Partikl Sound Synthesis Tutorial 1
Introducing sound synthesis
Partikl incorporates a very powerful and flexible software synthesizer. Partikl and its pop-up plugin editors are a new audio application suite, that supports editing of effect plugin settings. The features and flexibility of Partikl are such that, to make the best use of them you will find that a little understanding of the basics of sound synthesis will go a long way.
If you haven't delved too deeply into programming synthesizers before now, or if you fancy a quick refresher course, then this tutorial is for you. We will not be getting heavy with the physics and number crunching side of things here. We'll keep it practical and, hopefully useful. Let's go.
The naming of things
We have to start by establishing the meanings of the terms we will be using from here on in. Creating sound is all about finding new and interesting ways to shove air around. Here is an idealized illustration of what that might look like using a single pure tone.
Using this graphic we can identify some basic units and concepts in sound generation.
| The waveform | The waveform is the wiggly line, obviously! This one is a sine wave. |
| A cycle | The area between the vertical blue lines
in the graphic is a single cycle of this wave. In this instance it
starts at zero, rises to the highest point, drop back down to zero,
continues to the lowest point and rises up to zero again. You can start
a cycle at any point of the waveform. It doesn't have to start from
zero. The main thing to remember is, if you choose any arbitrary point
on the waveform to start from, when you reach that point again, so long
as you are traveling in the same direction as you were when you left
it, you have completed a single cycle. If you start the waveform at some other point that the one shown here (say, from the highest point on the graph) you have changed the phase of the waveform. It doesn't make it sound any different if you listen to the tone on its own but there are good reasons for being able to change the phase of a wave if you wish. We'll get to them soon. |
| Frequency | Describes the number of cycles in each
second. It is measured in Hertz (Hz), one hertz being one cycle per
second. If the frequency is in our hearing range we perceive it as the
pitch of a note. The human hearing range falls roughly between 20Hz at
the low end and about 20,000 Hz at the upper end. If you can hear much
higher than that then your owner needs to get you a dog licence. Human
ears aren't very good at detecting pitch at the extremes of our hearing
range but can be incredibly acute in the midranges. |
| Amplitude |
Describes the range of upward and downward movement the waveform
makes. We hear it as volume. Large amplitude values mean loud audio
signals. Small ones mean quiet ones. If you reduce the amplitude of a
wave you are said to attenuate it, if you increase it you are
amplifying the signal. These amounts are typically measured in decibels
(dB) which are a total pain to work with, mostly because they work to a
negative logarithmic scale where minus infinity is the quietest point
and zero is the point of optimal loudness. So we'll move quickly past.
In a wholly analogue system, like a Stratocaster plus a Marshall stack, amplifying a sound beyond that optimal point gives the desirable sort of distortion sound that has been putting food on guitarists' tables for years. No such luck with a digital system. In the digital world you cannot take the amplitude of a waveform beyond 0 dB. If you try, the wave looks like it hit a brick wall and sounds ghastly! We mention this because putting sound into an amplifier is only one way of increasing its amplitude. Adding another sound source also increases the amplitude of the sound we hear. Which is why a full string section is louder that a solo violin. In sound synthesis it is not uncommon to use several sound sources to create a single sound. Partikl has a built in limiter that manages sound levels internally for you to keep things out of the clipping zone. However, you will need to take some care of levels yourself if you want the best possible sound quality. A limiter working hard is often quite audible which might not be an effect you want to hear! |
| Zero crossing |
If you think about it, moving air around systematically involves
both pushing it and pulling it blowing and sucking. This is reflected
in the graphic in that there is a line drawn through the centre of the
waveform. Amplitudes above the line have a positive value, those below
have a negative one. In the jargon, audio signals are usually bipolar. The point at which a waveform has an amplitude of zero is particularly important in sampling, something we will cover later. But the location of the zero crossing line has a significance in synthesis also. For convenience, we show the zero line in the graphic as bisecting the waveform so there are equal amounts of waveform both above and below the line. Things don't always have to be this way and there are ways for us to move this line up or down. To do so, in the jargon once again, we apply a DC offset to the waveform. As moving this line up or down will make no appreciable difference to the sound of the tone, why worry about it? If an audio signal is what you want, in truth it is not worth bothering with. But, if you want to use a waveform for something other than audio, like using one waveshape to control the parameters of a second then it can be very important. As we might find out later! |
And that's about as much as we need to know about the components of a waveform. But there are a couple of other things we need to touch on to help understand how to synthesize sounds.
