The Four Basic Waveforms: Sine, Triangle, Sawtooth, Square
Short answer: A synthesiser starts from a simple repeating wave and shapes it. There are four classic ones. Sine is pure and soft. Triangle is soft with a little edge. Sawtooth is bright and buzzy. Square is hollow. They differ in how many extra, higher tones ride on top of the main note, and that is what gives each its character.
| Wave | Looks like | What rides on top | Sounds like | Good starting point for |
|---|---|---|---|---|
| Sine | A smooth curve | Nothing | Pure, soft, like a flute played very plainly | Low layers, calm tones |
| Triangle | A soft zigzag | A few higher tones, very quiet | Mellow, slightly more present | Gentle leads, soft mallets |
| Sawtooth | A ramp that snaps back | Every higher tone, strong | Bright, buzzy, full | Pads, basses, anything you will filter |
| Square | On, off, on, off | Every other higher tone | Hollow, woody, a bit like a clarinet | Old game sounds, reedy tones |
What a waveform is
Sound is air being pushed and pulled, many times a second. A waveform is the shape of one push and pull. Repeat that shape fast enough and you hear a note. Change the shape and the note stays the same while its character changes.
I think of it as a rubber stamp. The pitch is how fast you stamp. The waveform is what is carved on the stamp.
Why shape changes character
This was the part I didn't understand at first. A smooth shape is one pure tone. Any corner or sudden jump in the shape adds higher tones on top of the main note. They are called harmonics or overtones. The sharper the shape, the more of them and the brighter the sound.
- Sine has no corners, so it has no overtones. It is the main note alone, which is why it sounds thin by itself.
- Triangle has gentle corners. It adds every other overtone, and they fade away quickly, so it stays soft.
- Sawtooth has a sharp snap. It adds every overtone, odd and even, and they stay strong. That is the buzz.
- Square has two sharp jumps. It adds every other overtone, like the triangle, but much louder. Leaving out half of them is what makes it sound hollow.
Why these four
They are the simplest shapes to generate, and between them they cover the range from no overtones to all of them. The oscillator built into every web browser offers exactly these four. So do most synthesisers.
How a real sound grows out of one
A raw wave is only the start. Four or five tools do the rest:
- A filter removes some of the overtones. Take the top off a sawtooth and it turns warm. This is subtractive synthesis.
- An envelope shapes the volume over time: how fast the note arrives and how it fades. That is the difference between a pluck and a pad, and between a note and a click.
- A slow wobble, called an LFO, moves the volume or pitch gently so that a held note doesn't sound frozen.
- Mixing layers several waves into one sound.
- Effects such as echo and reverb put the result in a space.
Which one to reach for
- Calm, low or pure: sine.
- Soft, with a bit more presence: triangle.
- Rich, and you plan to filter it: sawtooth.
- Hollow or retro: square.
What I use
Only sines, as it turns out. My project is meant to be calm, so I never needed the bright shapes. Everything pitched in it is several sine waves layered together, plus noise for the textures. If I were making something with more bite, I would start from a sawtooth and a filter.
Sources
- Waveform, Wikipedia: which overtones each of the four shapes contains
Try it: hear what layered sines can do in Ocean. It is free and starts in one click, with no account.
Open Ocean, free