Today we’ll look at simple waveforms and, more importantly, how they can be combined to form more complex waveforms. Everything starts with an understanding of frequency, time, and oscillation.

To make this behavior clear, a one-hertz frequency is loaded into Adobe Edition.

• The duration of the clip is exactly one second
• Within that one second, there is one completed oscillation

That relationship is critical:

One oscillation per second equals one hertz.

This same logic applies as we move upward in frequency.

One Hertz, Two Hertz, Three Hertz—Seeing Frequency Visually

When we look at a two-hertz frequency:

• The duration is still one second
• There are two completed cycles within that second

That’s why we call it two hertz.

Move to three hertz, and the pattern continues:

• One second
• Three completed cycles

This visual relationship between time and oscillation makes frequency tangible. You don’t just hear pitch—you see it.

Combining Sine Waves to Create Complexity

Now things get interesting.

The one-hertz sine wave is copied and then mix-pasted into the two-hertz sine wave at the same amplitude.

The result?

• A waveform that no longer looks like a sine wave
• A signal that has become much more complex

This is the combination of two sine waves added together.

Undoing that, the same one-hertz wave is added to a three-hertz frequency instead.

This time:

• You can still see the shape of the one-hertz frequency
• But it’s been modulated by the three-hertz frequency

Both signals are still at the same amplitude, which is not something you’d normally encounter in real-world sound, but it makes the behavior extremely clear.

Beyond Sine Waves: Introducing Other Simple Waveforms

Sine waves are only the beginning. There are other simple waveforms that behave very differently.

Square Waves

A square wave looks exactly like the name suggests:

• Sharp edges
• Flat tops and bottoms
• A distinctly angular shape

Zoomed in, it appears as a perfect square-like pattern.

When played back at 220 hertz and compared directly with a sine wave at the same frequency:

The square wave sounds a lot more aggressive.

The pitch is identical, but the character is not.

Triangle Waves

Next is the triangle wave.

• A smooth, angular rise and fall
• Clearly shaped like a triangle
• Also set at 220 hertz

You can clearly hear the pitch, but once again:

It sounds more aggressive than the sine wave.

This difference in sound, despite identical frequency, comes purely from waveform shape.

Combining Square Waves at Different Frequencies

Simple waveforms don’t exist in isolation—they’re meant to be combined.

Here, a 220 hertz square wave is combined with a 440 hertz square wave.

Visually:

• One square wave sits at 220 hertz
• Another at 440 hertz
• The output is the sum of both signals

The resulting waveform is noticeably more complex, and the sound reflects that complexity.

This combined signal demonstrates how frequency relationships and waveform shape interact when layered together.

The Foundation of Synthesis

This process—combining, manipulating, and shaping waveforms—is essentially the basis of synthesis.

With simple waveforms, we can:

• Combine them
• Modulate them
• Filter them
• Manipulate amplitude and frequency

All synthetic sounds are built from simple waveforms.

Everything complex begins with something simple.

Mixing Different Waveform Types

Next, a square waveform is combined with a triangle waveform at the same frequency.

The resulting waveform:

• Retains the distinct angular character of the square wave
• Still shows the sloped shape of the triangle wave

This output is not one or the other—it’s clearly the combination of both.

Adjusting Amplitude and Frequency Relationships

To manage loudness, the amplitude is reduced to 75%.

Now the experiment changes slightly:

• A 110 hertz sine wave (one octave lower)
• Combined with the already layered 220 hertz square and triangle waves

This means:

• Three waveforms
• Three different components
• Two different frequency levels

When mixed and pasted together, the result becomes significantly louder and far more complex.

Visually:

• The waveform still repeats over time
• But the shape has become far more intricate

This is already starting to create some really interesting-looking waves.

And sonically, it sounds very different—a clear demonstration of synthesis in action.

Observing Carrier and Modulating Frequencies

Now let’s examine another interesting behavior of waves.

A 55 hertz sine wave is created, along with an 880 hertz sine wave.

Both are viewed at the same zoom level and duration.

When these two are combined:

• The main, low-frequency sine wave remains visible
• The higher frequency is added on top of it

The result shows that:

The lead, or main frequency, is still carrying the waveform.

But it has been enriched by the higher-frequency content.

Extreme Contrast: One Hertz and 880 Hertz

To make this even clearer, the 880 hertz sine wave is copied and mixed-pasted into a one hertz sine wave.

The result is striking.

• The one-hertz frequency acts as the carrier
• The waveform is clearly modulated
• Smaller sine waves appear within the larger one

Zoomed in, it looks like this:

A really thick sine wave.

This is a clear visual representation of how high-frequency content can ride on top of a very slow oscillation.

Setting the Stage for Harmonics and Analysis

All of these examples show how simple waveforms interact, how frequency relationships shape sound, and how complexity emerges through combination.

Next steps naturally follow from this foundation:

• Exploring harmonic content
• Understanding what harmonics do
• Using frequency analyzers
• Observing even more interesting behaviors of sound

This exploration of simple waveforms is the groundwork for everything that follows in sound design and synthesis.