The FiiO E17 “Alpin” + AIAIAI TMA-1 or Pro700 Mk2 seem like a mix you’d recommend, but I’m concerned those cans will be uncomfortable for day-long use.  Also I don’t know if that DAC/amp is the best for my style of music/headphones.  Third, some of my techno tracks have stunning vocals, and I don’t want to miss out on those high notes while enjoying the bass.
The Bose QuietComfort 35 II is arguably still the most comfortable pair of noise-canceling headphones you can buy. Released in the summer of 2018, you can think of the QuietComfort 35 II as simplified, less sophisticated and more affordable version of the new Headphones 700. The lack the transparency mode, superior call quality, USB-C charging port and on-ear gesture controls, but they still boast really impressive noise-canceling skills. The also have the tradional foldable design — it folds more compactly — that many travelers really like.

We run every pair through a rigorous testing process over several days or weeks. That includes playing them in all sorts of scenarios — be it on a bus, in the listening room, or at the office — and playing back from a wide array of sources. We know most people use their headphones with a smartphone, often with lower-quality MP3 resolution tracks, so we do, too.

If you just want to block out sound without active noise cancellation, good over-ear headphones will naturally do that to some extent. This is called noise isolation, and it simply works from the earcups forming a good seal over your ears to prevent outside noise from getting in. It's not as effective, but it's less expensive than active noise cancellation and doesn't require power.
Once you’ve got that all order, to put a cherry on top it would be ideal for the amp to play nice with my laptops (PC at work, Mac at home) *and* my *iPhone* 4S.  I haven’t found a headunit that works with PCs and iDevices.  If one doesn’t exist it would be a big plus for the amp to include inputs so I can get digital sound out of my iPhone (with the Pure i20 or its ilk) and into my headphones.
Over-ear and on-ear headphones effectively block out outside sounds, allowing you to hear your music or whatever else you're listening to crisply and without distraction. Over-ear headphones are sometimes known as full-size headphones because they completely envelop the wearer's ear. This results in what's known as passive noise reduction, which makes these some of the most-preferred headphones available. The only drawback is that your ears and the skin around your ears can get warm and sweaty. These are usually the heaviest type of headphones.
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