Metre divides music into measures of beats that are stressed or unstressed, accented or unaccented. These measures are what a song is made of; think of them as rhythmic building blocks, building blocks that have been built by metre. Using divided sections like these helps to define exactly what part of the metre is to be accented and adds structure and organization to a song. But these building blocks can't outshine the metre itself; measures may be the bookshelf, but metre is the books that fill it. It is, simply, rhythm. Beats. The backbone of a song that, without it, would be messy and chaotic (exempting, of course, some experimental music that strives to be so).
The metre of a song is indicated by that song's time signature; metre is the physical form of that notation. Just as a note is the written form of a pitch, time signature is the written form of metre. It gives us the specifics of a metre, but doesn't replace it. Understanding how time signatures function in the way that they do is the very basis of metre.
A song's metre is understood by two elements: how many beats are in one measure and what type of note constitutes one beat. A 4/4 metre, for instance, has four beats per each measure with the quarter note making up one beat. A 3/4 metre has three beats per measure with the quarter note making up the beat. A 6/8 metre isn't read like this, however; it has two beats per measure with a dotted quarter note making up the beat. This type of metre, the kind shown by a time signature with a top number of six or higher that is divisible by three, are compound and found by dividing the top number and multiplying the bottom number by three.
Metre comes in tons of forms, straightforward or syncopated. A 4/4 metre is the most common, used almost without exception in rock and pop songs because of its straightforward beat that makes writing to it (and following it) very easy. 3/4 metre is the second most common, creating a swingy, syncopated beat; this is also found in rock and pop songs, most typically in slower ballads. 6/8 metre is home to the waltz, 12/8 metre is used by blues musicians, and 2/2 metre (also called cut time) is what marches are made of. But other sorts of metre, like 6/4 or 5/8 or even 13/4, are often used to innovative effect, creating an effect that makes the rhythm hard to pin down. Though this type of metre, known as irregular, are largely known for being hard to follow, some musicians have made it clear that a song does not have to be in 4/4 to be catchy. Consider Pink Floyd, for instance. One of their most popular songs, "Money," is written in 5/8 metre. Sure, it isn't 4/4, it has an offbeat nature, but it certainly isn't hard to follow. The metre provides the heartbeat, and the rest of the song follows it; if that heartbeat keeps going strong, the listener is bound to follow it as well.
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