Posted Jan. 23, 2006, 1:03 p.m.
Noise is all around us. But what is it? Some people might find the scream of an internal combustion engine revving at 19,000 rpm to be a deafening noise, but it is like music to a fan of Formula 1 motor racing. Conversely, much of modern dance music is an incomprehensible noise to anybody over 50 years old, and my mother thought that even Mahler's symphonies were a horrible noise. In all of these cases, the word "noise" is simply being used to mean "a disliked sound", but in synthesis it has a much more precise set of meanings.
What is noise?
All electronically produced sounds are subject to noise. In the audio world, a simple view of a cyclic waveform might suggest that its peak amplitudes are +1 and –1 on some arbitrary scale, but the moment that you turn the perfect representation into something tangible, the thermal noise in the electronics adds or subtracts a small amount from the signal at every point in time. This means that the peaks may lie at 1.0003, or -1.0001, or +0.9992 or -0.9985, or whatever. What's more, every point between the peak values will also be subject to a small deviation from the ideal.
If these deviations are in some way systematic – say, caused by the superimposition of some form of a hum or buzz – you will hear a sound defined by each of the components, and the result will not be noise because it is not random. But if the deviations are truly random, you will hear broadband (i.e. covering a range of frequencies) noise which, on a simple level, can be described as the adding or subtracting of a random amplitude from the ideal signal at every frequency and at every point in time.
There are many sounds that you can consider to be valid examples of this type of signal, but they can be very different from one another. For example, the noise of tape hiss is very different from the noise generated by cheap air conditioning units, and both of these are very different from the sound of a truck rumbling down the street just outside your studio. So, what – apart from their loudness – is the principle difference between these signals? The answer is that they contain different amounts of noise at different frequencies. Tape hiss seems to contain predominantly higher frequencies, while the truck seems to generate predominantly lower frequencies, which we call rumble. Consequently, we must define broadband noise not only by its loudness, but also by the relative amounts of signal present at each of the frequencies in the audio spectrum.
The colour of noise
Because noise is random, we cannot say that a given frequency is present at any given moment or, if it is, at what power. We can only say that there is a probability of this frequency being present at that power at any given moment. If we then make this statement for every possible frequency, we create something called a power spectral density ("PSD").
If the PSD is constant across the audio spectrum, we can say that "averaged over a reasonable period, the amplitude of the noise at any frequency will be equal to a constant value". We call the resulting signal white noise because, when our eyes encounter visible light with all the frequencies present in equal amounts, it looks white to us.
You might think that, because all the frequencies in white noise are present in equal amounts, we would hear this noise as neutral, spread evenly across the whole audio spectrum. However, this proves not to be the case. Our ears and brain are such that, when presented with white noise, the higher frequencies seem to dominate, and we hear something that sounds predominantly hissy.
A PSD that sounds less ‘coloured' to the human ear is one in which the upper frequencies contain less power that the lower frequencies. If we define the PSD of the noise such that the power is inversely proportional to the frequency, we have described a type of broadband noise that rolls off at approximately 3dB/octave across the audible spectrum. This means that, instead of obtaining equal powers in bands of constant width, the noise has equal power per octave. This complements the response of the human ear in such a way that the noise now sounds evenly distributed. Extending the previously analogy with visible light, this PSD would look pink so, in the audio world, we refer to this noise as pink noise.
White and pink noise are not the only power spectral density functions, and other types of noise are also important, not just in audio, but in fields such as communications theory, image processing, and even chaos theory. If the noise rolls off inversely to the square of the frequency (which is what you obtain if you apply a 6dB/octave low-pass filter to white noise) you obtain red noise, so-called because light with this distribution would look red.
Alternatively, you could have a spectrum in which the noise power increases rather than decreases with frequency. The power spectral density of so-called blue noise is proportional – rather than inversely proportional – to the frequency, and the noise power increases by +3dB/octave. Likewise, the PSD of violet noise increases according to the square of the frequency (i.e. at 6dB/octave).
If the concepts presented here are a bit daunting, don't worry about it. I have shown all five of these noise types in figure 1, which should help to make everything clearer.
Figure 1: Types of noise
More types of noise
There are many types of noise that do not conform to this description of broadband noise. For example, some audio exhibits artefacts such as clicks and crackle. Clicks are individual impulses whose durations, in the digital domain, can vary from single samples to tens or even hundreds of samples. Crackle is generated by a high density of smaller impulses distributed randomly in time. (If these small impulses are regularly spaced, you hear a buzz rather than crackle, but we need not worry about that, here.) So... can we call clicks and crackle "noise"? Of course we can; they are simply forms of impulsive noise rather than broadband noise.
