Tempos and bars
"My favorite things in life don't cost any money. It's really clear that the most precious resource we all have is time."
- Steve Jobs

Just like Steve said, time is the most precious resource we have.
If you’ve heard to music sometime, which I assume you did, you already know that together with melodies goes a certain rhythm, a pace, a speed, whatever you want to call it.
The rhythm is what we will call beats, and there is a certain frequency of beats in every piece of music. Usually, they are expressed as BPM (beats per minute), which means that there are a fixed amount of beats in 60 seconds.
Now that we know the beat, you might also have noticed that all notes and sounds have a specific duration. This is what we will call note values.
This note values are a quick way of establishing the duration of notes and other sounds. As we saw before, the beat falls under one of these values, which is called a quarter note. This is the fundamental duration.
When we say that a certain rhythm has X BPM, it’s the same as saying that we can fit X number of quarter notes in 60 seconds. Just to be clear, if our song is in 60 BPM (which means 60 beats per minute, or 1 beat per second), we know that we can fit 60 quarter notes in a minute, and therefore every quarter note lasts for 1 second.
Starting from the quarter note, there will be durations that will be longer and also shorter, so take a look at the following table:

You might ask yourself why a quarter note has a duration of 1, or a sixteenth note ⅛, while their names evoke something with a “4” and “16”. You’ll see this down below.
Knowing the BPM and the duration of each, you can find out how many of those can fit in a minute. For example:
BPM 60 can fit:
15 whole notes.
30 half notes.
60 quarter notes.
120 eighth notes.
240 sixteenth notes.
BPM 100 can fit:
25 whole notes.
50 half notes.
100 quarter notes.
200 eighth notes.
400 sixteenth notes.
And so on.
Notice that we have seen how to note the duration of notes and sounds, but...music does not always involve sounds, or does it? Well, sometimes it also has times where no notes or sounds are played, and we have, in fact, silence.
What this means is that when we use silences in our music, we will also assign a duration to them, which can be of any of the values we just saw. We’ll see more of this later on.
Of course, music is not really made around the minute marks, rather it’s done around what we will call bar (not that bar, this bar does not serve any drinks!).
We will call a bar as a unit of our music, that repeats itself over and over. Another commonly used word is measure.
The bar is a figure where we can add our notes and sounds to compose our music, and because of that it is that we will assign a specific duration to it. As a general rule, we will say that the bar has a certain number of beats (or quarter notes).
The most common bars in pop and rock music has 4 beats. Other styles, like waltz, have 3 beats, tango has 2.
Because bars can have virtually any combination of beats, we use a code to note this. This is what’s called the time signature of the bar.
We use a fraction to tell this, composed of two numbers A / B:
B is the number of the note value used to note the bar length.
A is the number of those note values contained in the bar.
Remember what we said about the names of the note values and their duration? Well, this is what we’ll use for the number B, in this way:

So, if we want to note a bar with four beats, we would use 4 / 4, since quarter notes have a code of 4 and there are four of them on each bar.
In the case of a waltz, we would use 3 / 4, and tango 2 / 4.
I challenge you to find other common bar signatures and let me know.
When we learn how to write down our music, we'll see how to use this concepts and how to note them.