All about Additive Synthesis

Feb 16, 2007 7:58 PM, By Scott R. Garrigus

Putting sounds together one little piece at a time.

Resynthesis

Today, pure additive synthesis is still very scarce even with all of the computing power available on the desktop. That's because the sheer number of parameters that have to be set in order to accomplish even a fairly complex sound is overwhelming. And to accurately mimic acoustic instruments, you need to set the partials for every note because the partial characteristics change for every fundamental frequency, and to a lesser extent, for different loudness levels.

Instead of building sounds from scratch, however, you can try a more practical form of additive synthesis, which is resynthesis. With resynthesis, a computer uses the principles of the Fourier theorem and analyzes a complex waveform to find all of its basic partial components. In particular, it tracks the frequency and amplitude envelopes for as many partials as you want. The computer first samples the sound and then puts it through a mathematical function known as a Fast Fourier Transform (FFT). This makes it easy to take apart any sound, like a spoken word, and find the structure of its spectrum (see Fig. 2). Once you know the sound's frequency and amplitude parameters, you can manipulate these building blocks to create a slightly different or perhaps a radically altered new sound.

Even with today's available computing power, however, real-time resynthesizers are few and far between. The reason is that both analysis and resynthesis processes are very complex, and creating the software and hardware to handle them in real time can be expensive. One high-end system that handles real-time resynthesis is the Kyma system from Symbolic Sound. Kyma is a modular, software-based synthesis and processing workstation accelerated by DSP hardware. (For a review, see the January 1998 issue of EM.) Sound designers use a graphic signal flow editor on the screen of either a Macintosh or PC to specify how to analyze, process, and resynthesize the sound. The signal-flow diagram is turned into a program for the multiple-DSP Capybara hardware, which connects to the host computer via PCI, NuBus, ISA, or PCMCIA card.

All-natural Additives

Because of the difficulties associated with generating the hundreds of parameters necessary for true additive synthesis, some synthesizers offer a modified approach to the technique and use more complex waveforms as the building blocks for sound production. And rather than letting you manipulate individual partials, they'll provide a limited number of partials whose parameters can be changed in groups.

One such synthesizer is the Kawai K5000, which uses a technique called Advanced Additive Synthesis. The basic building block of a K5000 sound is a bank of 64 partials called a wave set. The wave set can be either partials 1 to 64 or partials 65 to 128 of the naturally occurring harmonic series. You can adjust the amplitude envelope of each partial but not its frequency, which means you can't include inharmonic partials. In order to make up for this, the instrument provides PCM samples that can be combined with the wave sets to create more complex waveforms. This feature makes for a very powerful system.

On the Desktop

If you want to get your feet wet in additive synthesis on your home computer, you can use several software-only applications. Audio-editing programs such as Sonic Foundry's Sound Forge and Syntrillium's Cool Edit Pro on the PC provide the means for creating and combining simple sine waves in unlimited numbers. Using the Simple Synthesis function in Sound Forge, you can create a sine wave with the specific frequency and amplitude of your choice. Then you build complex sounds by continuing to mix new sine waves with the original until you hear something you like. Cool Edit Pro's Generate Tones feature provides even more flexibility: simply choose the frequencies for up to five partials (harmonic or inharmonic) above the fundamental and let the program build the waveform for you (see Fig. 3). You can even put simple amplitude envelopes on the partials to vary the sound as it evolves.

There are other programs available that allow you to experiment with all aspects of additive synthesis. This program generates complex waveforms using additive synthesis. One dedicated additive program for the PC is Andy Bridle's Adsyn32 (see Fig. 4). This program generates complex waveforms using additive synthesis and allows you to create any number of partials, each with its own settings. Even though it doesn't perform its calculations in real time, it does them quite quickly and allows you to hear your results in a matter of seconds. Mac users can try out Mike Berry's GrainWave2, a shareware program that offers numerous synthesis methods in addition to additive, and it works in real time. You'll also find quite a few additive synthesis options in Csound, the crossplatform, public-domain synthesis language. This powerful application is the latest in a long line of sound-programming languages that extend directly back to Max Matthews's original Music program. Developed by Barry Vercoe at MIT, the program includes a number of additive examples in its basic distribution package. A real-time, PC version of Csound, developed by Gabriel Maldonado, provides dozens of partials that you can control from a MIDI keyboard.

If you're keen on trying out resynthesis, have a look at smsTools for the PC, developed by Xavier Serra and his research group at the Pompeu Fabra University of Barcelona. This program gives you extensive control over the analysis data in numerous ways before you resynthesize it. For example, you can modify just the frequency or amplitude envelopes, or combine the spectra of two different files. The results can be truly remarkable.

So now that you know a bit more about additive synthesis and its many facets, get out there and start building some cool sounds. Theoretically, it's possible to come up with any sound imaginable using pure additive synthesis. Who knows, you may invent something spectacular to replace the Windows start sound...please!

Sidebar
The Timbre Story
In sounds that have a clear pitch, the partials above the fundamental have frequencies that are related to the fundamental's frequency by simple ratios. For example, the second partial is twice the frequency of the fundamental, the third partial is three times, the fourth is four times, and so on. Nonpitched sounds, such as percussion, typically contain inharmonic partials, whose frequencies are not whole number multiples of the fundamental. In most sounds, the partials' frequencies remain relatively stable, but the amplitude of each partial can change over time. Static waveforms, for example the square or sawtooth, contain partials whose amplitudes are fixed, which is why these tones have, for the most part, a lifeless quality.

Just how much do the partials in a natural sound fluctuate? It's not unusual for the amplitudes of a natural sound to vary every 1/1000 of a second or so. Moreover, certain sounds, such as brass instruments, have a spectrum in which the upper partials enter after the lower ones and disappear sooner. Attempting to recreate the spectrum of a sound "from scratch" is not a trivial task and requires complex envelopes with hundreds or even thousands of breakpoints. Few devices can perform this task in real time.

Given the massive range of frequencies that can appear in a sound and the fact that these frequencies change in strength as the sound evolves, you can see why "sound quality," or timbre, is so difficult to define. Despite attempts by many researchers to classify and organize sound timbres, no widely accepted system of classification has yet appeared.