well... "sound" to you. compare it to eq settings you may change on your portable devices. for example:
-do you want a pair which is very detailed, articulate and focused on highs and mids but not so much on bass?
-do you want a pair which is more focused on really punchy bass but still alright for highs/mids but not quite as detailed?
-do you want a pair which is a good all rounder which has a neutral sound profile so excels in no one area but gives a balanced sound?
-do you want a set which is more detailed but may be a bit harsh, or one which is a bit smoother but may lack certain nuances or details?
-do sharp, detailed highs hurt your ears or cause fatigue?
-do you care if the headphones leak sound in/out? (if you do care and dont want this, going with a closed can is the fix but hurts soundstage alot)
-do you care about soundstage? basically how open the headphones feel. you can compare it to listening to a band in an open-air park and inside a bar. at the park you will have an airy quality to sound and you can tell distance and location. in the bar sound is more up-front in your face, direct and it will sound close to you though you can still tell direction. this is why many gamers like open headphones since they may give you an edge.
-do you wear glasses or have large ears or a large head which would affect comfort? some models are better for people with such prerequisites.
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no, i do not have a modmic myself though it is the single most popular add-on mic currently and gets rave reviews. if i did have a pair of headphones that i used for gaming and wanted a mic it would be my first choice (i use a hifi speaker system instead of my headphones for gaming and generally do not like using a mic... call me oldschool if you will).
you could use the blue yeti for gaming if you did not mind it sitting on the desk in front of you. its an exceptional microphone (on par with the at2020usb i listed earlier) and sound quality is certainly good for the price. your choice, but if that is not an option then i'd go with a modmic yes.
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want to know about virtual surround? put on any pair of headphones or earbuds and give the below a listen. if you dont have ANY headphones at all then you can listen with speakers but you may not get 100% of the effect.
https://www.youtube.com/watch?v=Y6ROujJ8Ae8
this compares stereo sound with dolby headphone with sbx. personally when i do rarely game with my headphones on (i use the m50s which has a small soundstage, closed design and more bass.. since it fits my taste profile best while perhaps not being ideal for gaming) such things as virtual surround dont bother me. typically games have enough visual and auditory clues to know whats going on around you to not require such software. virtual surround also distorts sound a little bit and i prefer to listen unaltered even if i do not gain any small advantages for positional audio. keep in mind some of the larger soundstage headphones have great positional even without this software.
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do you need an amp?
for some headphones like the hd598, hd558, and other low power cans.. no, you do not. onboard audio is fine and can power them fine. this is also mostly true with the ad500x and similar models. adding an amp or more powerful soundcard however can certainly improve sound quality a bit on them and give them a bit more low end.
some headphones like the dt990 you will definitely want to run with an amplifier since they are rather hard to drive. the hd600 can be ran with a powerful soundcard though it too likes an amp.
basically, the answer is "it depends" on the headphone you get. read the next section for additional clarification.
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so, confused about dac, amp, soundcards, etc?
onboard only: powers low power headphones easily. do not get virtual surround unless your motherboard supports it. some onboard is not quality and might give you buzzing, hissing, distortion or popping though it is highly dependent on your board and you need to test it out on your board so you know. some boards run great, others are not so great.
onboard + external amp: if you find that your onboard "sounds" good or has options you want like virtual surround but doesnt quite have the power output to get the most out of your new headphones then connecting up an external amp to the line-out will work great. or, you can double amp out of the headphone jack to the amp (at the cost of slight distortion) to use a lower powered external amp to get a similar effect as a larger amp since you're using both the motherboards amp and the external. or in the case of lower powered headphones even a small external works fine.
soundcard only: good for moderate to low powered headphones. sound quality increase over onboard and you can gain access to virtual surround if you wanted.
soundcard + external amp: if you wanted virtual surround as an option or if you wanted the processing to be done by a soundcard but it doesnt quite have the oomph to power your headphones this is a good option. connected up to the line-out with a decent amp is suggested though some people do double-amp if on the cheap at a slight cost of distortion.
external dac + external amp: for people who do not want or care for virtual surround and who want to pull all sound processing outside the pc for zero (or lowest possible) signal noise. great choice if you're an audiophile but an expensive choice if you are not.
notes: having an external amp with more demanding headphones (or having a small amp to just "boost" the bass on low or medium powered headphones) means that you can also use this portable for on-the-go use with portable devices. they also do make portable dac+amp units as well which can be used both in-home and portable though you did not stress any desire to do this.
while it depends on your choice of headphone.. i'm thinking either onboard only or soundcard (if you choose easy to power headphones or a soundcard +external amp if you choose something heavy.
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....i've run out of time to continue to work down your list of questions. if i didnt answer fully any of them feel free to respond below with any additional questions you have.