A basic Additive synthesizer such as the one I’m describing has one notable difference- no filter, and no waveform selection. In this design we’re doing all the timbral alteration by selecting the levels of the harmonics. The overall structure is shown below. I’ll break it down stage by stage.
The Harmonic Generator.
The Harmonic Generator container is our fundamental oscillator. This is the pitch that we are using for the note we want to play. Everything else is generated in our Even Harmonics Container and our Odd Harmonics containers.
The Fundamental Oscillator.
This is simple, just an Oscillator HD module, with the waveform preset to Sine wave, pitch input and Audio Output.
Even Harmonics. These are our 2nd, 4th, 6th, 8th and 10th harmonics so for Standard A at 440 Hz Hz they will be; 880 Hz, 1760 Hz, 2540 Hz, 3520 Hz, and 4400 Hz. We use the same HD Oscillator module again set to a sine wave output. The harmonic frequencies are generated by the offset voltages in the Fixed Values (Volts) module, the voltages are as follows; 2nd Harmonic Osc 1 V 4th Harmonic Osc 2 V 6th Harmonic Osc 2.585 V 8th Harmonic Osc 3 V 10th Harmonic Osc 3.322 V
Odd Harmonics. These are our 3rd, 5th, 7th, 9th and 11th harmonics so for Standard A at 440 Hz Hz they will be; 1320 Hz, 2200 Hz, 3080 Hz, 3960 Hz, and 4840Hz. We use the same HD Oscillator module again set to a sine wave output. The harmonic frequencies are generated by the offset voltages in the Fixed Values (Volts) module, the voltages are as follows; 2nd Harmonic Osc 1.585 V 4th Harmonic Osc 2.322 V 6th Harmonic Osc 2.807 V 8th Harmonic Osc 3.170 V 10th Harmonic Osc 3.459 V
Controlling the levels of the Partials (Harmonics).
This is just an audio mixer. I have used VCA modules rather than Adjust Level modules for a more natural “feel” to the control over the levels.
The Final stage.
Here we are just using the standard Synth output of a VCA and ADSR module connected up as usual. The waveshaper was something I included to check that I was not getting any unexpected frequencies out of the Harmonic Generator.
Although I haven’t included any other modules such as Waveshapers, filters etc. there’s no reason not to include them and make it more of a hybrid synthesizer.
Additive synthesis is a technique that is little known and often poorly understood–especially compared to the more usual subtractive and FM synthesis methods of sound sculpting. However when used effectively, it can be a powerful tool for making sounds that are difficult to create by other means. So what is additive synthesis , and how can we create an instrument that uses it? First we need to understand exactly what it is and how it works to create sounds.
How additive synthesis works.
To understand additive synthesis, let’s compare it to the better known, subtractive synthesis as used in the early Moog, Roland and ARP synthesizers. A subtractive synth starts by generating a rich, full waveform, like a square or sawtooth wave. We then use filters, envelopes etc to tailor this sound, until we achieve the sound we want. This is the method along with FM that we are more familiar with. Additive synthesis starts work from the opposite end. Rather than starting with a complex sound and changing it to our needs, we build our sound from scratch, one element at a time. This sounds dauntingly complex, but approached piece by piece it’s quite easily understood and managed. A Hammond drawbar organ for example can be considered as a basic additive synthesizer We start with our strong fundamental frequency that give the tone its definite pitch. Lets take 440 Hz (A4) to start with, we can then start adding in more tones such as 2nd harmonic 880 Hz (A5), 3rd harmonic 1320 Hz (A6), and so on. Doesn’t sound so daunting when compared to a Hammond organ does it?
To further understand how this works, we’ll need to understand harmonics. A very basic example is; as we have already seen, complex sounds can be approximated by layering sine waves at different frequencies (pitches) and amplitudes (volumes). These extra tones are known as “Partials” rather than harmonics (you’ll see why later). A harmonic waveform, like a square or a sawtooth, contains a sine wave at the “fundamental frequency”: that’s the lowest frequency in the sound, and the one whose pitch we hear. It’s also called the first harmonic. After this we have more layers of sine waves, or harmonics (partials) which all add together to create our unique sound. In this case they are at whole-number multiples of that fundamental frequency (x2, x3, x4 etc). As an example: A 100 Hz sawtooth wave will contain the fundamental frequency at 100 Hz, and can then be created using more sine waves (or harmonics) at 200 Hz, 300 Hz, 400 Hz, and so on, gradually diminishing in level as we increase in frequency. The number of upper harmonics that are present in a sound, and how loud they are, is what gives the sound it’s distinctive timbre. A square wave, for example, features only harmonics that are odd-numbered multiples of the first harmonic: so, 300 Hz, 500 Hz, and so on (x3, x5, x7) but they are still whole number multiples. In the illustration below you can see (especially in the lower frequency region) the difference in harmonic (partial) structure of the sawtooth and square wave signals, which are both set at 220 Hz.
Additive synthesis makes use of this, allowing us to build new sounds from scratch by controlling the frequency and amplitude (volume) of their harmonics. Naturally, this is a long-winded way to make a square or a sawtooth wave: for that we just need to switch on our faithful Moog or ARP. Stepping outside the boundaries. However by getting involved in controlling the individual harmonic components of our sounds, we can leap far beyond the bounds of these familiar sounds, and create sounds that are less accessible using other forms of synthesis. By changing the amplitudes of a sounds constituent harmonics over time, by using LFOs or Envelopes we can create some really interesting sounds that are completely unlike other instruments. Inharmonic Partials. A further leap forward is also possible by introducing inharmonic (not harmonically related) partials which are not whole number relatives, but partial numbers such as x2.5 for example, we can then create some really unusual sounds, such as percussion, bells, metallic sounds and some quite “other worldly” effects, we end up with sounds that are sometimes like ring modulation and some that are beyond what we can do with a ring modulator and two VCOs.
If you want a really in depth explanation of the principles of additive synthesis (warning: there’s a lot of advanced maths in this article- think Fourier analysis) then have a read of this Wikipedia article on the subject.
In the next post I’ll start to delve into how we can achieve some of this in Synthedit.
