# Subtractive Synthesis

This is the second in a series of articles on how to use Sonic Pi for sound design. Last month we looked at additive synthesis which we discovered was the simple act of playing multiple sounds at the same time to make a new combined sound. For example we could combine different sounding synths or even the same synth at different pitches to build a new complex sound from simple ingredients. This month we’ll look at a new technique commonly called subtractive synthesis which is simply the act of taking an existing complex sound and removing parts of it to create something new. This is a technique which is commonly associated with the sound of analog synthesisers of the 1960s and 1970s but also with the recent renaissance of modular analog synths through popular standards such as Eurorack.

Despite this sounding like a particularly complicated and advanced technique, Sonic Pi makes it surprisingly simple and easy - so let’s dive right in.

## Complex Source Signal

For a sound to work well with subtractive synthesis, it typically needs to be fairly rich and interesting. This doesn’t mean we need something hugely complex - in fact, just a standard `:square` or `:saw` wave will do:

    synth :saw, note: :e2, release: 4

Notice that this sound is already pretty interesting and contains many different frequencies above `:e2` (the second E on a piano) which add to create the timbre. If that didn’t make much sense to you, try comparing it with the `:beep`:

    synth :beep, note: :e2, release: 4

As the `:beep` synth is just a sine wave, you’ll hear a much purer tone and only at `:e2` and none of the high crispy/buzzy sounds which you heard in the `:saw`. It’s this buzziness and variation from a pure sine wave that we can play with when we use subtractive synthesis.

## Filters

Once we have our raw source signal, the next step is to pass it through a filter of some kind which will modify the sound by removing or reducing parts of it. One of the most common filters used for subtractive synthesis is something called a low pass filter. This will allow all the low parts of the sound through but will reduce or remove the higher parts. Sonic Pi has a powerful yet simple to use FX system that includes a low pass filter, called `:lpf`. Let’s play with it:

    with_fx :lpf, cutoff: 100 do
      synth :saw, note: :e2, release: 4
    end

If you listen carefully you’ll hear how some of that buzziness and crispiness has been removed. In fact, all the frequencies in the sound above note `100` have been reduced or removed and only the ones below are still present in the sound. Try changing that `cutoff:` point to lower notes, say `70` and then `50` and compare the sounds.

Of course, the `:lpf` isn’t the only filter you can use to manipulate the source signal. Another important FX is the high pass filter referred to as `:hpf` in Sonic Pi. This does the opposite to `:lpf` in that it lets the high parts of the sound through and cuts off the low parts.

    with_fx :hpf, cutoff: 90 do
      synth :saw, note: :e2, release: 4
    end

Notice how this sounds much more buzzy and raspy now that all the low frequency sounds have been removed. Play around with the cutoff value - notice how lower values let more of the original bass parts of the source signal through and higher values sound increasingly tinny and quiet.

## Low Pass Filter

The low pass filter is such an important part of every subtractive synthesis toolkit that it’s worth taking a deeper look at how it works. This diagram shows the same sound wave (the `:prophet` synth) with varying amounts of filtering. At the top, section A shows the audio wave with no filtering. Notice how the wave form is very pointy and contains lots of sharp edges. It is these hard, sharp angles that produce the high crispy/buzzy parts of the sound. Section B shows the low pass filter in action - notice how it is less pointy and more rounded than the wave form above. This means that the sound will have fewer high frequencies giving it a more mellow rounded feel. Section C shows the low pass filter with a fairly low cutoff value - this means that even more of the high frequencies have been removed from the signal resulting in an even softer, rounder wave form. Finally, notice how the size of the wave form, which represents the amplitude, decreases as we move from A to C. Subtractive synthesis works by removing parts of the signal which means that the overall amplitude is reduced as the amount of filtering that is taking place increases.

## Filter Modulation

So far we’ve just produced fairly static sounds. In other words, the sound doesn’t change in any way for the entirety of its duration. Often you might want some movement in the sound to give the timbre some life. One way to achieve this is via filter modulation - changing the filter’s options through time. Luckily Sonic Pi gives you powerful tools to manipulate an FX’s opts through time. For example, you can set a slide time to each modulatable opt to specify how long it should take for the current value to linearly slide to the target value:

    with_fx :lpf, cutoff: 50 do |fx|
      control fx, cutoff_slide: 3, cutoff: 130
      synth :prophet, note: :e2, sustain: 3.5
    end

Let’s take a quick look at what’s going on here. Firstly we start an `:lpf` FX block as normal with an initial `cutoff:` of a low `50`. However, the first line also finishes with the strange `|fx|` at the end. This is an optional part of the `with_fx` syntax which allows you to directly name and control the running FX synth. Line 2 does exactly this and controls the FX to set the `cutoff_slide:` opt to 3 and the new target `cutoff:` to be `130`. The FX will now start sliding the `cutoff:` opt’s value from `50` to `130` over a period of 3 beats. Finally we also trigger a source signal synth so we can hear the effect of the modulated low pass filter.

## Bringing it all together

This is just a very basic taster of what’s possible when you use filters to modify and change a source sound. Try playing with Sonic Pi’s many built-in FX to see what crazy sounds you can design. If your sound feels too static, remember you can start modulating the options to create some movement.

Let’s finish by designing a function which will play a new sound created with subtractive synthesis. See if you can figure out what’s going on here - and for the advanced Sonic Pi readers out there - see if you can work out why I wrapped everything inside a call to `at` (please send answers to @samaaron on Twitter).

    define :subt_synth do |note, sus|
      at do
        with_fx :lpf, cutoff: 40, amp: 2 do |fx|
          control fx, cutoff_slide: 6, cutoff: 100
          synth :prophet, note: note, sustain: sus
        end
        with_fx :hpf, cutoff_slide: 0.01 do |fx|
          synth :dsaw, note: note + 12, sustain: sus
          (sus * 8).times do
            control fx, cutoff: rrand(70, 110)
            sleep 0.125
          end
        end
      end
    end
    subt_synth :e1, 8
    sleep 8
    subt_synth :e1 - 4, 8