I've removed the links because this forum cannot be held responsible for their content and you could potentially be infecting members' computers with malware. If you wish to demonstrate music content, please use streaming links like Youtube or Soundcloud.Talking about "modern music" is like talking about "past music". You'd need to be more specific. There are rules for baroque music, for example, and similar rules for pop music.
In The Manual by Bill Drummond & Jimmy Cauty, they are very specific:
Firstly, it has to have a dance groove that will run all the way through the record and that the current 7" buying generation will find irresistible. Secondly, it must be no longer than three minutes and thirty seconds (just under 3’20 is preferable). If they are any longer Radio One daytime DJs will start fading early or talking over the end, when the chorus is finally being hammered home – the most important part of any record. Thirdly, it must consist of an intro, a verse, a chorus, second verse, a second chorus, a breakdown section, back into a double length chorus and outro. Fourthly, lyrics. You will need some, but not many.
That formula worked for them in the 1980s but there are many songs to break those rules and still be recogniseably - even archetypically - pop. I call this "the perfect pop song", and its structure goes intro, 2x verse, middle 8, chorus, bridge, verse, middle 8, chorus, breakdown, 2x chorus, outro: http://www.youtube.com/watch?v=z2q3FJTFgtk. Then again, that song does follow Drummond/Cauty's rules of combining familiar elements from other pop songs. I can immediately identify the http://www.youtube.com/watch?v=JWULhhL2F18 bassline with http://www.youtube.com/watch?v=-ihs-vT9T3Q pop hooks. It sounds from the first listen like something you've heard before because - hey - you have. Similarly, you can build Lady Gaga's http://www.youtube.com/watch?v=qrO4YZeyl0I&ob=av2e from http://www.youtube.com/watch?v=9jK-NcRmVcw&ob=av2e and http://www.youtube.com/watch?v=lDK9QqIzhwk&ob=av2e.
The trajectory of modern pop is based on http://www.youtube.com/watch?v=MHPcEmswDnE, which begat http://www.youtube.com/watch?v=F5fsqYctXgM and http://www.youtube.com/watch?v=1FYAB74OIeI. Rhythm & blues turned into http://www.youtube.com/watch?v=-2GmzyeeXnQ, which spawned http://www.youtube.com/watch?v=Oeyt9wNYhnQ.
Garage rock mutated into http://www.youtube.com/watch?v=Bif2q_Zo3-4, http://www.youtube.com/watch?v=G8sdsW93ThQ&ob=av3n and http://www.youtube.com/watch?v=2i3mRc-ufUI. Meanwhile, rhythm and blues turned into http://www.youtube.com/watch?v=1Hm08f5b8tc, http://www.youtube.com/watch?v=WtwT492YDvg and http://www.youtube.com/watch?v=eH3giaIzONA&ob=av2e. Hybrids between the electronic-based "dance" genres and the guitar-based "rock" spectrum gave birth to http://www.youtube.com/watch?v=9RoqISei_2I, http://www.youtube.com/watch?v=pmUTBDuUGz8, http://www.youtube.com/watch?v=6_PAHbqq-o4 and http://www.youtube.com/watch?v=s5FyfQDO5g0. http://www.youtube.com/watch?v=f_zLxPNUIqw splintered into http://www.youtube.com/watch?v=iva_Y9W3hJ0, http://www.youtube.com/watch?v=Shvo9t2qznw, http://www.youtube.com/watch?v=aHnFIaLp_ys, http://www.youtube.com/watch?v=9CtDErVTsoA, http://www.youtube.com/watch?v=9kMjAF0nF98 (which is equally influenced by 20th century classical like John Cage), etc. and there are about a billion and two different types of metal/heavy rock-type music.
That pretty much brings us up to the present day. I know I've left out a lot, but you see the general evolution of the thing.