This kind of approach was predominant in the first half of the century and the jagged approach to rhythm increased:
Most listeners were not won over by this kind of music which left the door open for an entirely new approach which began in the 1960s. An early work is Terry Riley's In C, written in 1964:
What makes this such a revolutionary break are two elements: the fixed rhythmic pulse and the return to tonality, hence the title, In C. A few years later Philip Glass began to write similar music:
Coming from a slightly different angle was Steve Reich. With a background in both philosophy and percussion, his early pieces used tape loops:
What is going on here is that a short tape loop is duplicated and the different loops slowly drift away from one another--go out of phase. From this Reich developed the idea of 'phasing', doing the same thing in live performance:
This may seem a bit arid, but it is actually the first genuinely new rhythmic idea to appear in music in a very long time. The inspiration was probably equally due to the mechanism of tape loops and Reich's study of drumming in Ghana. He developed the idea in the large piece Drumming. Here is an excerpt:
The phasing was slowly phased out, but Reich added tonal harmony to the basic idea of pulse:
Melody even started coming back: listen to the lovely bebop-like flute tune starting around 2:14.
Despite what the article in the Guardian says, this really isn't about minimalism at all. What happened in the 1960s and 70s was similar to what happened around 1600: a well-established musical style started to become perceived as too structured, too remote from the kind of expression composers were looking for. So they tossed it out and went back to the fundamental elements of music. In their case they tossed out the complexities of late 16th century counterpoint such as this:
They replaced austere counterpoint with harmonic and expressive immediacy, as in this music:
The collection was even called "le nuove musiche". What is happening in both transitions is inspired by what I call the racinative impulse, the need from time to time to renew music by returning to the most basic fundamentals. I talk about that in this post.