Fundamentals, harmonics and the rest.
If you play a note on any tuned musical instrument you will hear an astonishing complexity of sound. But, despite that complexity you will (hopefully) perceive a pitch. That's the fundamental. In all sounds that we perceive as pitched there is one frequency that stands out from all the other noises in there and this is the one the ear uses as the pitch reference. A piano, violin and oboe sound totally different to each other but, if they all play note A4 you will hear three distinctive sounds all having a common fundamental frequency of 440 Hz or thereabouts.
If you listen more closely to the sound of a single instrument playing a single note, once you get past hearing the fundamental you will hear a range of other tones. Some of these work in a musical way and sound rather like chordal notes related to the fundamental. Others have a more uneasy relationship to the fundamental or are completely atonal.
The musical ones are harmonics. They sound musical because they have a very precise mathematical relationship with the fundamental frequency. The frequency of the harmonics are always a whole number (integer) ratio of the fundamental frequency.
Just to confuse matters slightly, the fundamental is also called the first harmonic. So, a tone with a fundamental frequency of 100Hz will have the second harmonic at 200Hz (an octave), the third at 300Hz (octave plus a fifth), the fourth at 400Hz (two octaves) and so on to the limits of our hearing.
The other sounds that you can hear are called aharmonics. These are frequencies that have a non integer ratio to the fundamental. When there are a lot of these present we tend to perceive the sound as clangorous or bell like.
If these three elements were all present in a sound in similar proportions we wouldn't hear a musical note at all. We would hear noise. So, to make musical sounds we need to find some way of establishing a balance between the fundamental, the harmonics and the aharmonics for any given frequency. And that's what synthesis is all about.
There are three major routes to doing this. One is that we can start off with basic sounds that are very rich in harmonics and then use a filter to reduce or remove the ones we don't want. Oddly enough, that is called subtractive synthesis.
We can also do the exact opposite. We can take very simple tones and add them together to create complex sound. Additive synthesis, surprisingly hard to do well.
The third route is a kind of middle way between these two. If the properties of one waveform can be used to vary those of another at audio frequencies, new and complex waveforms can be generated. You could call this synthesis by modulation. The most common methods used are amplitude modulation and frequency modulation.
In reality we mix and match, using elements from all three main routes as we need them.
Blocking it out
The components of most synthesizers can be categorized into four broad groups.
The first group could be called sources. These are the devices that produce the raw sound you will work with. Partikl allows you to use samples as sources as well as including some very well featured tone generators.
The next group we can call modifiers. Included here would be envelopes that shape the sound over time and filters that remove or emphasize certain frequencies.
The third group are modulators. They apply regular, repeated change over time to specific sound parameters. The most common of these is the low frequency oscillator, the LFO.
Finally there are the effectors. These are signal processing devices, reverberation modules, delays and so on. Usually they act at the end of the synthesis chain.
It is usual to define the output from modifiers and modulators as control signals; being as their usual job is to control the parameters of other devices in the synthesis chain. In the days of monster analogue modular synths it was considered sensible to use different coloured patch cords for control signals to distinguish them from audio and other signals. When using Partikl it is also important to distinguish control signals from the audio path. We'll explain why in a moment.
For now, let's have a look at the first three device types in turn.
The right wave for the right job
Any self-respecting synthesizer will have a tone generator offering several basic waveforms as a starting point for sound creation. Why? What distinguishes one waveform from another? The answer lies in the harmonics on offer. So lets just quickly run through the more common waveforms and see what distinguishes one from the other.
| Sine wave | Is a pure tone. It has no harmonics at all so there is not much point in applying a filter to one. Nothing to filter! This purity of tone make it very good for adding low end definition or kick to a bass sound. It is also good for additive synthesis where you don't want harmonics unless you put them there yourself. Put three or four of these waves together for an instant electronic organ type of sound. |
| Sawtooth wave | Is the most harmonically rich waveform in the box. Characteristically bright and buzzy. The starting point for thousands of classic synth sounds. A sawtooth wave has every harmonic present (theoretically) but their amplitude decreases from that of the fundamental by 1/the harmonic number. So the second harmonic is ½ as loud as the fundamental, the third harmonic is 1/3 as loud as the fundamental and so on until you hearing fails. |
| Triangle wave | Really just a sine wave straightened out. It doesn't have many harmonics and those that are present are quite high up. So, if you want hard and aggressive sounds this is not the wave to choose. Nice for flute sounds and soft leads though. |
| Square wave | A bit complex this one. A graph of a true
square wave looks rather like a child's drawing of castle battlements.
