as many people have said... practice... it took me HOURS with the same two tracks to figure out how to beat match...
years to perfect... now i can do it with my eyes closed (or in a dark @ss club lol) there is no short cut... however...
Here are two things you might want to try -
----Get doubles of a song (two of the exact same track) play one and then beat match the other track with it... then speed one track up (with the pitch, and repeat) this should help you get the feel for what it should sound like (when the track is perfectly matched you'll hear a flanger sound)
----Try House -
Hiphop is actually really hard to start learning (beatmatch wise) pick up some house tracks and match those (the beat hits a little more consistently which makes it easier) once you get it down... switch back to hiphop.
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cliffnotes at the bottom
To answer your other question about pitch and octive- this also comes with time, as a rule you never really want to mix songs that are too far apart in BPM because (as you have discovered) it just doesn't sound natural.
Word of advice dont start mixing songs by "BPM" because the BPM is not always accurate, some songs that are really fast will be read really slow 140 bpm read as 70 bpm or
viceversa, if your using a BPM machine, or it's part of the program your using if that goes out, then you will be screwed... it's nice to use as a reference but dont become dependent on the BPM.
there is software or turntables that will change the tempo and pitch so you wont get that chipmunk or screwed sound... however it's expensive and your much better off mixing songs that are closer in BPM.
You'll learn what works for you, however when i'm in the club i'll speed something up a lot faster than i'll slow it down. i.e. if a song is 95 BPM and the other is 102 i'll speed up the 95 rather than slowing down...
going down lower then about -3 is going to be noticable and up about +4/5 the same. so you want songs to be within that range, again different songs work better with one another.
----cliff----
listen to other dj's that you like, see what they mix, go home and try and do what they do... once you get good enough then start doing things on your own. the best advice is to practice and dont give up... no one is good when they first start.
if you can find a dj that will teach you.