One of the most important and fundamental characteristics of any music is rhythm.
Rhythm can be in time (following a steady pulse), or free time (not necessarily following a pulse).
This is also one of the most important elements of writing or improvising any form of melodic or harmonic phrases.
Though it can get complicated very easily, knowing some simple concepts and understanding them clearly will help you make things easier for yourself.
The Basics
The skeleton of any rhythm is pulse. You can think of it as the heartbeat of any track if you wish.
The speed of the pulse is referred to as tempo, measured in BPM (Beats Per Minute).
When we subdivide this pulse and create a sequence, we end up with a rhythm. We can then loop these sequences, creating a longer rhythm.
And to make things simpler, we divide this longer rhythm into bars/measures.
This gives us the opportunity to break down our rhythm into sections which we can further subdivide.
Subdivisions
Every bar, and every beat of a bar as well, can be subdivided further to create rhythmic sequences.
In western music, specifically in 'jazz' terms we divide them into the following:
Whole Notes: Notes/rhythms that last for 4 counts.
Half Notes: Notes/rhythms that last for 2 counts.
Quarter Notes: Notes/rhythms that last for 1 count.
Eighth Notes: Notes/rhythms that last for 1/2 a count.
There are further subdivisions, but those can get very fast, and are not advisable for beginners to work on.
Time Signatures
Time signatures are essentially groups of counts within a bar, which act as our basis for creating rhythmic sequences. They are written as a fraction. For example, 4/4 or 3/4 etc.
The top number of the fraction refers to the maximum/total number of counts in bar. For example, 4/4 means, each bar has a maximum of 4 counts.
Similarly, if the top number is 3, then we have 3 counts. 5 would mean, 5 counts, and so on.
The bottom number refers to the rhythmic value of each count. For example, 4/4 means each count in the bar is a quarter note long.
Here's an outline of what the bottom number might mean:
If the bottom number is 2, it refers to Half Notes.
If the bottom number is 4, it refers to Quarter Notes.
If the bottom number is 8, it refers to Eighth Notes.
Conclusion
So based on this whole discussion, let's look at some common (simple and odd) time signatures.
Common time signatures with 4 in the bottom:
4/4 - Four quarter notes/counts in a bar.
3/4 - Three quarter notes/counts in a bar.
2/4 - Two quarter notes/counts in a bar.
5/4 - Five quarter notes/counts in a bar.
6/4 - Six quarter notes/counts in a bar.
7/4 - Seven quarter notes/counts in a bar.
Common time signatures with 2 in the bottom:
4/2 - Four half notes/counts in a bar.
3/2 - Three half notes/counts in a bar.
2/2 - Two half notes/counts in a bar.
5/2 - Five half notes/counts in a bar.
6/2 - Six half notes/counts in a bar.
7/2 - Seven half notes/counts in a bar.
Common time signatures with 8 in the bottom:
4/8 - Four eighth notes/counts in a bar.
3/8 - Three eighth notes/counts in a bar.
2/8 - Two eighth notes/counts in a bar.
5/8 - Five eighth notes/counts in a bar.
6/8 - Six eighth notes/counts in a bar.
7/8 - Seven eighth notes/counts in a bar.
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