Complex waveforms are the combination of hundreds of waves. If a voice sounds bright it is usually because it is producing upper harmonics at higher amplitudes. If it is duller sounding, it has less upper harmonic content. The combination of all of these different simple sound waves at different frequencies and different amplitudes (levels) produces complex waveforms. These variations in complexity and harmonic structure are how we can tell the difference between the sound of a guitar and a trumpet, a knock on metal or wood, and a real human voice verses a synthesized one. There are a handful of basic waves not commonly found in nature, but easily created with electronics. These basic waves are the building blocks of many synthesizers, basic MIDI, and warning systems.
The most basic and simple waveform, a sine wave has a simple hollow sound. It does not exist in nature, but is the simplest sound to reproduce with electronics, which is why you may recognize it from warning tones and beeps. Listen to it below.
100Hz Sine Wave
500Hz Sine Wave
1KHz Sine Wave
Now let’s look at harmonics. Most sounds in nature contain harmonics, meaning that they have the fundamental or main pitch or note, plus they have higher pitches that are voiced above the fundamental. The amount and intensity of these pitches help to define the timbre of a sound. The sine wave is unique because it only contains a fundamental, so just the one note.
After the sine wave we jump in complexity to the sawtooth wave. The sawtooth produces a lot of harmonic content and therefore a full buzzing sound. Notice how the wave looks like the teeth of a saw, hence the name. Look below to listen to examples of a sawtooth wave.
100 Hz Sawtooth Wave
500 Hz Sawtooth Wave
1 kHz Sawtooth Wave
The sawtooth wave has a fundamental with all harmonics present. The second harmonic is quite strong being ½ the amplitude of the fundamental, with the third harmonic at 1/3 the amplitude of the fundamental, and the fourth at ¼ the amplitude. This produces a good deal of harmonic content and therefore a full buzzing sound.
Now let’s look at the square wave, which differs a bit from the previous two. Notice how the waves seem to form a square shape. The square wave has only odd harmonics. This harmonic structure gives the square wave a little more bite to the sound. It kind of has a buzzing sound, but is not as intense as the sawtooth. Have a listen below.
100 Hz Square Wave
500 Hz Square Wave
1 kHz Square Wave
The square wave has only odd harmonics. The interesting similarity to the sawtooth wave is that each harmonic decreases in the same manner except the third harmonic is ½ the amplitude of the fundamental, with the fifth harmonic at 1/3 the amplitude of the fundamental, and continuing along in that manner.
Finally we’ll look at the triangle wave, which is very similar to the square wave. The triangle wave has only odd harmonics like the square wave, but their amplitude is far weaker in comparison to the fundamental. This causes the waves to take on a bit more of the shape of a sine wave, while maintaining the sharp edges of a square wave.
100 Hz Triangle Wave
500 Hz Triangle Wave
1 kHz Triangle Wave
The third harmonic is only 1/9 of the amplitude of the fundamental and progresses in a similar manner from there. The triangle wave sounds more similar to a sine wave, because of its soft harmonic content, but it still shares some characteristics of the square wave having only odd harmonics. Listen here to see what it sounds like.
These main four waves can be seen in most synthesizers, DAWs, and testing equipment. There are some variations that include the sawtooth wave going in opposite directions and the lopsided square wave (being larger on the top and smaller on the bottom or vice versa). Depending on the device these waves can be added together to create complex waveforms, can be used to modulate a signal, or can create the pattern for a pulsating filter sweep.