I'm new to the "music scene". Well, at least the more technical parts of it.
In ninth grade, our music teacher taught us how to do a tapping/drumming thing where we tap 3 times on one leg and 4 times on the other in 4 beats.
What is this called? How to do it?
Polyrhythm. It's good thing to learn to do. 4 against 3 is nice, before that you should normally try 3 against 2.
Normally it's hard to do at the start. I had to break it down, splitting the beats. For 3 against 2 you need to split the pattern into 6, for 4 against 3 into 12. I made two grids to show how:
It takes a bit of practice but it is very good for your time feel as a musician to learn to tap these. Normally you use two hands, one doing each line, or a hand and a foot. It helps if you use two "instruments" (whatever comes to hand) that have quite different tones. (And soon you'll have people around you saying "will you stop that tapping" ...)
There is a common mnemonic for learning the 3:4 poly-rhythm. Apologies for the minor profanity, but it goes like so:
Get two people, call them "3" and "4" and give them the following instructions:
Both phrases include the word "Pass", so they should say that at the same time. If you get the timing right, you'll get the following somewhat impolite request at the dinner table:
The natural way of saying of that phrase is basically a perfect 3:4 poly-rhythm.
Overlaying two different evenly-spaced subdivisions with no immediate common factor, is called polyrhythm:
https://en.wikipedia.org/wiki/Polyrhythm
Polyrhythm is the simultaneous use of two or more rhythms that are not readily perceived as deriving from one another, or as simple manifestations of the same meter.
When starting out for the most common polyrhythms involving 2/3/4, if you subdivide down to eighth notes or triplet eighths as the common factor you can find where each larger beat will land.
You can conceptualize 3-over-4 as a case of 3-over-2 with the 2's subdivided once more (which only requires a divisor of 6-per-bar to map them together), and this older question addresses the 3-over-4 case specifically with notation:
How to count polyrhythm 3 against 4 in common time?
(When you get into wackier polyrhythms involving 5s and 7s over base-2's, this mathematical fractions method becomes useless and you start going by feel and true limb independence. But that takes a while of practice internalizing how the basic 3-vs-2 polyrhythms feel, and playing stuff in odd meters with 5's or 7's instead of just 3/4 and 4/4)
The late drum teacher Charles Dowd called this the Rhythm of Life. [I assumed this was in reference to a song utilizing this rhythm.] He taught it in the context of an Afro-Cuban-style pattern on drum set:
The two top-line patterns are equivalent, but it is the bass drum (lower line) that names the underlying pulse. If one instead plays the 2nd pattern with dotted eighth notes on the bass drum, it becomes the 1st pattern, but now thought of in 3/4 time. The perceived change between time signatures comes from changing from 3 to 4 on the bass drum.
Eventually, this is most rewarding when one plays, say, the 2nd pattern with hi-hat on quarters and changes bass drum to dotted eighths. [This makes the 4 over 3 happen between both feet.] Then continue to play the top-line pattern on bell of cymbal and finally include a clave-style rhythm with left hand.
Splitting up a 4 against 3 pattern into 12 equal parts doesn't really work except at a very slow tempo. You just need to get train your brain (and hands) to do different things at the same time.
A good way to learn to do this is set a metronome to a slow tempo corresponding to one "beat" per bar. Start by tapping with each hand separately for several bars. Then alternate one bar with each hand, and finally put both hands together.
Three against two or three against four is fairly simple. Here's a snippet of organ music where you have 3 against 2 both with your left hand, simultaneously with 5 in your right hand, and 4, 6, 5 and 7 with your feet, on successive beats.
Trying to count out "7 against 5 against 3" by splitting up to beat into 105 tiny parts isn't a practical idea!
Drummers ought to be able to keep four different rhythms going at the same time - one with each hand and one with each foot.
A small contribution to your "What is it called?" question:
I have heard this type of rhythm described as the "dog-gone" rhythm in a lesson from Bob Brozman, the guitar player, here:
