Making Waves

Understanding synthesizers and the physics of sound

Sound Wave AnimationOriginal Source: YouTube

Fundamentally, sound is caused by vibrations: When a physical object – like a guitar string or a speaker cone – vibrates, it moves the air around it. The movement of the air molecules leads to a dynamic change in pressure – a sound wave, propagating at over 750 mph in every direction. When this sound wave reaches our ears, it’s converted to an electrical signal and processed by the brain at incredible speed. Almost instantly, we can discern the volume, pitch, and timbre of a sound, as well as mentally separate its different components (individual voices in a choir, for example) and consider its harmonic content. 

It rains a lot in Portland (Waveform)Original Source: Wikimedia

Visualising Waves

No matter how simple or complex a sound, it can be visualized using a so-called waveform. The sound of a human voice, breaking glass, or even a whole symphonic orchestra can all, once recorded, be represented in their entirety by a simple, two-dimensional graph.

How Sound moves through the AirOriginal Source: YouTube

The Shape of Sound
Think of the waveform as depicting the journey of a single air molecule: Time is represented by the horizontal axis, while the motion of the molecule towards and away from the source is represented on the vertical axis.

Waveform, non-peridocialOriginal Source: Wikipedia

Quiet and loud

The further air molecules are displaced, the more energy is being transmitted, and the louder a sound will be perceived. A waveform then, can show us the changing volume of a sound over time, making it easy to distinguish the loud crack of a snare drum from a slowly swelling violin note or the constant hum of an electric fan.

Waveform Sinus 50 & 60 Hertz (2020)Original Source: Wikimedia COmmons

High and Low

This graph shows a sine wave. It’s the simplest waveform we can draw, and the fundamental building block of all other sounds. At this level, it’s easy to see a pattern – the wave repeats exactly the same way again and again. Known as periodicity, this is what allows us to perceive sounds as having a musical pitch.These repetitions may occur anywhere from just a few times per second to thousands of times per second. Their frequency is measured in Hertz (Hz), which denotes the number of cycles per second and corresponds to perceived pitch. We can see this on the waveform too – the closer the peaks, the faster the vibration, and the higher the note. A pure sine wave like this one never actually occurs in nature – it can only be synthesized. That said, the human whistle comes remarkably close. Try whistling along!

SoundwaveOriginal Source: Pixabay

Sine wave descending in octaves

More interesting waves
The sine wave, though fascinating in theory, doesn’t actually sound particularly interesting. The waveforms produced by musical instruments are far more complex and nuanced. The method of sound creation a particular instrument employs has a large impact on its waveform, allowing us to recognise the difference between brass instruments, stringed instruments, percussion, and so on. Beyond that, factors such as size, materials, and the way an instrument is played each impart their own sonic qualities to the waveforms. 

Guitar with NylonstringsOriginal Source: Adria Tormo

How we hear
Let’s take the example of a guitar string. By taking a quick look at the waveform, or indeed by listening, we can confirm that it’s a more complex sound than our sine wave. Our brain doesn’t analyse it as a single sound, however, so much as a sum of different sounds, known as harmonics or overtones.

Acoustic instruments produce overtones at different multiples of the fundamental frequency, that is, the note that’s actually being played. Different instruments produce these overtones in different proportions, and it’s this that allows us to differentiate between different instruments playing the exact same note. An instrument that produces many high overtones may sound ‘bright,’ whereas one that has very little harmonic content in the upper range of our hearing will sound more ‘mellow’ or ‘darker’.

Our brains are exceptionally good at analysing overtones, to the extent that we can, for example, hear a clear difference between the sound of a steel or a nylon string being plucked.

Moog Modular SynthesizerOriginal Source: Steve Harvey

Synthesizing sounds from scratch
Now we’re familiar with waveforms and why they matter, let’s take a look at how a synthesizer uses them to create new sounds.

As we’ve seen, acoustic instruments use some type of physically vibrating device to create periodic sound waves. A synthesizer, in contrast, doesn’t vibrate at all. Instead, it uses an electronic device called oscillator to create a rapid change in electrical current – which in turn is amplified to drive a speaker cone. The change over time of this current (which we can represent as a waveform) corresponds exactly to the movement of the cone and therefore the resulting sound wave.

Bow on Violin String, Slow MotionOriginal Source: YouTube

How an oscillator works
The archetypical oscillators used in synthesis have sine, sawtooth, square and triangle waveforms - each created by specific electronic circuits and resulting in a characteristic harmonic spectrum. Let’s look at the sawtooth operator.

The sawtooth wave is often compared to the sound of a bowed string, and indeed the waveform produced by the latter does resemble the classic sawtooth shape. It’s created by the string repeatedly and gradually being pulled out of place by the friction of the bow, then snapping back suddenly under its own tension.

This build-up and sudden release of energy is mimicked by the sawtooth operator. Here, the circuitry gradually outputs a current up until a certain point, at which it short-circuits, effectively snapping back to zero and starting again.

Pink Trombone "Speech Synthesis"Original Source: YouTube

As an aside, the human voice can be thought of as analogous to a subtractive synthesizer – the vocal chords act as an oscillator, and the sound they produce is effectively filtered by the mouth and throat. Vowel sounds are distinct from one another due to the attenuation or pronunciation of different parts of the harmonic series.

Crumar Bit 99 Signal PathOriginal Source: Underground Production

Subtractive synths
Many classic synthesizers make use of a principle known as subtractive synthesis. The basic idea here is to start with a waveform that’s rich in harmonic content, then use filters to selectively remove some of it and sculpt the desired sound. It’s the bright, overtone-rich character of the sawtooth wave that makes it a staple option on most synthesizers.

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