Square wave is a shorthand way of saying "pulse wave that spends as
much time at the highest point as it does at the lowest". In this form
it has a sound that is usually described as "hollow". The reason is
that every second harmonic is missing, there are only odd numbered
harmonics present. But this absence of even harmonics only holds true if the time between "high" and "low" in the cycle are the same. If the wave spends half of its time at the top the ratio between the high points and the low points of the waveform is 1:2 and, as we already know, every second harmonic is missing. If we change this ratio to 1:3 (i.e. the wave spends 33.3% of its time at the top) some of the missing harmonics return. We now only loose every third harmonic instead. If the ratio was 1:4 (25%) we would only loose every fourth harmonic. And so on. If there was a way of shifting this ratio in real-time we would be able to hear these harmonics coming and going. We could call it pulse width modulation and use it to recreate classic synth string sounds, all kinds of shimmery pad like sounds and some unforgettable bass tones. Sounds like a plan! |
| Combination waves | Unsurprisingly, combination waves can have the characteristics of most of the above. Partikl includes one waveform that can be "morphed" from triangle to sawtooth to pulse wave. If you've followed us this far you should have realised that this gives you the option of tailoring the harmonic content of the waveform quite closely; a very powerful option indeed. Similarly, being able to change the shape of a wave in real-time can open the door to a whole new bag of sonic tricks. Pulse width modulation on steroids! |
Envelopes
Envelopes give us a way of shaping a sound in time. Every synthesizer will always have at least one to control the amplitude of a signal. More sophisticated synthesizers will have several envelope generators which can be assigned to control other important parameters.
Envelopes are usually "one-shot" devices. An event triggers their start and, once underway, they transmit values that correspond to the envelope shape until they are done. They then do nothing until they are triggered again. Amplitude envelopes are usually triggered by the equivalent of a note being pressed on a keyboard.
Envelopes can be described by the stages they go through. Partikl amplitude envelope is a multi-stage envelope, having separate stages for Attack (how quickly the envelope moves from zero to maximum), Hold (how long it stays at the final attack level), Decay (how quickly the level falls to the..), Sustain (the lowest possible level during a note event) and Release (how long the sound will take to fall to zero from wherever it was when the note event stopped). There is a set of stages associated with when the note stops.
The control signals sent by the envelope unit in Partikl can be bipolar; i.e. the control signal value can be positive or negative. This has got some implications if you want to combine control signals from more than one device.
Say you want to combine the output from an envelope and a LFO to create a LFO that fades up or down. As these could both be bipolar signals, shoving them into an adding unit (a simple mixer) won't work as you expect. Adding a minus value to a positive one is subtraction by another name so doing this will result in periodic signal cancellations and other unexpected behaviour.
If you recall your basic grade maths, you'll remember that a negative (minus) value multiplied by a positive always gives a negative result. So, if you want to combine bipolar control signals, use a negative scaling factor on one or more of your control-rate junction input scale factors!
Filters
Amongst some synth nerds, filters can acquire a mythical status, becoming objects to be worshipped or argued about into the small hours. This is rather off-putting for the rest of us and obscures the fact that, from a users point of view, they are actually rather simple devices.
There are only four things you need to know about a filter; its shape, its slope, its cutoff point and whether it is resonant.
The shape is usually what gives the filter its name. So it is a safe bet that a low pass filter will allow low frequencies through and exclude higher ones. Similarly, a high pass filter will do the opposite. A band pass will allow through frequencies that fall into a certain range and a band reject will allow everything through except frequencies in the defined range. Nothing mysterious about that.
The cutoff point is the frequency at which the filter will start to do its stuff. So a low pass with a cutoff point of 600Hz will start to attenuate anything over 600Hz but leave all the lower frequencies alone.
The slope of a filter simply determines how sharp the attenuation will be. It is sometimes expressed in dB per octave and sometimes in "poles". The famous Moog filter had a 4 pole slope which equates to a reduction of 24dB per octave. If the earlier example of a 600Hz lowpass cutoff was a 4 pole type it would mean that, by the time we got to frequencies of 1200 Hz they would be attenuated by 24dB compared to the ones at 600Hz. This is quite a steep reduction and would leave very little audible signal by the time we got beyond 1500Hz. Something more gentle, like a 2 pole slope would only attenuate frequencies by 12dB per octave. So you would hear more of the higher harmonics.
