Here are some examples of the DJ notation in use. The great thing about the proposed DJ notation is that it's as granular as you make it. Some DJs only need to know how the track starts and ends, other ones need specific times.

Song examples

~#-
This track starts with a melodic sequence with no beats and ends with beats only. Conclusion: the track might be difficult to beat-match into, but on the other hand it will be easy to transition from this track to the next one. A good start of a set, maybe?

-#-
This is the basic notation of a song which starts and ends with beats only. In other words: dj-friendly, easy to mix in and out.
Most dance tracks actually look more like this: -=#=- but in most cases, when you know the song well, you won't need to be that elaborate.

#
The track starts away with beats + melody and ends the same way. Your best bet here is to mix into this track from beats only and also transition to a beats-only sequence.

<###>
This track is even more of a pain than the one above. It fades in with a melody, so you have to seek into the track to beat-match effectively. It also fades out, so you have to be very careful when transitioning to the next song.

-
A beats-only track, probably a dj tool. Simple to mix, but boring. Use to spice up a track or to transition to an "unmixable" song (like # above).

!=#=-
A detuned song. Normally, a drone (notation =) is pretty easy to mix into when you are harmonic-mixing. Not in this case. "Detuned" generally means that you should avoid mixing this track into any other melody, drone or riff. Stay safe with beats-only.

-(1:06)#(5:48)=-
The track starts with beats-only (easy to mix). At 1:06 the riff kicks in. The song plays until 5:48 when it breaks down to a drone and after that to beats-only. There may be any number of break downs and/or beats-only between 1:06 and 5:48. The DJ decided he doesn't need to know (he'll play the whole track).

-(0:23)=(0:46)#(6:12)\(6:48)-->
A very elaborate DJ notation. This track starts with 23 seconds of beats only. Then a simple melodic sound comes in (still pretty easy to mix in). At 0:46, the track really starts rolling. The DJ shouldn't be doing anything significant until about 6:12 when the final climax breaks down (presumably into a much more orderly melody). From 6:48 on there are only beats. They continue for some (unspecified time) and then they fade out.

You would read the last example out by saying: "beats, zero twenty-three drone, zero forty-six riff, six twelve break down, six forty-eight beats, beats faded out".

DJ set examples

DJ notation is also great to write down mixes or sets. Just use fixed-width font and overlay the notations on two or more lines.

~#=-
  -=#--
     ~#-
       -=#~

Hear the story of this particular DJ set notation:

Above is a simple four-song DJ set. The DJ, let's call him DJ Notation, started out with a melody without beats. That's always a good start, isn't it? The beats of the first song kicked in after a while. The DJ played the whole song and when it broke down to a drone, he mixed in the starting beats of the next song. When the drone of the first song ended, the other one's drone started. Lucky him!

The second mix was a little harder. DJ Notation waited till the second track breaks down to beats-only and mixed in the melody-only of track number 3. When the riff of the third track kicked in, the beats of track 2 were still in the mix.

The last mix was a bummer, though. The riff of track 3 ended unexpectedly, so DJ Notation mixed one beats-only sequence into another one. Yawn! The audience threw some beers so DJ Notation let the last song end with a melody-only sequence and left the booth.

The end.