"I think words operate like musical notes that the eyeball hears." - David Mitchell
You must already have the concept of what a note is: it’s a kind of “sound”. Yes, that’s it.
You must also already know that notes also have names, which we’ll see right away.
We are going to divide the whole spectrum of sounds into 12 distinct notes, and we’ll see that they repeat.
There are two major ways in which notes are called: a Latin way, and an English way:
Each of those notes will have a certain frequency of sound, which means that we can define a distance between each note. We will call these distances whole tone and semitone, in which two semi tones are equal to a whole tone.
In that way, we’ll define the following distances between each note:
Right at the beginning, we said that the notes repeat themselves. What actually happens is that one semitone above B lies another C note, therefore we need one more row on the table:
Looking into it another way, we get the following:
You might be asking yourself why do we have a distance of a whole tone in some cases and a single tone on others. That’s because we define a few in-between notes where there are whole tones, by adding what are called as accidentals.
We define two kinds of accidentals:
Sharp - #
Flat - b
The way we use these accidentals is adding them after a note.
Sharp (#) means the note which is one semitone after.
Flat (b) means the note which is one semitone before.
With this, we get the following list of notes:
In the last list, the notes on each row are one semitone apart from their neighbor rows.
Note that when we talk about C# and Db (and the rest of the cases with two notes on the same cell) we are actually talking about the same note.
From this list of distances of the notes, we can define what we call intervals, which are noted as numbers which start from the first note (also called root note):
Notice in the last row, that we started from a C note, and went all the way round to the next C note, and the interval is called 8th, but is commonly named as octave. The octaves of a note are the same note, but of different pitch (can be higher or lower).
Of course, we can do the same analysis but starting from a note different than C. Let’s do the same for E:
Note that the distances did not change, only the notes have because we’ve shifted our frame starting from C to E.
Don’t worry if you get a little stuck on the notes, semitones, intervals. For now, I want you to know the fundamentals.
I have created a note and interval calculator that you can use to know each interval for each note. Just change the root note in yellow and you'll get each interval note in blue.