When I was a kid I was lucky (and privileged) to have basic music lessons as part of art class. I didn’t become a musician and never learned to play the flute, as I was never able to understand which holes I needed to cover to play the notes I wanted. At least I learned the name of the musical notes.
Our professor told us that music was just math. That caught my attention. “Music is math? I’m good at math, maybe I can also be good at making music.” I was surprised that the only numbers I saw on music sheets were the time signature, but that didn’t say much about the meaning of the notes. There was no addition or subtraction, concepts that fit my definition of mathematics back then.
Many years later, I realized that music really is math. From the nature of how sound waves are created, to the way we divide the octave into twelve pitches of equal temperament. But my biggest realization was the fact that music was all about intervals.
You don’t need to have the exact notes to reproduce a melody or chord, you just need the intervals between the notes (unless you have perfect pitch or you are playing on a different key in a group of musicians). This is similar to how we can understand people saying the same word despite their voices having different pitches.
I like the piano / keyboard because it’s a very intuitive way to learn about music. All the notes are laid out for you, and things start to make sense once you realize that the white keys are no more important than the black keys.
An interval of one is a semitone. That is, the distance between two keys, regardless of color. An interval of twelve, an octave. How many intervals are there? Here are the most important ones:
Now, what about musical scales? Again, they are just a series of intervals, If you play all the white notes, starting from C, you get:
0 +2 +2 +1 +2 +2 +2 (+1 and back to C)
That corresponds to the major scale. Notice how the third note is 4 semitones away from the root (C). That’s why the interval of four semitones is called a major third. In music theory there is a lot of unintuitive nomenclature like that.
If you play all the white keys, starting from A, you get the minor scale:
0 +2 +1 +2 +2 +1 +2 (+2 and back to A)
This time the third note of the scale is three semitones away from the root. Notice how on both scales the fourth and fifth notes are the same distance away from the root. These two intervals harmonize really well with the root note.
If you repeat these patterns for any key as the root note, you can build the major and minor scales in that key.
Now, what about chords? Chords are just a group of notes separated by intervals:
There are many more chords of course, but these are some of the most common. Also, chords can be played using notes from different octaves, so you can add or subtract 12 to any of the intervals to position the note on a different octave. These are also known as chord inversions.
Chord progressions are a seres of chords that sound nice when played in sequence. They are the basis of many popular songs. Once more, chord progressions are intervals separated by intervals!
Let’s the 50s chord progression: I - vi - IV - V. They are represented with roman numerals. Don’t worry if you don’t see the name of any notes, we only need the intervals to play them!
To transform this progression into a series of notes you can play you must first pick a key. It can be any key, but if you are trying to follow a song, you should match the key it’s being played in, otherwise you will be out of tune. For this example I will use the key of C.
The first chord is I. Since it’s an uppercase number, it is a major chord, played on the first note of the C major scale. So using the intervals for a major chord we get the notes: C, E, G.
The second chord is vi, a minor chord (lowercase number) played on the sixth note of the C major scale. These are the notes A, C, E.
For the third chord IV, we get F, A, C.
And finally, for V we have G, B, D.
I’m well aware that calculating intervals on the fly, while your fingers are on the keyboard and the metronome is ticking seems impossible. But just like with any activity that deserves effort, practice is the key to weave these patterns in the mind.
This is a very brief introduction to music theory. I don’t think this is how theory is usually taught, but I wanted to write this because understanding intervals makes many other concepts so much easier to learn and understand.