Katrina and the Waveforms

So we’ve mentioned in some detail a number of waveforms commonly found in oscillators. I’m going to concentrate on five: sine, triangle, pulse, sawtooth and noise. Let’s start with the sine wave.

This is the most basic waveform available to us – it’s just a single frequency with no overtones or harmonics. Overtones are frequencies which appear above the fundamental (the note you play, or the lowest loudest note); harmonics are integer multiples of that fundamental, though we’ll cover this in another article.

I’m going to be using Voxengo SPAN, which is a great free spectral analyser, to monitor overtones. In addition I’m going to use an oscilloscope called s(M)exoscope (which is sadly 32-bit only) but is also a free download.

Here’s what our sine wave looks like:

A simple curved waveform which you might recognise from maths or physics (if you remember anything at all from them, of which I remember very little). Great for sub bass, g-funk style leads and pseudo-organ pads.

Notice it’s just a single frequency with no harmonics or overtones above it. The note I’m playing is A at 110 Hz. Hz is cycles per second, so a cycle will be completed one hundred and ten times per second to sound that pitch.

Let’s have a look at the triangle wave:

As the name suggests, a triangle shaped waveform. Great for bass and leads as it’s a bit rougher than a sine. Can sound a bit computer-gamey to some.

I’m playing the same note as in the first examples but we can see other frequencies above the 110 Hz. In-fact we can see 330 Hz, 550 Hz, 770 Hz, 990 Hz etc. Triangle waves contain the odd harmonics (remember harmonics are integer multiples of the fundamental).

Let’s move on to our pulse:

A pulse wave can be square (as above); this has a ratio of positive:negative of 50:50 and adjusting the balance of this is known as pulse-width modulation (PWM). Great for basses at more symmetrical values; the more the width is offset, the thinner the sound becomes.

Adjusting the balance a little:

Adjusting the balance further still:

You might notice that this has the same overtones present as the triangle (though we can see the ones in the upper frequencies more clearly), the only difference being that these are a lot louder: the second harmonic (330 Hz) is almost the same volume as the fundamental, and the third (550 Hz) nearly as loud again, and so on.

Next we’ll look at our sawtooth:

Imaginatively named as it looks like the teeth of a saw. Good for rich pads, lead lines, distorted DnB basses.

This contains all of the harmonics, i.e 110, 220, 330, 440, 550, 660 etc This is what makes the sawtooth good for richer, more complex patches.

Finally, let’s have a look at the noise waveform:

A very complex looking waveform, as close to random as a computer can handle. White noise is every frequency at equal amplitude (as we can see from SPAN below this isn’t the case, so this is likely to be blue noise). This makes it useful for synthesising hi-hats, snares and risers or transitional effects in dance music. It can also be a useful layer in a bass or pad patch to dirty it up a bit.

Filters

The next stage of our subtractive synth is the filter. I’m going to explain the basics of low-pass, high-pass and band-pass filters, but be aware there are other types such as notch, comb, formant etc. Most subtractives have at least a low-pass filter.

Low-pass filters work by only allowing frequencies below the filter cutoff to pass through. I’m going to use the Novation BassStation plug-in for our source sound, which will be a sawtooth. Here’s the unfiltered sound:

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Here’s what the SPAN looks like (I’ve changed the colour to white so we can overlay the filtered sound on top afterwards):

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I’m using Live’s Auto Filter for this demonstration, but really any multi-mode filter will do. I’ve brought our low-pass filter down to 1.5 kHz – have a look at the frequencies we’re left with (which will be coloured red):

lp_1.png

As we can see (and hear), frequencies above the cutoff become attenuated. The amount of attenuation is defined by our slope, typically measured in dB/octave (6, 12, 24, 32). The higher the dB/oct, the stronger the filter will sound. Now I’m going to drop the filter down to 250 Hz:

lp_2.png

Again, we can see the red (filter sounded) super-imposed over the white (original sound). Although we are hearing frequencies as high as 600 Hz they will be very quiet, and it’s that response that gives this particular filter it’s characteristic sound. Before moving on to high-pass filters, I’m going to increase the resonance to maximum and move the cutoff to 400 Hz:

LP3.png

The resonant point is now louder that our fundamental, giving the synth a new tone. Hear the cutoff being swept with this resonance value? This is what’s called self-oscillation, where the resonance is so high our ear perceives it as a new tone:

Now let’s look at a high-pass filter with the same source sound and staying with 400 Hz:

hp1.jpg

Now, only frequencies above the cutoff are allowed to pass. One more example before moving on, this time at 2 kHz:

hp2.jpg

High-pass filters are obviously not a great idea to use on bass sounds but work nicely on pads or leads as filtering out the bottom end clears space for other instruments. High-pass filters (also known as low-cut) are a key ingredient to EQing a good mix, too.

A band-pass filter is like a high-pass glued to a low-pass, isolating a frequency spectrum in the middle of the sound. Here’s a band-pass filter at 300 Hz:

bp1.jpg

And here’s one being swept from 100 Hz right up to 14 kHz. At lower frequencies it could be mistaken for a low-pass filter and right at the top we’re left with just the upper frequencies of our sound:

With these waveforms and filter types we can do most anything, though having them static or manually affecting them could be tedious. Envelopes and LFOs are built in modulation sources that can do some of the work for us. Let’s first look at LFOs.

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