All posts tagged “Synthesis”
To understand what filters do, and why they are one of the most important building blocks in synthesis, you have to understand a little about the nature of sound itself and, in particular, the nature of waveforms. So I’m going to introduce this series of tutorials about Thor’s filters by talking first about what constitutes the sound generated by an oscillator, whether analogue, virtual analogue or sample-based.
Mathematics tells us that any waveform can be represented either as a wave whose amplitude is plotted against time or as a series of components whose amplitudes are plotted against frequency. Often, these components will lie at integer multiples of the lowest frequency present – for example, 100Hz, 200Hz, 300Hz… and so on – and these are then known as the fundamental and its overtones, or as harmonics. In more complex sounds, there may be components that lie at non-integer frequencies, and these are sometimes called enharmonics. The sound may also include noise that is distributed over a range of frequencies and whose precise nature is determined by all manner of factors that we need not discuss here. Figure 1 illustrates all of these.
Why were wavetables developed?
We now hold early wavetable synths such as the PPGs in high esteem and think of them as expensive examples of early digital synthesisers. However, wavetables were actually invented to make possible relatively low-cost instruments that avoided the shortcomings of existing digital synthesis methods such as FM and additive synthesis, and to overcome the immense technological limitations of the day.
To understand this, imagine that you want to use a piece of audio equipment today to record, store and replay the sound of a someone saying “wow”. You choose a suitable recorder or sampler, capture the sound and, without any need to understand how the equipment does what it does, you can then replay it. If you used a digital recorder, you do so simply by pressing the Play button; if you used a sampler, you allocate the sample to a key or pad, then press that to listen to the recording that you’ve made.
However, we don’t have to travel back many years to a time when none of this was practical. The problem was two-fold. Firstly, early memory chips were extremely limited in capacity, and storing anything more than a fraction of a second of audio was very expensive. Secondly, even if you could store the audio, the primitive microprocessors available at the dawn of digital synthesis were barely able to address the memory and replay it at an adequate speed.
Let’s consider the word “wow”, which takes about a second to say. Using the sampling specification introduced for the audio CD (44,100 16-bit samples per channel per second) you would require 88.2KB of RAM to record the word in mono, and double that if it were recorded in stereo. Nowadays, we wouldn’t blink at that sort of requirement, but when the earliest digital audio equipment appeared, you needed as many as eight chips for just 2KB of RAM. Sure, samplers were shipped with boards stuffed full of dozens of these, but you would have needed no fewer than 352 of them to store the word “wow” at CD quality!
Clearly, this was impractical so, while various digital tape formats were able to provide the hundreds of megabytes of audio data storage needed to edit and master whole albums of music, developers of digital musical instruments were looking at much more efficient ways to record, store and replay sounds for use in synthesis. The wavetable was one such method.
So, we finally come to the sixth and final oscillator in Thor’s armoury of sound generators. This is the wavetable oscillator that first appeared in general use in the PPG Wave Computers, and shortly thereafter in the PPG 2.x series. Like other digital oscillators, this is an often misunderstood beastie, so let’s first discuss what a wavetable actually is.
There have been a number of different uses of the word wavetable in recent years, and some of them are rather misleading. For example, I have seen texts that use the name to describe a ROM that holds a selection of unrelated PCM samples such as clarinets, electric guitars, bouzoukis and Mongolian nose flutes. There are lots of waves in the ROM and these are accessed using a lookup table, so the ROM must be a wavetable, right? Wrong!
More justifiably, academics use the word to describe the sequence of numbers that represent a single cycle of a regular, periodic waveform. One can then talk about replaying one such “wavetable” (say, a digital representation of a sine wave) or a second (say, a digital representation of a sawtooth wave).
But this is still not the definition used by most people who talk about wavetable synthesis. So let’s be explicit. For our purposes, a wavetable is not a single wave, it is a selection of (usually related) single-cycle waveforms or their harmonic representations stored digitally and sequentially in such as way that that a sound designer can create musically pleasing timbres by stepping though them while a note is being played.
Unfortunately, while the principle makes sense, this would not sound very pleasant. Imagine a ROM containing just two waveforms: the aforementioned sine and sawtooth waves. Now imagine hearing a sound comprising a few cycles of the sine wave followed by a few cycles of the sawtooth wave, followed by a few cycles of the sine wave followed by the few cycles of a sawtooth wave… and so on. The resulting waveform would exhibit discontinuities each time that one waveform replaced the other, and you would therefore hear a succession of clicks polluting the sound. Consequently, a wavetable synthesiser has to be a bit cleverer than that, providing a mechanism for morphing from one wave to the next. Instead of swapping instantly from the sine wave to the sawtooth wave, there would be a transition period during which the waveform changed smoothly from one extreme (the sine wave) to the other (the sawtooth wave) and back again.
“More than just DX pianos”
In the last tutorial, I introduced the concept of FM algorithms, the ways in which FM operators can be connected together to create sounds. A Thor FM Pair Osc comprises two operators – a modulator that is permanently connected to the FM input of a carrier – and we can represent this as shown in figure 1.
Of course, Thor has three oscillator slots, and you can place an FM Pair in each of these so, by default, the standard algorithm offered by Thor is as shown in figure 2: three pairs that can be mixed together, but which don’t – for the moment – interact in any other way. There are many uses for this algorithm, which can be used to create very interesting string ensemble and organ patches, among others. But I fancy stepping beyond these, so I’m going to demonstrate this algorithm by showing you how to create an evolving pad that has a rich, analogue flavour.
Frequency Modulation (FM) has become the bogeyman of synthesis. Whereas, in the 1960s, people quickly grasped the concepts of these new-fangled oscillators, filters and contour thingies, the second generation of players shied away from the concepts of FM, to the extent that most FM synths were used for little more than their presets and the professionally programmed sounds that you could buy for them. Even today, if you look closely at Thor’s refills, you’ll find very few patches based upon its FM Pair Oscillator. This is a great shame, because FM is a very elegant system capable of remarkable feats of sound generation. So, this time, I’m going to introduce you to the principles of FM, and show you how to create what may well be your first FM sound.