Filter resonance (sometimes called Q for reasons that don't matter) is also pretty straightforward. All this does is emphasize the frequencies around the cutoff point. It is a kind of feedback loop. The higher the Q the more pronounced are the sounds at the cutoff frequency. On some old analogue synths you could crank this up so high that the only thing you could hear was the cutoff frequency so the filter would start to behave like an oscillator. This was called self-resonance. It is not so easy to do in a digital system.
And that's filters really. If they were fix and forget devices they would be little more than glorified tone controls. But, if we can use envelopes or LFO's to change the cutoff frequency or resonance in a dynamic way, then they are the heart of a subtractive synthesis system. Hence all the attention they get.
Modulators Part 1 Slow and gentle
We've made passing reference to it before but it is now time to get into some detail about modulation. It is a huge topic because there are so many possibilities. The skillful use of modulation techniques is probably the single most important factor in getting dynamic, expressive, musical sounds out of a synthesizer.
We'll start with a definition. In synthesis, modulation is the process of using one signal to apply regular, usually cyclical change to one or more parameters of a second signal. Lets look at a simple practical example.
A violinist often gives expression to a piece by adding vibrato. When he or she waggles their finger on the fretboard the net result is that they are making small regular changes to the fundamental frequency of the note they are currently playing. We can do exactly the same thing with our instruments.
To create vibrato on a synthesized voice we simply apply small regular, cyclical changes to the oscillator frequency. We do that by routing the output of one, low frequency (i.e. slow) oscillator to the frequency controls of the main, audio oscillator.
The change this will make depends upon the properties of the signal sent from the low frequency oscillator (LFO). And, when we use a LFO as a controller of other parameters, some things that are not important to the sound of a waveform become very relevant indeed.
There are five aspects to a LFO waveform that are important to consider; the actual shape of the wave, its frequency and amplitude, its phase and its DC offset.
Frequency and amplitude are quite easy to come to terms with. The higher the frequency of the LFO the more changes per second will be made. Amplitude is an interesting one. In our violin example, sending a 100% amplitude sine wave from the LFO to the tone generator frequency control would not give us vibrato. It would give us the sonic equivalent of seasickness. You use the amplitude controls of an LFO to determine how much change is to be applied. For vibrato, very small amplitudes around 3% will do fine.
It is useful to be able to visualise the wave shape of an LFO. If we are generating a sawtooth wave at audio frequencies then the direction of the sloping part of the wave is irrelevant to the sound. A wave that has a slope to the left sounds the same as one with a slope to the right. However, if we want to use an LFO to make gradual change to one parameter, then fall down to the beginning and start again, we would not want to use a waveform with a left facing slope. Visualise it!
Phase and DC offset are related to some degree. Lets consider phase first.
In the vibrato example, for the main oscillator to remain in tune we need the LFO to start from the zero crossing point. If it started at any other place it would automatically add something to the main oscillator and cause it to sound out of tune.
There might be other occasions when we want the effect that comes with starting the LFO at somewhere other than zero. In those circumstances we would adjust the phase to suit our purpose. Again, the best advice is to try to visualise what you want to achieve, then program it accordingly.
Finally there is the DC offset for the LFO. To go back to our violinist (for the last time, honest!) a vibrato effect that shifts the fundamental pitch up and down by equal amounts is not very natural sounding. It actually sounds far more realistic if we push the frequency in one predominant direction. The way to do this with an LFO is to shift the DC offset.
Think about it like this. The LFO is sending numerical values out to be added to the frequency of the main oscillator. As a bipolar signal with no DC offset, half of these values will be positive and half will be negative. Changing the DC offset will shift this balance. If we only want the vibrato to work up from the fundamental we would need to shift the zero crossing point right down so that the LFO sent out only positive values.
This can be hard to visualise just by applying a numerical offset value so the Partikl application makes it very easy by giving you an option to set the ratio between positive and negative values transmitted by the LFO using two sliders. Nice!
There is a catch to doing this though. If you change the DC offset it will obviously have a non-zero value. Less obviously, if you sent this DC offset LFO to the pitch control of another oscillator you will automatically add the DC offset value to it, taking the oscillator out of tune! So, if you are shifting DC offsets in this way you need to retune the destination oscillator to compensate.
Exactly the same principles apply when using LFO to modulate parameters other than oscillator frequency. We've mentioned how the harmonics present in a pulse wave change depending upon the pulse width ratio. If you route a slow LFO to modulate the width of a pulse wave type oscillator you get a rich shimmering sort of sound as harmonics come and go that has been the basis for synth string patches since forever. It also gives some astonishing bass sounds in the lower registers. Pulse width modulation was actually hardwired into the infamous Moog Taurus bass pedals so beloved by `70's prog-rockers.
