Additive Synthesis Explained – What is Additive Synthesis?

Additive Synthesis ExplainedMention the term “additive synthesis” to a roomful of musicians….

…. and you’re likely to come up with a few different reactions.

Even if the audience includes a number of experienced synthesists, there will still probably be some contention as to what additive synthesis is, what it is for, and what sounds it can produce.

So in this article we will, as we have in our previous articles on synthesis, investigate and understand what additive synthesis is.

And we’ll do that it in such a way that’s easy to understand and applicable to our craft as music producers.

Let’s begin!


Read the other articles on audio synthesis:


Additive Synthesis Explained – Introduction

Of all the available methods for generating or synthesizing sounds, additive synthesis is one of the least understood.

Many people think of additive synthesis as only suitable for approximating organ sounds or for producing harsh, clangorous timbres. But just like its more familiar counterparts–subtractive, FM, and phase distortion–additive synthesis is actually capable of producing quite a diverse range of sounds.

Definition of Additive Synthesis

At its most basic, additive synthesis is a sound generation method that involves the combination of simple waveforms. This is in order to produce a more complex sound.

Like in FM synthesis, sine waves are the most commonly utilized waveforms (as they’re the simplest and most basic to work with). In practice however, most any type of waveform can be used, and some systems even utilize short segments of recorded sound.

The individual waveforms used in additive synthesis typically have different frequencies and amplitudes. When combined, these differences affect the length and tone of the final sound to varying degrees.

Origins of Additive Synthesis

Although additive synthesis might seem like a wildly innovative and esoteric form of synthesis to some, its origins can actually be traced to the earliest days of electrical theory.

Time for some history!

In the early years of the 19th century, the French mathematician Jean Baptiste Joseph Fourier put forth the theory that complex sounds can be broken up into several, quite simple component sounds.

Conversely, Fourier also believed that even the most complex sounds could be created by combining the simplest of sounds, which are sine waves. For Fourier, sine waves are the simplest identifiable units of sound, in the same way that atoms are the smallest units of any element.

In what would eventually come to be known as the Fourier Theorem, the mathematician stated that combining sine waves would result in complex sounds. This essentially formed the basis for additive synthesis.

How Additive Synthesis Works

As anyone pretty familiar with synthesis would know, sine waves by themselves aren’t really all that exciting in isolation. That “puuuurp” sound doesn’t really inspire great musical tracks, since their pure and characteristically unwavering tone doesn’t exactly call to mind complex synthesis as much as it does television test tones or ocarina patches on the most rudimentary toy keyboards.

But put some sine waves together and introduce a bit of modulation, and weird and wonderful things begin to happen.

Sine waves essentially have only a specific frequency and amplitude. But when combined with other sine waves of different frequencies and amplitudes, they can produce radically different sounds, with the combined sound taking on a wildly different character.

That is essentially the basis of additive synthesis… like the name suggested all along, you’re simply adding waveforms together to get other sounds.

But let’s go deeper…

Partials

Pitch partials of a bell
Pitch partials of a bell sound [source]
In additive synthesis, the individual sine waves that make up a sound are referred to as ‘partials’.

The first partial, which is also known as the “fundamental frequency,” is considered the most important to the overall sound. This fundamental frequency essentially determines the overall loudness and pitch of the composite sound.

The other partials also have an effect on the loudness and pitch of the final sound. But what is more apparent is their effect on the overall tone or timbre of the resulting sound.

Partials help determine whether a sound is loud or soft, harsh or mellow, bright or dark, and so on. They can also affect the pitch of the sound, or introduce different pitches that, when combined, result in distinct tonalities.

Most every additive synthesizer works in this manner: combining several different sine waves in real time, each with its own tonal characteristics. The process is very mathematically-intensive as you might imagine, and considerable processing power is often necessary. This is one of the reasons why additive synthesis is often implemented in digital, rather than analog circuitry.

Properties of Additive Synthesis

To some extent, everything that has been said about the tonal characteristics of additive synthesis is true. Harsh, brassy, cold, grating…all of these and more are in fact frequently characteristic of additive sounds.

