Additive Synthesis


Additive synthesis is the method of creating sound by summing sine waves together.  Sine waves are one of the most fundamental constructs in mathematics and are useful in many aspects of science and engineering.  When the ear hears a single sine wave, it sounds clean and pure. The FS-256 from Differential Audio Inc. uses additive synthesis for its architecture.  Additive synthesis relates to how we all hear, and does so by building sound from the ground up - one frequency at a time.

Please see the blog post Intro to Additive Synthesis for a simple but technical explanation.

The Human Ear:  From Time Domain to Frequency Domain

The human ear works like this: the eardrum vibrates in response to time domain stimulus from the environment which then stimulates the three little bones. This then vibrates fluid into an organ named the cochlea.  The cochlea is shaped like a snail shell, with thousands of small hairs (in the Organ of Corti) that can each detect a particular sound frequency. The hairs generate electrical impulses to the brain which is what gives us the sense of hearing. Shorter hairs located at the outside of the cochlea detect higher pitch sounds, and longer hairs deeper inside the cochlea detect lower pitch sounds.  A single sine wave will resonate only a select group of these hairs, and what we hear is a pure tone with no other frequency content in the sound. The cochlea is an amazing organ, as it is essentially a time domain to frequency domain converter.

Music Synthesis: Time Domain vs Frequency Domain

In music synthesis, viewing a time domain signal such as a square, triangle or sawtooth wave (or other) on an oscilloscope gives most listeners very little idea of what that signal will actually sound like - visualizing a time domain signal does not explain its sound. Following on how the cochlea converts time domain signals into the frequency domain, we need to understand what a signal looks like in the frequency domain to understand what it sounds like. Fourier analysis is a mathematical technique that allows us to view the frequency content of a time domain signal - thankfully though we don't need to understand the math behind it.  All we need to understand is that we can change our perspective by viewing signals in the frequency domain, rather than in the time domain. This is a feature which Differential Audio Inc.'s products will have.

A single sine wave, when viewed in the frequency domain, represents a single frequency at the amplitude of the time domain signal. It is a pure, single tone.

Square, triangle and sawtooth waves contain multiple harmonics in the frequency domain, each of which are integer multiples of the fundamental frequency. When viewed in the frequency domain using Fourier analysis (FFT), we'll see multiple frequencies represented (each of which are picked up by the cochlea), and this makes these signals sound more interesting than a single sine wave on its own. These sounds are richer in timbre than a single sine wave.

Subtractive Synthesis

From the dawn of electronic synthesis in 1945 from Ottawa's Hugh Le Cain's Sackbut, to modern day synthesizers, analog and digital time domain oscillators have dominated. Prior to the digital revolution, analog circuitry was the only tool available to synthesizer designers. These analog circuits could generate interesting frequency content using square, triangle or sawtooth time domain waves, rich in harmonics, at a cost of scale. 

Many or most synthesizers built to date employ a form of subtractive synthesis - that is, they create sound using an oscillator with more frequency content than just a single sine wave: the square, triangle or sawtooth. When the ear hears one of these signals, the hairs of the cochlea are resonating at many integer multiples of the fundamental. 

Subtractive synthesis typically then applies a frequency domain filter (low pass or high pass) to modify the frequency content of the signal to make it sound more interesting and dynamic. The problem with this is that the square, triangle and sawtooth waveforms are fixed in the frequency content from the beginning (1.0x, 3.0x, 5.0x etc. of the fundamental), and subtractive synthesis can only remove what is already there. It is like a sculptor removing clay, rather than a painter adding paint.

Bells, acoustic guitars and pianos have frequency content in their sound that are not integer multiples of the fundamental frequency. These sounds cannot be replicated using time domain square, sawtooth and triangle waves, as those types of oscillator's frequency content is fixed at integer multiples. 

Wavetable and FM synthesizers have improved on the subtractive synthesis approach by generating more interesting frequency content than traditional waveforms, but these approaches give the user little control of what frequency content is being generated.

Last and Current Generation Additive Synthesis

Hardware additive synthesis has existed in the past but the technology was not ready to provide a cost effective, user friendly and powerful enough synthesis engine.

Today, some additive synthesizers exist, either in VST or modular format, which is great as it shows that there is some interest in the approach. However, additive synthesis is computationally expensive, and software or modular hardware formats are limited in their computational power.

Next Generation Additive Synthesis

Differential Audio Inc. is moving forward with the FS-256: an easy to use, desktop, FPGA based additive synthesizer that has plenty of compute power.

Digital technology allows us to control the behavior of each sine wave in an oscillator over time, such that the pitch, amplitude and other variables can have their own envelope that develops uniquely from each MIDI key press and release. The potential for sound design is enormous.

Partials can be compressed into a noisy percussion sound, expanded with inharmonic intervals, or express varying degrees of frequency and amplitude deviation over the course of a single note.

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