Waveforms: Add, Subtract & Multiply

ADDITION

What happens when we Add a Phase-Offset wave with the Original wave - See graphs on Left.

For SQUARE-waves, addition generates "stepped pulse-waves.

For SAW-waves, addition generates double saw-waves, which are similar to "Osc. Sync" function.

For TRIANGLE-waves, addition generates trapezoid-waves or "plateau waves".

If you have looked at delayed signals before, you may recognise these patterns. After all, a delayed signal is a waveform starting later (in time). Delayed signals are added to the original signal to create interference. You can read more about that at Chorus and Flangers.

Note: "Oscillator Sync" is where one detuned (slave) oscillator is forced to reset the wave in in sync with another (master) oscillator.

SUBTRACTION

What happens when we Subtract a Phase-Offset wave with the Original wave - See graphs on Right.

For SQUARE-waves, subtraction generates "stepped pulse-waves" (similar to addition).

For SAW-waves, subtraction generates a version of Pulse-waves (rectangle-waves). This is very useful.

For TRIANGLE-waves, subtraction generates trapezoid-waves or "plateau waves" (similar to addition).

The Subtractor synth for Propellerhead's Reason music software. For Reason users, it is their most used software synth and the default "go to" synth. Its heavy usage and huge availability of patches evolves from the fact that Subtractor is Reason's earliest synthesizer and that it is free of charge. To say it's popular would be arguable. To say it's endearing would be to exaggerate. It's free... so everybody has it... and uses it.

Apart from just Saw, Square & Tri, Subtractor has a total of 32 waveforms to choose from. The essence of waveform shaping is the "Mode" button (next to the Waveform selector):-

[x] multiply

[-] subtract

[0] none

This is used with the Phase knob... plus various modulation possibilities.

Beyond that, Subtractor also has options for FM (Frequency Modulation) and Ring Modulation.

Yes, this opens up a lot of sonic possibilities. But it is not obvious if you just want Pulse Width Modulation (PWM) -or- Saw-wave Sync. Both PWM & Sync have been staple sounds in electronic music since the Stone Age (Woodstock was 1969).

According to the Operation Manual, Subtractor is easily capable of PWM & Sync and much much more. All we have to do is to load some presets, twiddle a few knobs and use our ears. It's so simple. And yet, it's better if we have some guidance, ya?

- - Things To Note - -

[1] The PHASE Knob values of 0, 63, 127 are equivalent to 0°, 90°, 180° {see Test 1}.

[2] The LFO AMOUNT Knob values of 0, 63, 127 is equivalent to a Modulation Range of 0°, 90°, 180° {see Test 2}.

● So the LFO-1 "Amount" is the "actual Value" range (in our case, the Phase range). Example: If we set Phase = 70 & set LFO-1 Amount = 40, then the LFO will modulate the Phase between the values of 50 and 90 (total 40).

[3] The LFO(s) will modulate the Phase beyond the knob range. It can modulate from -270° to +270° {see Test 3}.

● So we can modulate below zero (0°, knob min.) and more than full (180°, knob max.).

- - Sound Design using Subtractor - -

Let's make some sounds using Subtractor.

a. Setting Up

b. Saw: Subtract - A generic Synth Strings using PWM with LFO

c. Saw: Subtract - A generic Synth Bass using PWM using Envelope

d. Exploring the other Subtraction Waves

e. Saw: Multiply - A generic Synth Brass using Osc.Sync

f. Exploring the other Multiplication Waves

g. Bonus Section

- - a. Setting Up - -

Initialisation - Resetting:

● Init Patch: Select "Reset Device"

● do Filter 1: Freq = 100%

● do Amp Envelope: S (Sustain) = 127 (full)

Our project:

○ We are using OSC-1 only.

Subtractor

Subtractor's PHASE knob and LFO AMOUNT knob equivalent

Test 1 : Phase knob output {non-essential reading}

Wave output of Subtract with Square-wave: with Phase knob 000= 0°, 063= 90°(25%), 127= 180°(50%)

Wave output of Multiply with Saw-wave: with Phase knob 000= 0°, 063= 90°(25%), 127= 180°(50%)

Test 2 : LFO Amount {non-essential reading} - as follows:-

○ LFO-1: Wave = SQUARE (for testing)

○ LFO-1: Amount = 127 (yes, full)

○ OSC-1: Phase = 63 (90°, the middle)

● Move the Phase knob from about 95 down to 63. With the Square LFO, you can hear one side going exactly silent (at zero) and the other side is Square wave. This means from Phase= 63, at full LFO Amount= 127, the LFO is modulating from Phase= 0 to Phase= 127.