Incidentally, if you are using an LFO to modulate pulse width you will need to attend to its amplitude. Too much modulation and you can get to the stage where there are no harmonics at all - not even the first one! Silence is not always golden.
Modulation by slow, sub-audio oscillators is not too difficult to get to grips with. But there is no rule that says that modulators always have to be inaudible. However, what happens when you crank the modulator signal up into the audio range can get pretty wild. One option is to use a device called a Ring Modulator.
With this device you simply take two sound sources and plug 'em into it. In effect what happens after that is that the first audio signal gets spliced with other signal at the frequency of that second signal. What you end up with is a new signal that consists of the sum and the difference of the two incoming signals. Which is OK if the two are pure sine waves. But if they have harmonics attached...:)
At low modulator speeds a ring modulator just chops up the sound in quite an obvious way. This was how they made the Daleks speak! But at high modulator speeds you can get all manner of crazy, unpredictable effects, especially if the modulator frequency is either fixed or changes in a way not related to the carrier. If you want one of those "car crash in a steel foundry" moments (and who doesn't) head for the ring modulator.
As we are talking about high speed modulation it is probably worth mentioning something that isn't going to work in the way you might think. At this point we need to get a bit technical about the workings of Partikl. Remember what we said about distinguishing control signals from audio signals? Here's why you need to do it.
Partikl is a digital synth (obviously!) so everything going on under the hood has to have a sample rate to work to. In order to save resources for the things that matter, Partikl gives absolute priority to rendering the audio signal at a reasonable sample rate, typically 22Khz on a modest PC. To save CPU time, all control signals are rendered at a very low sample rate. The default rate is 100Hz..
In most circumstances, this low sample rate isn't an issue. You don't need to hear the actual output of an LFO or envelope unit so there is no point in rendering it at CD quality when we can do better things with the resources available. However, it does mean that you can't just stick the output of one tone generator into the frequency control input of another because the (incoming) modulating signal will be interpreted as being a control signal and so will be capped at the control signal sample rate frequency.
Going granular
Granular synthesis is a relative newcomer as a synthesis method, mainly because the tools and processing power needed to do it easily haven't been readily available until recent times. As powerful computers tended to be in academic institutions it gathered a reputation for being "something for the boffins". While the underlying maths might be the stuff of nightmares, the concept of granular synthesis is dead easy. Here goes.
If you take a very small section out of a waveform ( a few milliseconds at most), add an similarly small section of silence and loop play the result at audio frequencies you get an entirely new, and rather complex waveform. The audio content of this waveform will be determined by several different things; the size and content of the original mini sample (the grain), the length of the silence, the nature of the boundary between the two (is it abrupt or does it fade and by how much?) and the playback speed.
If you think about it, this is not a million miles away in principle from good old amplitude modulation. But then we take it to another level!
If you move away from using a single grain to using multiple grains, all with different frequencies, or if we modulate the grain size and/or the grain end crossfades it all gets very strange. You very soon start to generate mutated, wholly original sounds that are not easy to achieve by other means. Which is what the buzz about granular synthesis is all about.
Now we wouldn't be telling you all this if there wasn't a way to do it with Partikl. One of the modules available is a "particle generator" and mainstream this is not! What this module does is generate up to twenty little bits of simple waveforms which are then used as the grains in creating a more complex overall sound. You control a range of the more useful and interesting parameters, most of which can be modulated by other Partikl modules.
What comes out of the business end of this module is not always predictable. It is very easy to get it to generate complex, untuned warbling or twinkling sounds. With a little more effort you can make some breathtaking, animated, tuned soft lead sounds. As it is hard to describe the indescribable the best way to learn about this little beastie is simply to play with it. Think about it as a hands on introduction to chaos theory!
A quick word about hybrid synthesis
The use of "real world" sounds instead of tone generators as the starting point for sound synthesis is hardly a new concept. But it wasn't until the 1980's and the development of affordable digital recording technology that the full potential of this could begin to be realised. The ability to process and manipulate recorded sounds using the familiar shaping and modulating tools is a form of hybrid synthesis.
The simplest implementation of this can be seen in most samplers which basically slap a subtractive synthesis engine onto a digital sample playback device. You can do this with Partikl, no problem. And we will. Later.
But that is more than enough background for this tutorial. We can now take this knowledge forward with us and explore Partikl in more practical terms by starting to build our own instruments within Partikl.
