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# SQUARE ONE: Add It Up

September 1, 2007

Additive synthesis may be the ultimate synthesis technique. Any conceivable sound can be generated using additive synthesis, at least in theory. Two factors have pushed additive out to the fringe, however. First, designing musically useful or expressive sounds with additive is harder than with other, simpler technologies. Second, additive synthesis requires so much number crunching that until a few years ago, it couldn't be done in real time.

However, the picture is changing. Today's desktop computers can do additive synthesis in real time, although it's still more CPU intensive than most other types of synthesis. And several commercially available software synthesizers now use additive synthesis in one form or another. In this column, I'll provide a quick refresher course for those who are unfamiliar with the concepts of additive, and then take a quick look at a couple of the more interesting software instruments that use it.

FIG. 1: An additive-based software synth might provide a two-dimensional vector envelope, such as this one in Camel Audio Cameleon 5000. The envelope is used to morph among four separate additive spectra.

## E Pluribus Unum

As most electronic musicians know, the simplest possible sound is a sine wave. A sine wave contains energy at only one frequency. If you listen to a pure sine wave by selecting one in a synth oscillator and playing a MIDI note, then the sine wave will sound completely muted and colorless. (For more on sine waves and the basics of additive synthesis, see the article “All About Additive Synthesis” by Scott R. Garrigus, available online at www.emusician.com.)

Most sounds, both natural and synthesized, contain energy at many different frequencies. Without getting into the math, which is fairly dense, we can say that any sound can be described mathematically as the sum of one or more sine waves. Looking at the makeup of sound is known as Fourier analysis; if you want to learn more about it, a quick Web search will get you started. Each of the sine waves in a complex sound will have its own amplitude (loudness) envelope, frequency, and phase.

Classic analog-style synthesis is called subtractive synthesis. In subtractive synthesis, we start with a complex tone (such as a sawtooth wave coming from an oscillator) and use a filter to get rid of the portion of the frequency spectrum that we don't want.

Additive synthesis is just the opposite; in fact, additive synthesizers may not have any filters. With this approach, we build up a complex, musically interesting tone by mixing (adding) a bunch of sine waves, each of which is called a partial. Though you'll sometimes hear sine waves described as “overtones” or “harmonics,” these terms refer only to partials that are harmonically related to one another. That means their frequencies are in simple mathematical ratios to each other, such as 2:1, 3:1, and so on. In additive synthesis, each sine wave can have any arbitrary frequency you want, in which case the term partial is more accurate. (Partials can be harmonic, but they don't have to be.)

Defining the sound of a musical instrument using raw additive synthesis is difficult because the sound will likely have dozens of partials, each with its own amplitude envelope. And these aren't simple ADSR envelopes, either: the amplitude of a given sine wave may rise and fall several times within a few milliseconds.

To use additive synthesis in a practical, musical way, we need to take a few shortcuts. Additive synthesis programs offer different ways of doing this, but they all typically offer macro controls of one sort or another that provide high-level control over the partials. Some synths allow the user to load the partial data for a sound (a trumpet note, for example) and then massage that data using controls such as knobs or sliders. A single control would typically adjust the amplitudes of many high partials simultaneously or could speed up or slow down multiple envelope segments per partial during some portion of the sound.

## The Monster Morph

Two soft synths, VirSyn Cube (www.virsyn.com) and Camel Audio Cameleon 5000 (www.camel audio.com), use similar approaches to additive synthesis (see each manufacturer's Web site for free downloadable demo versions). In either program, you can load up to four additive templates at once. These templates are positioned at the four corners of a square and contain the analysis data of either real-world or artificial sounds. To synthesize an entirely original sound, create a two-dimensional vector envelope that morphs among them (see Fig. 1).

Morphing is quite different from mixing. In mixing, two or more source sounds are added together in their original form. When a synth morphs between templates, however, it interpolates between the mathematical values that define the separate sounds. For instance, if it morphs from a short, plucked sound such as a string pizzicato to a more sustained sound such as an organ note, the amplitude envelopes of individual partials will gradually get longer as the morphing envelope moves toward the organ template.

The details of how the synthesis algorithms do this can be complex and are not too interesting for most musicians. For the most part, you interact with the program by loading some templates and playing with the controls until you get something you like. The results can be hard to predict, but they're often quite striking.

In Cameleon, you can morph the harmonic spectrum, the noise contour, and the amplitude envelopes separately. Exotic breathy sounds, unusual plucked tones, swirling pads, and throbbing rhythms are easy to create (see Web Clip 1). The blending of partials can be modulated in real time using MIDI Control Change messages.

## Picture Perfect

Synesthesia is a mental faculty in which the sensations coming from different senses are combined in the brain. For example, a sound might evoke the feeling of sandpaper or oil on the skin. Some additive synthesizers allow a form of reverse synesthesia: you load a graphics file (such as a BMP or JPEG) and then convert the visual data into sound. The results tend to be unpredictable, but once in a while you'll find a gorgeous texture that would have been impossible to arrive at any other way.

FIG. 2: The spectrum editor in VirSyn Cube 2 provides graphic tools with which you can warp the spectrum. Each horizontal line represents a different sine wave partial.

The first well-known program to use this image-to-sound model was U&I's Mac-only MetaSynth (www.uisoftware.com). MetaSynth is not a real-time instrument; it's a graphic-based sound-editing and rendering platform with several unique capabilities. You can “paint” sounds additively: each horizontal line of pixels is a separate partial, and the brightness of the color corresponds to the amplitude of the sound. You can also use mouse tools to create rhythms, cut and paste, transform preexisting images, and more.

VirSyn includes graphical editing of additive sound spectra as part of its Cube 2 and Poseidon programs (see Fig. 2). Image-Line FL Studio (www.flstudio.com) has a built-in soft synth called BeepMap that can load graphics files (but not edit them) and use them for additive synthesis.

A number of software synths allow you to create your own oscillator waves using a simplified form of additive synthesis. Usually, the sine wave partials will all be harmonically related. Instruments in this category include Image-Line Sytrus and u-he Zebra2 (www.u-he.com; see Fig. 3). Both can combine additive synthesis with other techniques, such as frequency modulation (FM).

FIG. 3: Each oscillator in u-he Zebra2 has 16 user-defined additive spectra, which are selectable with the small boxes along the bottom. The waveform knob blends smoothly from one spectrum to another.

When the partials are all whole-number multiples of the fundamental, the waveform will sound pure. You can add color and animation in these hybrid synths by mixing two or more oscillator tones that are detuned from one another. When each oscillator has its own amplitude envelope and the harmonic spectrum of each oscillator is morphing, the tone will have movement and life.

Thanks to fast computers, additive synthesis has taken its place alongside sample playback, subtractive, FM, waveshaping, and other synthesis techniques in a musician's palette of electronic tones.

Jim Aikin writes about electronic music for various magazines, plays electric cello, and writes interactive fiction. You can visit him at www.musicwords.net.

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