Understanding Synthesizers Properly
Many explanations online of synths fail to teach key concepts properly
I decided to write this article because I have been confused as a beginner of how synthesizers work. Now that I look back, I realize that experts at the music stores I went to as well as on YouTube taught me some of the core concepts wrong. That made it hard for me to fully grasp how a synthesizer is actually used to build up a sound in multiple steps.
The thing many fail to explain properly is why a synthesizer generates square waves or sawtooth waves at is source rather than sine waves. If that is clear to you already, then you don't need to read this article. But, if you are like me and wondered why a synthesizer would start its whole pipeline for generating electronic sounds by making harsh sounding square waves and sawtooth waves instead of more natural sounding sine waves, then you have come to the right place.
If you have no idea what I am even talking about, but still want to learn about how synthesizers work, then read on anyway because I will take this slowly from the start.
A Guitar Analogy for Synthesizers
I have always loved analogies to teach complex concepts. I first understood electronics and electric current when my teacher explained it using a water analogy. In the water analogy, a battery is a water pump. The volume of water is the charge, and the volume of water passing a section of a pipe per time unit is the current. Voltage is easily explained as the water pressure.
We could replace water with a gas flowing through some tubes under pressure. That is also useful when talking about sound. Sound can be thought of alternation of gas pressure going through the air. Thus, a speaker is translating, converting an alternating flow of electrons through a copper wire to an alternating flow of air molecules.
Sound spreads through air in waves, akin to how ripples spread through water when you drop a stone into it. You can drop two stones, each creating their own circles, and they will overlap creating more complex wave shapes. The same happens when we play music. Every instrument or every string is like a little stone dropped in the water. We get a complex wave pattern of overlapping waves emanating from every individual string.
Each string vibrates with a different frequency, which means the wavelengths of the waves produced from each string are different. Putting all of this together produces a complex pattern of waves, which we experience as beautiful music. Well, assuming it is put together in a nice way.
Thus, sound starts with something vibrating or oscillating, such as a string. The length of the string determines the frequency of that vibration. That is why the strings on string instruments have different lengths.
The frequency a string will vibrate at is one divided by the length of the string times two. In other words, if you double the length of a guitar string, you will get one fourth of the frequency. In reality, this is a bit more complex as you multiply with a factory determined by the tension in the string and the mass of the string.
Lighter strings give higher frequency. So does higher tension in the string. That is why we can tune a string by increasing the tension in it.
With a synthesizer, all of these things happen electronically. Instead of strings, we have something called oscillators. Analog synths have voltage controlled oscillators (VCO) which works the following way: Every 1 voltage increase the frequency by 1 octave.
When I first read this, I didn't even know what an octave was. That is useful to know in this context. Every note A, B, C, D, E, F, G can be played in 8 different octaves. When you increase the octave, you double the frequency. So for instance if A4 (the A above middle C) is typically tuned to 440 Hz, then:
A5 would be 880 Hz (440 Hz * 2)
A3 would be 220 Hz (440 Hz / 2)
This doubling or halving of frequency results in pitches that sound similar to each other but with differences in their perceived "height" or "depth". Octaves are fundamental to musical theory and are the basis for many musical intervals and harmonies.
In musical theory, we actually have 12 half-notes (semitones) spread across an octave:
A
A#
B
C
C#
D
D#
E
F
F#
G
G#
Think of an octave as a frequency range. But just like there is not a fixed frequency gap between octaves, but a doubling, semitones are also logarithmic. That means the frequency gap between A and A# is smaller than between A# and B.
I was reluctant to learn this music theory, but it really helps in understanding how a synthesizer works and what each setting does.
Typically, on a synth, you decide the frequency through two dials:
Octave – Makes the largest jumps in frequencies.
Pitch – Fine adjustment of frequency in a 1 octave range.
You could think of the Pitch dial as setting one of the 12 semitones found within an octave frequency range. And let me repeat this point again: An octave is not a fixed frequency range. A4 to A5 could be 440 Hz while A3 to A4 could be 220 Hz.
Why Do Synths Use Sawtooth and Square Waves
Sawtooth and square waves give sharp, unpleasant sounds. I asked at my local music store why they used those waves instead of a nice sine wave which sounds much smoother and better.
I got told that it was because a sine wave was just impossible to make in electronics. That is actually bullshit and not the real reason why Sawtooth and square waves are used in synths.
The reason can be understood from the mathematical theory of signals. Any signal can be approximated by combining an infinite number of sine waves of different frequency and amplitude.
In other words, a sawtooth or square signal can be viewed as a very large number of sine waves combined.
That helps explain the sharp, unpleasant sounds. It is essentially like a base frequency with lots of very high-frequency harmonics and overtones. It is these higher frequency waves layered on top which give the sharp, unpleasant sound.
So why use them? Why deliberately create a nasty sound?
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