A couple years ago, the idiot I was purchased
a pair of Beats Solo HD Drenched in Color. Now that I am beginning to turn into an audiophile, I realize my mistake. Do I need to get new headphones, or am I still able to appreciate the difference between mp3 and CD quality music? Also two other mini questions: Is it okay if I don't have an amp? I didn't even know headphone amps existed until recently. 2. Should I "equalize" my headphones? If so, how?

Even when the sound of the Beats Solo isn't the greatest you should stay with the thinks you like. If you like them it is okay, it's all about`personal preference.
Since the Solo HD isn't really famous for its clarity hearing a difference between CD and mp3 is a little bit harder but possible. This depends on the quality of the mp3 file and the actual recording of the CD. The questions you should ask yourself is: 1. Do you need to hear the difference between CD and mp3? 2. Did you enjoy one more than the other? 3. Are you unhappy with the sound of your Beats headphone?
 
Equalizing is a good way to adjust the sound of your headphone to your personal preference. I often use the Equalizer according to the music genre I am listening. But take care, some headphones are not really adjustable and changing the equalizer won't make a big difference. The Headphone I use is the Fidelio X1 which is very sensible in case of equalizing. I don't know how the Solo HD act, so just give it a try. 
 
I think you don`t need an AMP when your headphone is easy to drive (low impedance/ohm). Having a headphone which is over 50 ohm a smartphone could have it's problems while a good soundcard on your computer could deal with it. Since the Solo HD have 32ohm I don't think you need an amp.
Some people use an amp not because of it is necessary to drive the headphone but to colour the sound and improve the sound quality. My personal experience is that a cheap amp (<60€) can't really improve your sound when the source itself could power the headphone by itself. Using mp3 is also a limiting factor. 

It's too late. You're already in. Time to search for bassy audiophile headphones. 
 
In reality if you like the bassy character of your headphones and your music matches that character you might be disappointed by headphones audiophiles find better quality. But you wouldn't be here if you weren't curious so look into bass emphasis headphones and surely you'll eventually find something that has as fun a bass emphasis as your beats but with better detail, separation, resolution, etc. 
 
Most consumer headphones you don't need an amplifier until you get into real audiophile territory. 

Find a musical instrument store that sells headphones. in the US there are stores such as Guitar Center. Listen to some headphones by brands such as Sennheiser, Beyerdynamics, Audio Technica, and the better quality AKG headphones. 
 
As for mp3 files, those at 320kbps or 256kbps can sound quite good.

You may or may not hear a difference between lossless and MP3. Depends on the bit rate too. You most likely will never hear a difference between 256 kbps AAC and lossless with any gear, ever.
 
You don't need new headphones, but you will definitely get better sound by upgrading to better models. You could go down the path of trying out various headphones that are readily available, but here's a tip: electrostats sound better than everything else to many people, including myself. A bit more advanced, but well worth the trouble. (I can offer advice if you want the best sound quality without spending too much money.) On the other hand, as others have mentioned, you may prefer a more "colored" sound over a serious audiophile headphone.
 
If you want to do serious equalization, check out these resources:
http://www.sonarworks.com/headphones/overview
http://www.head-fi.org/t/413900/how-to-equalize-your-headphones-a-tutorial
http://www.head-fi.org/t/587703/how-to-equalize-your-headphones-a-tutorial-part-2
http://www.head-fi.org/t/615417/how-to-equalize-your-headphones-advanced-tutorial-in-progress

How do you not click into a Head-Fi thread with this title?

The obvious answer is and always will be...YES! Even if you've been gifted several TOTL cans, amps, and dacs...this is Head-Fi for cryin' out loud.

May I suggest changing the title to "What new headphones should I buy?"

Get a pair of Phillips X1s. They are open headphones--not for portable use--but you should enjoy their bass and big soundstage

I don't care about bass nearly as much as I care about sound replication. I don't want distorted sound. I want the headphones to emit what is put in. I want the sound to be exactly what the audio file is.

flacisntgudinuf said:

I don't care about bass nearly as much as I care about sound replication. I don't want distorted sound. I want the headphones to emit what is put in. I want the sound to be exactly what the audio file is.

Click to expand...

 
No headphone can do that, but electrostatic ones can get the closest. Here's why.

Stay with Beats.....anything less is a total waste of money!

What's the cheapest pair of good electrostatic headphones you can get?


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vexun said:

What's the cheapest pair of good electrostatic headphones you can get?

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Used ones on eBay, usually out of production models. They also require an electrostatic headphone amp. (Or an adapter powered by a speaker amp.)

flacisntgudinuf said:

I don't care about bass nearly as much as I care about sound replication. I don't want distorted sound. I want the headphones to emit what is put in. I want the sound to be exactly what the audio file is.

Click to expand...

OK.

So (1) What is your overall budget? (2) What source devices (phone, computer, etc.) do you have to use? Make and model?

vexun said:

What's the cheapest pair of good electrostatic headphones you can get?


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Click to expand...

Right now Koss ESP-950s are $700 including the amp -- NIB with lifetime warranty.

Here's a review by Jude...
http://www.head-fi.org/a/head-fi-buying-guide-ultra-high-end-headphones-summit-fi#user_koss_esp950

Well electrostatic headphones are too expensive for my budget lol. I got Beats because they were under $200