But they don’t always necessarily have to be that way. Additive synthesis is actually capable of a much wider array of different sounds.

On the one hand, additive synthesis can produce sounds of incredible harshness, often with a distinctly metallic character.  On the other hand, it is also capable of producing sounds of unspeakable gentleness, mellowness, and beauty.

Lush, undulating waves of atmospheric alien-landscape sounds are also the domain of additive synthesis, just as much as brash and excessively bright timbres. You only have to listen to the sounds produced by a fully featured and capable additive synthesizer in order to realize the diversity of sounds possible.

Sound Applications for Additive Synthesis

Pipe Organ

If you are familiar with the sound of an organ, you already know what additive synthesis is capable of. Additive synthesis is perfectly suited to the production of organ tones, most of which are simple combinations of unaltered sine waves. In fact, organs are actually considered rudimentary types of additive synthesizers.

Bells

Additive synthesis is also ideally suited to synthesizing bell sounds. Most bell tones consist of a fundamental along with multiple partials that shape its overall pitch, tone, and amplitude. With additive synthesizers, it is possible to simulate a wide variety of bell sounds, from the familiar and almost-realistic to the strange and otherworldly.

Plucks and Percussion

Additive synthesis is also frequently employed in the creation of plucked string or drum sounds. By combining sine waves of varying lengths, timbres, and amplitudes, it is possible to recreate the component sections of a more complex percussive sound, such as its attack, sustain, and so on.

Miscellaneous

Of course, additive synthesis can also produce harsh and wildly dissonant sounds, some of which can be quite similar to those produced by FM synthesis. These types of sounds typically result from the incorporation of inharmonic partials. Depending on the pitch variance between the different partials, the resulting sound can range from slightly wavering or beating to dissonant and atonal.

Although additive synthesis isn’t really the simplest or most straightforward way to achieve warm and lush tones (subtractive synthesis is probably better suited to the production of such sounds), they can be produced fairly easily by most additive synthesizers.

The method can also be used to produce rich, evolving soundscapes, which typically involves modulating the attack times and durations of the individual sine waves. Properly implemented, an additive synthesizer can produce sounds that are just as rich and thick as those produced by fully spec’d polyphonic analog synthesizers with extensive modulation options.

Musical Instruments that Use Additive Synthesis

As potentially groundbreaking as Fourier’s Theorem was, there wasn’t any practical way to support its premise in the early 19th century. The world had to wait until the 1860s, which was when Hermann von Helmholtz built a machine that proved Fourier’s theorem. The device consisted of several tuning forks, each producing sound via electricity and tuned to a specific pitch.

Helmholtz Sound Synthesizer

Helmholtz Sound Synthesizer
Helmholtz Sound Synthesizer

Although Helmholtz’ device is now widely considered to be the world’s first synthesizer, it was not a musical instrument by any definition of the term. The device was capable of producing only a single sound– and only at a specific pitch at that–so its musical application was quite limited, as you could imagine.

Thaddeus Cahill Telharmonium

Thaddeus Cahill Telharmonium
Thaddeus Cahill’s Telharmonium

The first actual additive synthesizer was the Telharmonium, which was invented by Thaddeus Cahill. Also the first electronic musical instrument, it employed an array of alternators that spun rapidly, producing sine waves that in turn produced some fairly complex sounds for the time.

It was played via a keyboard, so the Telharmonium was a polyphonic beast of an instrument, and weighing more than 200 tons. Because of its sheer size and weight–and the unavailability of any practical means to amplify its sound–Cahill’s device failed to take the world by storm.

Hammond Organ

Hammond Organ
Hammond Organ

The Hammond organ is the most successful  of the early synths, and was a significant step forward in the development of additive synthesis.

Invented in 1935, it utilized a similar alternator system as the Telharmonium, albeit powered by more efficient technology. Partials were implemented via banks of switches known as drawbars, which are still familiar features in organs to this day. The different positions of the various drawbars could produce countless combinations, resulting in as many as 300,000 distinct sounds.

