Chords

Before we can create our melodies, we need to build the foundation of the melody: the chords.

A chord is a set of 3 or more notes that sound at the same time.
For example:

However, not all combinations of notes produce the same auditory effect.

Listen to how these 2 notes sound when played simultaneously.

As you will see, playing 2 notes that are next to each other on a keyboard, or in a scale, doesn't sound quite right.

Now listen to these 2 notes played at the same time:

Notice that playing 2 notes separated by 5 positions in our scale sounds much better. Why is one combination so pleasant and the other not? Let's find out! To understand it better, let's analyze how a note is constructed from a sound perspective.

So far we have physically represented a note as a sine wave:

But when we actually play a note on an instrument, the waveform looks more like this.

A note produced by a real instrument is not a single simple sine wave, but the sum of several waves. If we break down this mixture into its individual waves, we would see something like this:

Imagine that the graph belongs to a piano when we play the note C4. The first simple wave you see in the graph would correspond to the frequency of the note C4, which is 262 Hz. Next, we find a set of waves with increasingly higher frequencies, but each with less energy. Notice how all these waves have frequencies that are multiples of the fundamental, multiples of 264 Hz.

For example, let's imagine we play the note C4 on a piano:

If the frequency of the note C4 is 262 Hz, when we play it from an instrument, we not only have the frequency of 262 Hz, but also that of double the frequency (2x), triple (3x), 4x, 5x...

Now comes the most interesting part! Let's associate each of those frequencies with the note it corresponds to:

Look, the first wave corresponds to the frequency C4, the note we are playing. But the second wave has double the frequency (2x). What note has double the frequency of C4? The same note one octave higher: C5.

Next, if we continue to ascend, the wave with the frequency 3x corresponds to the note G5 (on the keyboard we will show it as G4 to keep it in the same visual octave).

Subsequently, the 4x wave gives us the same C again, now in C6, and the 5x frequency approximately matches the note E6.

Here is the key. A note played on an instrument contains other notes within it. We could also say that the C4 itself played on an instrument behaves like a chord by itself.

With this in mind, what notes do you think would sound good if we played them alongside the note C4? Just the ones we found in the note itself! C5, E4, G4...

Let's try:

As expected, they indeed sound good!

Let's look at each note separately.

C

Let's start with the note C itself. The first overtone is 2x, and we already know that the double frequency of a note is the same note one octave higher. Let's see what happens if we compare the frequencies when playing C4 and C5.

In yellow, you can see all the frequencies that match the 2 notes. All the frequencies of C5 already appear in the note C4 (even though we are not drawing all of them), which is why we perceive both notes as part of the same family. All the even frequencies of C4 match some frequency of C5.

G

Next, let's observe what happens with the fifth. The second overtone, at a frequency of 3x the fundamental, coincides with the note G.

Let's compare the frequencies:

In yellow, you can see the matches. In this case, for every 3 frequencies of C4, there is a match with G5.

E

Finally, let's review what happens with the third.

Remember that the fifth harmonic (5x) of C4 approximately matches the frequency of E6. Let's compare:

Every 5 frequencies of C4 matches one of E6.

The Rest of the Notes

Now, what happens when you play two notes very close together, like C and D?

Let's compare their frequencies:

There is only one match! Moreover, it is at a frequency that already has low energy. This creates a sense of dissonance, tension, or "clash": your ears do not find reinforcing patterns.

Does this mean that seconds are "bad"? Not at all! Tension is a powerful musical tool.

Once we know which notes sound good with C4, we can create our first chord:

Remember that the specific notes don't really matter; what’s important are the positions. If you recall, the notes of our scale were the white keys on the keyboard, and the ones we said sound good are the following.

The notes in positions 1, 3, 5 (counting only the white keys, as they are the only notes included in our Major scale). In Strudel, the positions start from 0 instead of 1, so it will be 0, 2, 4.

In the next lesson, we will continue with chords. 👉>>