Originally Posted by initialsBB
Polyrhythm ... Polyrhythm - Wikipedia, the free encyclopedia
Polymeter ... Meter (music) - Wikipedia, the free encyclopedia
As somebody mentioned above - Chuck Berry was a king of Polyrhythm ... a lot of those old r&b or r&r songs had a strange mix of straight and shuffle timing that always used to throw me ... part of the voodoo ...
Poly simply means "many". So you can put more than one rhythmn together, and both can be 4/4. Polyrhythmn should not be confused with Polymeter, such as Led Zeps Kashmir where the drums stay in 4/4 but guitars and orchestra play a 6/4 part that only coincides on the One every 12 bars ... fun stuff to play and compelling to listen to.
And simply cutting out or inserting the odd beat here and there to make songs cooler is something else and best done by feel. I'm sure Burt Bacharach and Lennon, McCartney & Harrison never really thought to much about what time signature they were in when they wrote. Burt would have had to think about it when he notated it, and George Martin would have figured something out for The Beatles.
Some of the timing effects were created with tape editing. For example in McCartneys's Let Me Roll It, there is a cool timing bit where a bar gets repeated and that was a tape edit mistake that sounded so cool they kept it.
If writing a song and it starts to get a bit boring, consider chopping a beat out to make it cooler. Or adding some beats as required. Force dancers to change their leading foot ...
I always find the timing of that song from Babe (the pig movie) ... to be very compelling (If I had words to make a day for you) ... and even 'How Great Thou Art' has an interesting timing that throws most people. Imo it's all part of why those songs were massive hits in their day. I actually think it's a feature of some older church music that influenced Western music.