Meter is how we describe how individual beats act in groups. This is often conflated with time signatures (briefly covered here: https://functionalanalysis.blog/2017/07/02/basic-rhythm-reading/ ) but it is slightly different. Time signatures are a purely visual phenomenon – how we write music out on a page. Meter is aural – how you hear it. Generally, these two things match, but sometimes there are reasons they don’t. Also, there are more different ways of writing out time signatures then there are types of meter.
Simple meter is any meter that has its beat unit subdivided primarily in 2. Common time (4/4), is an example of simple meter. This meter is usually indicated with a 4 on the bottom of the time signature, but there are also ways to write it with 8 or 2. 2/2, 4/8 are also both used to show simple meters.
Unless otherwise indicated, all subdivisions will be in factors of two: quarter notes to eighth notes, eighths to sixteenth, etc. This is a simple duple meter. Not only do the beats subdivide into two, but also longer part of the measure group into twos as well, two quarter notes group together, or even two half notes. While 4/4 is perhaps the most common simple meter, any time signature that has a multiple of two on the top is going to be duple: 2/4, 2/8, 4/8, 4/2 etc.
Here’s a Lied by Fanny Hensel (Neue Leibe, Neues Leben). Listen to it and tap along. Pretty much every beat grouping happens in multiples or factors of two.
Simple triple meter is a meter that has subdivisions in twos (eighths, sixteenths etc), but larger groups in threes. Waltzes are a good example of this. The smaller units tend to be twos, but the larger measure unit is three. Usually indicated with a 3/4 time signature, but could also be 3/8, 3/2. (6/8 is a compound meter – which is a separate post coming soon.)
Here’s a “Waltz for Zizi” by Yoko Kanno from Cowboy Bebop: https://www.youtube.com/watch?v=Qbip5oZVL94
Notice how the measure is counted one-two-three, but when there are subdivisions, they are still mostly in twos.