2 x 4

It’s often said that D’Arienzo returned to the 2 x 4 rhythm (In Spanish, “dos por cuatro”, or 2 by 4), but what does this mean? What is the 2 x 4?

In music notation, the “2” means, that there are two beats per bar, and the “4” means, that each beat is what musicians call a crotchet (a quarter note).
real 2x4
Sounds like:
1, 2

In tango, however, 2 x 4 means something different. It refers to the rhythm of milonga (the same rhythm used in habanera) which was the basis of the first tangos at the end of the 19th century. In the milonga rhythm, both beats are divided but the first beat is not divided equally. The first note gets longer at the expense of the second, which arrives later than expected. Here it is in music notation:
1 2 3 4 5 6 7 8
1 x x 4 5 x 7 x
sounds like:
1 (and) a 2, and

The unequal division of the first beat, a kind of syncopation, creates a choppiness to the rhythm. It’s fun but also limiting because it’s the same every time.

The next step was simply to divide both beats equally. Now we’ve got the 4×8:
1 and 2 and

The choppiness of the syncopation is gone, so everything sounds smoother, although one is free to add syncopation (change the emphasis) anywhere one wishes. This change took place as early as 1916. Confusingly, all the music was also written with a 2 x 4 time signature.

The next development comes from De Caro in 1924: use longer notes. Strictly speaking, this doesn’t require a change of time signature, but that’s the simplest way to show this change, like this:
1, 2, 3, 4

This is the 4 x 4. It allows phrases to be longer and hence more expressive but the choppy energy of the 2 x 4 is completely gone. D’Arienzo doesn’t really return to the 2 x 4 at all, but to its more sophisticated brother, the 4 x 8. This music was written with a 2 x 4 time signature and is still referred to in tango circles as the 2 x 4.