Waveforms: Different Shaped Waves
You already know pitch (how fast the air vibrates) and volume (how hard it vibrates). But two instruments can play the exact same note at the exact same loudness, and you can still tell them apart. A flute and a trumpet playing middle C sound nothing alike. Why?
Timbre. Pronounced "TAM-ber." It's the shape of the vibration. The character. The texture. The thing that makes a violin sound like a violin and not a kazoo.
Here's the machine. Play a note, then switch between the four waveform buttons while it's running. Listen to how the character changes even though the pitch stays the same.
What you're hearing is the difference between waveforms - different shapes of vibration. The shape determines which harmonics (extra higher vibrations) are present in the sound. Same note, same volume, completely different character.
Harmonics are extra vibrations hiding inside a sound. They vibrate at exact integer multiples of the base frequency. If the base note is 100 Hz, the harmonics are at 200 Hz, 300 Hz, 400 Hz, and so on forever. Which harmonics are present, and how loud each one is, determines the timbre.
The shapes of sound
Each card shows one waveform scrolling past, exactly as it would appear on an oscilloscope. This is literally what the air does when these waves play.
The purest possible tone. One single frequency, zero harmonics. This is what a tuning fork produces. It's the atom of sound - the simplest vibration that can exist. Sounds clean, hollow, a bit eerie.
Only odd harmonics (3rd, 5th, 7th...), and they fade away quickly. The result is softer, woodier - a bit like a quiet clarinet. Often used for gentle bass sounds and subtle pads.
All harmonics present - every integer multiple, odd and even. The brightest, richest waveform. The classic starting point for synthesisers since the 1960s. Most leads and basses start here, then carve the sound with filters.
Only odd harmonics, louder than in a triangle wave. Buzzy, hollow, aggressive. If you played a NES or Game Boy, this is the sound of your childhood. The Tetris theme is mostly square waves.
A square wave with unequal halves. The ratio of "up" time to "down" time is called the duty cycle. Change it and the timbre shifts - from hollow to nasal to reedy. Same basic idea, completely different character.
There are infinite waveforms
Those five shapes aren't the only waveforms that exist. They're not even really "types." They're landmarks on a continuous spectrum.
Think of colour. Red, blue, green are useful labels - but between red and blue there are infinite shades. Waveforms work the same way. Between a sine wave and a square wave there are infinite shapes, each with its own sound.
Here's proof. The row below starts with a pure sine. Each step adds more odd harmonics on top. Watch the shape gradually transform:
With 1 harmonic it's a pure sine. By step 6 it's nearly a square wave. Every shape in between is a perfectly valid waveform with its own distinct sound. There's nothing special about the "big four" - they're just the shapes that happen to have simple mathematical descriptions.
You can smoothly slide between any of them. A pulse wave is a square wave with unequal halves. A triangle is like a square with quieter harmonics. These "different" waveforms are all points on the same infinite continuum.
Complex waves
Real-world sounds aren't clean, simple shapes. A guitar string, a human voice, rain on a window - these produce messy, complicated waveforms that change shape every moment.
This wave combines three frequencies at different volumes. It still repeats, but the shape is far more intricate than any single basic waveform. Notice how it's lopsided - real sounds often are.
Most sounds in nature and music look like this, or even messier - and they change shape constantly as the sound evolves. The "basic" waveforms are building blocks, not finished products.
The big idea
Fourier's theorem: every sound that exists, or could ever exist, is just sine waves added together.
A square wave is literally an infinite stack of sine waves - one at the fundamental frequency, one at 3×, one at 5×, one at 7×, going up forever. You just saw this in the spectrum above. A dog barking, a door slamming, your voice saying "banana" - all of it is sine waves combined at different frequencies and amplitudes.
Jean-Baptiste Joseph Fourier figured this out in 1807 while studying heat. This is why the sine wave is special: it's the atom. Every other sound is a recipe of sine waves. Synthesisers are machines for choosing which sine waves to combine and how loud each one should be.
© ectoplasma.org
ectoplasma.org