Generally speaking, chords change with the first beat of the bar, but again, this is strictly up to the composer. They can change anytime at all but to be able to be enjoyed by the masses, a certain regularity and even predictability must be included. Most people prefer to listen to music they can tap along to. Most of us seem to have a deep-rooted understanding of rhythm, something that goes way back. Strange time signatures thwart that foot-tapping. Symmetry seems to be the prerequisite for that to happen naturally.
An example of an asymmetrical rhythm is 5/4. I prefer to count that as "One Two Three One Two" ... same with 7/4. I would count that as "One Two Three Four One Two Three". I find it much easier to hear that time signature if I break it down into smaller groupings.
"Phrasing" is a word used to describe how time is manipulated. Singers and instrumentalists often "bend" perfect time as a way of adding emotion to their performance, which is an aspect of something even subtler known as "Feel". So, instead of keeping, for example, the melody line notes exactly synchronized with the underlying beats, the player or singer can either push the notes slightly ahead of the beat, or lag them slightly behind. Listen to any Frank Sinatra tune ... he was the master.
The main thing to remember is that underlying every piece of music is a steady regular pulse — that foot tapping thing — each unit being one beat.
We've had a good look at the sound element of music — notes, and the way they're organized into scales — but, to become music, they need a chunk of time to be played in. So, before we look at the most important aspect of the sound element, chords, lets first get an idea of how that mysterious, undefinable thing we call time comes into play.
The basic units of time are 'beats' and the timeline of a piece of music is divided into 'bars' or 'measures' which consist of a certain number of beats. That number is determined by the composer of the piece and is written as the 'Time signature'. I'll use some graphics to explain, with time flowing from left —›› to right —››.
Time signatures are those numbers you see on sheet music at the beginning of the first line. They look like fractions. The top number indicates how many beats you're going to find in each measure; the bottom number tells you what kind of beats. The most common time signature is 4/4, which means 4 beats per measure, each beat being a quarter note. We humans seem to like the repetition of rhythms in groups of four.
If you read out loud the the numbers below at a steady rate, stressing the 1, you'll hear the essence of two bars of 4/4. You can also listen to several measures of these examples by clicking the little arrow to the right of each image.
Now, without changing the rate, do the same with the two measures below and you'll hear the essence of 4/4 in eighth notes ...
Do the same with each beat divided into three. Each beat is a 'triplet' ... this is sometimes called 12/8.
And, finally, we'll divide each beat into four, which means sixteenths notes.
And so on ... we won't bother with 32nds and 64ths. The important thing to note is that it isn't the tempo that is changing, it's the number of subdivisions per beat. All these have been based on 4 beats per bar.
The next most common time signature is 3/4, otherwise known as a Waltz. So it has 3 quarter notes per bar and they can be sub-divided just like the 4/4 examples above. The example below shows 3/4 time with each beat divided into 3.
Those are just the main ones. There are all kinds of time signatures, but they're all measured in the same way with that double digit symbol: number of beats / kind of beats.