Tutorial: Music theory basics
Now that we have established what the 12 note chromatic scale is and how those notes relate to their physical frequencies, we can leave the realm of physics and start talking about some more involved music theory subjects. What are scales? What is the difference between a major and a minor scale? How is this applied when writing a song? Let's go.
What is a scale
When musicians play a song, they always want to know in what key the song is. The key of a song determines which of the 12 notes that we have at our disposal sound good together. You can't just randomly play any of the 12 notes and expect things to work out, because not every note always combines well with every other note. What we do instead is we pick a set of seven notes that work well together (based on the key of the song) and limit ourselves to playing just these notes. This set of notes is called a scale.
A single key can be played using a variety of scales. For now, we'll stick to the two most basic scales: natural major and natural minor (often referred to as just the major scale and the minor scale). These two scales work very similarly. From a non-technical point of view, major scales tend to be used for songs that need to have an uplifting, happy sort of sound. The major scales end up having a more bright, sparkling sound resulting in frivolous, joyful songs. The minor scale has the opposite effect. Sad or angry songs are usually written in a minor key.
Natural major
So how do we know which notes are part of a natural major scale? We start off by taking the root (also called tonic). Let's take the natural major scale of C as an example. In this key, our root is the C. It's that simple. If we were to play in G major, our root would be G. Once we have established the root, we take our 12-note chromatic scale, start at the root and go up with predefined intervals:
Whole Whole Half Whole Whole Whole Half
It might sound a bit confusing, but it's a relatively simple idea. If we write down all 12 notes in the chromatic scale, starting at our root, we get the following:
C C♯ D D♯ E F F♯ G G♯ A A♯ B
Remember that the interval between each of these notes is half a step. When we apply the whole/half pattern for major scales and we need to make a half step, we simply pick the next note in the chromatic scale. When we need to make a whole step we skip a note and pick the following note. The result can be seen below. The notes we ended up picking for our scale are in bold:
C major
C C♯ D D♯ E F F♯ G G♯ A A♯ B C
The notes in the C major scale are C, D, E, F, G, A and B. The intervals for the C major scale match the intervals of the white piano keys. No sharps or flats (black keys) required.
If we take a look at a different example, like the D major scale, things get a little more interesting. We apply the same whole/half pattern but this time, we start at D.
D major
D D♯ E F F♯ G G♯ A A♯ B C C♯ D
We start at D and, according to the major whole/half pattern, we jump ahead a whole note and land on E. Then we need to make another whole jump, but because the interval between the E and F is only half a note, we end up landing on the F♯. The next jump will be half a note. That brings us to the G. The next two whole steps bring us to A and B. After that, we need to make one more whole step, but because the interval between B and C is only half a step, we need to jump ahead to the C♯. The final half step lands us on D again. So the notes in the scale of D major are D, E, F♯, G, A, B, C♯. As you can see, there are two sharp notes in there.
In any major key, whether it's A, B, C, D, E, F or G major, this whole/half pattern can be applied to find the notes in the natural major scale for that key. Stick to those notes and you'll never play a note that sounds bad.
Natural minor
We've seen the natural major scale, but there's also the natural minor scale. The idea behind the natural minor scale is the same as the natural major scale, except for the whole/half pattern. It's slightly different:Whole Half Whole Whole Half Whole Whole
The order of the pattern is the same as in major, but for minor scales, the whole pattern has been shifted to the right two steps. Let's take a look at what the scale of E minor looks like. We start at the root again, which in this case is the E and then follow the minor whole/half pattern to find the notes for our scale.
E minor E F F♯ G G♯ A A♯ B C C♯ D D♯ E
So want to rock out with a great sounding guitar solo in E minor? Play nothing but E, F♯, G, A, B, C and D and you're good to go. For good measure, let's throw in a second example. That of B minor.
B minor
B C C♯ D D♯ E F F♯ G G♯ A A♯ B
The notes to play in a B minor scale are B, C♯, D, E, F♯, G and A.
Relative major and minor keys
There's something odd about the last major example and the last minor example showed above (D major and B minor). We saw that D major has D, E, F♯, G, A, B and C♯ as notes. B minor has B, C♯, D, E, F♯, G and A as notes. If we list these sets of notes but both start them with the A, we get the same list twice: A, B, C♯, D, E, F♯ and G. The notes found in D major and B minor are the same! We call two keys like these relative keys. They share the same notes but have a different root. Every major key has a relative minor key and vice versa.
This might be somewhat of a surprise, because the keys of D major and B minor do have a different sound and different feel to them, despite consisting of exactly the same seven notes. This is because the notes are played in a different context. If you'd randomly start playing these notes just by themselves, the root note (and thus the context) wouldn't be clear. At least, not immediately. It would be impossible to tell which key we are in. When we play a song, however, the underlying chord progression will be different and tell us what key we are in. The chords played in a D major key are usually different than the chords played in a B minor key.
If we want to find the relative minor key for any major key, we simply take the major key's root and go down three semi-tones. You can see how this works in our D major/B minor example
D major to B minor D C♯ C B
Or another example, to find the relative minor key for F major
F major to D minor F E D♯ D
Similarly you can go up three semi-tones to find the relative major key for any minor key.
E minor to G major E F F♯ G
Knowing this transformation can be done might be beneficial in certain situations. If you're asked to play a song in A minor but you don't immediately know which notes go with A minor, you can find the relative major key (which is C major) and maybe you do know the notes then. But keep in mind that we were asked to play in A minor and not C major, because that will become important later on.