Even with the potential to produce so many sounds, the Hammond organ was still a fairly rudimentary instrument. Even though they continue to be in demand for even the most electronically driven tracks, truly complex sounds still remains out of reach.

It wasn’t until the advent of computer technology that additive synthesis could finally live up to its potential. This development also led to the wider spread accessibility of additive synthesizers.

Additive Synthesis in Modern Technology

In the frenzied period of discovery and innovation that followed, a number of important developments took place in the world of additive synthesis. Digital mainframe computers were employed in the manipulation of partials during the 1950s to the 1960s, resulting in quite complex sounds. This period also saw the development of Max Matthews’ Music I sound programming language and David Luce’s resynthesis machine, which was a more efficient implementation of the principles of additive synthesis.

More Recent Hardware Additive Synthesis

By this time, it was fairly obvious that real-time additive synthesis was a pretty complex and resource-intensive process that exacted a heavy toll on even the most powerful computers.

For this reason, ‘true’ additive synthesizers that actually synthesized sound in real-time were quite rare, prohibitively expensive, and oftentimes both. One notable exception was the Kyma system from Symbolic Sound.

Although still too expensive for most musicians, the Kyma was the next important step forward in the evolution of additive synthesis. A modular system, it was a lot more accessible than previous implementations of additive synthesis, relying on a combination of software synthesis algorithms and the Capybara DSP hardware.

Kawai K5000
Kawai K5000

Much more affordable was the Kawai K5000, which is still regarded as the most effective implementation of additive synthesis in a hardware instrument. The K5000 employed an ingenious system that simplified the inherent complexity of additive synthesis by allowing the manipulation of entire groups of partials, instead of altering them individually. In addition to making the principles behind additive synthesis much easier to grasp, this also made it possible to mass-produce a true additive synthesizer and price it more affordably.

Additive Synthesis Enters Software Age

The advent of software synthesizer technology has made additive synthesis even more accessible to the masses. The powerful processors of modern computers proved to be ideally suited to the resource-intensive number-crunching required by additive synthesis. Consequently, a number of software developers rolled out quite a few software synthesizers that make full use of the resources available.

Razor by Native Instruments
Razor by Native Instruments

One example is Razor by Native Instruments. Known for its bright, cutting sounds, it has been around since 2011. Even today, it is still capable of producing some futuristic and otherworldly sounds.

Older still is VirSyn’s Cube, which is still one of the simplest and easiest to understand implementations of additive synthesis. Now available in a mobile app, Cube is billed as an “Easy to Program Additive Synth Engine”, with up to 512 partials for each of its eight voices. With harmonic, inharmonic, and noise waveforms, morphable filters, and tempo-synced envelopes, Cube is capable of producing a diverse range of sounds, many of them far removed from typical additive tones.

u-he’s Zebra is also well worth considering for a modern implementation of additive synthesis. Marketed as a “sound-design playground”, it is a powerful software synthesizer that utilizes additive waveforms among other types of synthesis. Zebra is a popular tool for soundtrack composers and sound designers alike, serving up a near-limitless array of sounds in a unique and innovative package with an excellent user interface.

Audio Example of Additive Synthesis

Here are some examples of the sounds produced via additive synthesis.

In this example, you will first hear two harmonic partials played together, and then split apart, resulting in a wavering, modulated pitch.

The second example starts off with a single sine wave, to which harmonic partials are added one by one.

With each succeeding higher-pitched partial, the combined sound gets brighter and brighter, approximating the sound of a filter opening up in a subtractive synthesizer.


Final Thoughts

As you can see, additive synthesis is a lot more versatile and capable than a lot of people give it credit for.

If you are looking for an alternative to the more familiar sounds produced by subtractive or even FM synthesis, you might want to consider looking into incorporating additive synthesis in your next musical project.

If you want to learn more about synthesis, check out the other posts in this series, where we talk about subtractive, wavetable and FM.

And be sure leave a comment if you have any questions and valuable remarks.

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