Throughout this explanation these terms will be used:
Minim: Half note
Dotted Minim: Dotted half note
Crotchet: Quarter Note
Dotted Crotchet: Dotted Quarter note
Quaver: Eighth Note
Dotted Quaver: Dotted Eighth Note
Semiquaver: Sixteenth Note
In a time signature, the numerator denotes the number of beats and the denominator denotes the type of beats.
In a simple time signature like 3/8, 3 says that the number of beats is three and 8 says that the type of beats is Quavers; meaning 3 Quaver beats in a bar
Similarly 4/4 :
4 Crotchet beats in a bar
But, this is slightly different for compound time signatures when it comes to grouping.
First of all, let us take a look at some compound time signatures and what they mean:
6/8 :Literally this means 6 quaver beats. These 6 quavers can be grouped into 2 dotted crotchet beats in a bar.
9/8: 9 Quaver beats=3 dotted crotchets
12/8: 12 Quaver beats= 4 dotted crotchets
6/4: 6 Crotchet beats= 2 dotted Minims
9/4: 9 Crotchet beats = 3 dotted Minims
12/4: 12 Crotchet beats= 4 dotted Minims
6/16: 6 Semiquaver beats= 2 dotted Quavers
9/16: 9 Semiquaver beats= 3 dotted Quavers
12/16: 12 Semiquaver beats =4 dotted Quavers
In all of the above compound time signatures, the numerator could be divided into equal sub groups.
However, there are situations when this is not possible. Such time signatures are known as Irregular time signatures.
Some examples are:
5/8: 5 Quaver beats in a bar
7/8: 7 Quaver beats in a bar
5/4 : 5 Crotchet beats in a bar
7/4: 7 Crotchet beats in a bar
In these time signatures, as the top figure cannot be divided into equal subgroups, they must be divided unequally.
5/8 could be divided into a Crotchet and a dotted Crotchet
5/4 could be divided into a Minim and a dotted Minim
Therefore Irregular time signatures are a different concept than compound time signatures.