[DocVS]

Hi!
I am looking for closed or hybrid over-ear headphones. I listen to a lot of indie-rock, but rap and hip-hop are also common for me to listen to. I would like a slightly bassy signature.

 

[KG Jag]

What will be driving these cans?
 
Do you want them for portable use?

 

[DocVS]

I am also looking for some other source, right now I only am using an iPhone. What to you suggest for a higher quality audio source? I have a budget for new headphones and ahigher quality set up of about $900

It would need to be portable.

 

[reddog]

I would get the HE-400i, a great, fun sounding headphone, that is ever so easy to wear and drive.

 

[KG Jag]

Get an Astell & Kern AK100 at closeout prices.  Buydig selling through eBay (for example) offers a great deal at under $400:
 
http://www.ebay.com/itm/Astell-Kern-AK100-Mastering-Quality-Sound-MQS-Portable-System-Memory-Bundle-/321512982150?pt=Cassette_Players&hash=item4adbaac686

 

[KG Jag]

I would get the HE-400i, a great, fun sounding headphone, that is ever so easy to wear and drive.

 
It's open and big.
 
OP wants portable and closed (or "hybrid"--whatever is meant by that).