Now, having classified these sounds as noise, and having defined some of the colours of broadband noise in a mathematical sense, I have to confuse the issue further because there are many signals that – in isolation – may be considered to be noise, but which are nonetheless important and wanted components in musical sounds. The most obvious examples of this are percussion instruments. Their sounds are based in very large part on impulses plus shaped broadband noise yet, played appropriately, they sound musical rather than noisy. Even instruments that generate primarily harmonic sounds generate signals that are "noisy". Examples include the breathiness of a flute or panpipe, the plucking sound of a guitar, the hammer noise of a piano, the sibilants of human voices... and many, many more. These are all noise, and yet they are also hugely important part of the genuine sounds, and therefore an important part of synthesis.
Yet another type of noise: Tuned broadband noise
So far, I have only discussed noise as contained within or superimposed upon a wanted signal. But ask yourself what happens when the noise is generated when there would otherwise be silence. The answer, of course, is that the noise is the totality of the signal. In other words, the sound you hear is only noise, and most synthesisers offer a means to generate broadband noise in isolation, at the same level as the cyclic waveforms that form the basis of harmonic sounds.
Imagine that you have a white noise generator on your synthesiser, and that you filter it in some fashion. I have already explained that, if you apply a 3dB/oct low-pass filter you will obtain pink noise, and a 6dB/oct LPF will give you red noise, so it's simple to extrapolate that the common 12dB/oct and 24dB/oct LPFs will create what we might call "infra-red" noise spectra. Conversely, if you apply 3dB/oct high-pass filtering to the white noise signal you will obtain blue noise, a 6dB/oct HPF will create violet noise and – by extension –steeper HPFs will create various forms of "ultra-violet" spectra. In the next tutorial, I'll demonstrate how you can use these types of noise to generate a range of sounds but, before that, I want to ask what you'll obtain if you apply band-pass filtering...
As figure 2 shows, you can constrain the bandwidth of white noise more and more tightly until, at the extreme, only a tiny band of frequencies can pass, and at this point the sound becomes less like noise and more like a somewhat "noisy" oscillator. The sound thus produced has a unique character that can form the basis for many of the so-called "spectral" patches that became popular after the launch of the Roland D50. Happily, Thor is more than capable of recreating these, as I will now show...
Figure 2: Filtering noise to create tones
Figure 3 shows Thor's Noise Oscillator, with its band-pass option ("BAND") selected, and the noise parameter knob (the one in the lower right-hand corner) turned to its maximum value, which causes the oscillator to produce an approximation to white noise.
Figure 3: Thor's Noise Oscillator in BAND mode
If you invoke the starting patch from previous tutorials and insert the noise oscillator into the oscillator 1 slot, you will obtain the patch shown in figure 4. Set it up as shown, with KYBD=127, Oct=5, Semi=0, and Tune=0. If you now press any key, you will hear white noise. Furthermore, this sound is invariant no matter where you play on the keyboard. If you think about it, this is correct... if there is no tonal content or variation in the noise spectrum, the very definition of the sound precludes you from hearing higher or lower notes.
(In truth, there is some variation to the character of the noise in Thor's noise oscillator, and you will hear that it becomes ‘grainy' when you play low notes. This is a consequence of the coding within Thor, and not something that you would hear in a mathematically perfect "noisy" world.)
Figure 4: A simple white noise patch
If you now listen to sounds #1 , #2 and #3 , you can hear how this patch sounds. This is the same note played firstly with the noise parameter at 127 (white noise), secondly with it set to 64 (band limited noise), and thirdly with it set to zero (tightly tuned noise).
I'm now going to create a simple envelope to soften the effect of sound #3, with an Attack of approximately 0.5s, and a release of around 2s. Since I find the fully tuned sound in #3 a little too pure, I am also going to broaden the spectrum a touch by increasing the noise parameter value to 6. This results in a haunting sound that lies somewhere between the sound of a blown bottle, a finger rubbed around the rim of a wineglass, and a siren (the mythological and rather alluring Greek female, not the klaxon that you find on top of a police car). To turn this patch into something that sounds like it may have come from a D50, I need only add reverb. To demonstrate this, I selected the RV7000 Advanced Reverb module within Reason and loaded the factory preset "EFX Scary Verb", and then played a simple chord sequence to create sound #4 :
Figure 5: "Bottled Sirens"
I love this sound, but it lacks the depth that I want today, so I'm now going to add a second oscillator, set up in exactly the same way, but tuned an octave lower than the first. (See figure 5.) If I now play the same chords, I obtain sound #5:
You have to admit, this is a pretty amazing sound given that there no filters involved, no LFOs, no modulation of any other sort, no chorus, no delay, the simplest of AR envelopes, and just reverb that adds ambience to the output from Thor itself. What's more, you can't easily obtain this type of sound in any other way.
Finally, to demonstrate how powerful tuned noise can be as a generator of superb synthesised sounds, I added a single module within Thor to the patch in figure 5, and then recorded sound #6 :
However, I'm not going to tell you what that module was. Can you work it out? Answers on a postcard...
Text & Music by Gordon Reid