Therefore, LFO-1 "Amount" is the "actual Value" range (in our case, the Phase range).

Test 3 : Range of Phase Modulation {non-essential reading}

...continuing from above, as follows:-

● Next, turn the Phase knob down to 62, 61, 60. You can hear the waveforms below zero coming out. Keep turning the knob downwards to hear more.

● If we set Phase= 0° with LFO Amount= 180°, the full LFO range would be from -270° to 90°. If we set Phase= 180° with LFO Amount= 180°, the full LFO range would be from 90° to 270°. Therefore, at these settings, Phase knob at 0% and at 100% would sound the same. Try it and they do sound the same!

Therefore, LFO-1 can modulate the Phase beyond the knob range modulating from -270° to +270°.

Early 80s polyphonic synth with one oscillator, PWM & one envelope generator.

- Selecting MODE

○ OSC-1 Mode = [x] multiply

○ OSC-1 Mode = [-] subtract

○ OSC-1 Mode = [0] none

- Selecting WAVES

○ OSC-1 Wave = Saw (ramp)

○ OSC-1 Wave = Square

○ OSC-1 Wave = Triangle

- For modulation using LFO

● LFO-1: Dest = Phase

● LFO-1: Wave = Tri (for normal use)

● LFO-1: Rate = 50 (just for now)

- For modulation using Envelope

● Mod Env: Dest = Phase

- - b. Saw: Subtract - A generic Synth Strings using PWM with LFO - -

Initialise patch as described above.

Saw: Subtract set-up

● OSC-1: Mode = [-] subtract

● OSC-1: Wave = Saw (ramp)

● LFO-1: Dest = Phase

● LFO-1: Wave = Tri

● LFO-1: Rate = 50

Turn the Phase knob and get familiar with the Pulse-wave sound. The Phase knob at zero (0°) is silent while knob at full (180°) is Square-wave.

● OSC-1: Phase = 127 (180°) for Square wave

You can choose between 2 variants of PWM Strings:-

Mild PWM: 70s PWM strings was a way for a single oscillator synths to sound like they had two oscillators (detuned). Typically, a larger LFO amount would use a slower LFO rate. When in doubt, use less LFO amount.

○ LFO-1: Amount = 42 to 84 {medium}

○ LFO-1: Rate = 30 to 60 {medium}

Big PWM: In the 80s, PWM became a standard feature, especially in single oscillator synths. PWM became its own sound & people were happy with a lot of it.

○ LFO-1: Amount = 127 {medium}

○ LFO-1: Rate = 20 to 50 {medium}

For the Filter, we're going for a "half Freq & half Envelope" style sound. Set both the same.

● Filter-1: Type= LP24, Freq= 25

● Filter Env: Amount= 25

Also set both the Filter Envelope & Amp Envelope the same. This is a medium-attack setting for strings. The decay & sustain are to have some small variation when holding chords for a long time.

● Filter Env: A= 40, D= 105, S= 100, R=50

● Amp Env: A= 40, D= 105, S= 100, R=50

Finish off with a tiny amount of Resonance and Vibrato.

● Filter-1: Res= 15

● LFO-2: Dest= Osc 1&2, Rate= 65, Amount= 5, Delay= 35

Save this generic String patch as we will use it later.

Note: Using Pulse= 127 and LFO Amount= 127, the LFO range is from 90° to 270°.

Additional Info: So far, we have used a Square-wave (180°) as the centre and modulating to the sides of it. At centre point 180°, we can use the maximum modulation Range. But you may want to use a different centre, example 120°. Just be aware that the timbre of points 0° and 180° are quite audibly obvious. As such, you might want to vastly reduce the modulation Range so as not to cross these points (You'd get a double-wobble effect).

- - c. Saw: Subtract - A generic Synth Bass using PWM using Envelope - -

Initialise patch as described above.

Saw: Subtract set-up

● OSC-1: Mode = [-] subtract

● OSC-1: Wave = Saw (ramp)

● LFO-1: Mod Env: Dest = Phase

Turn the Phase knob and get familiar with the Pulse-wave sound. The Phase knob at zero (0°) is silent while knob at full (180°) is Square-wave.

● OSC-1: Phase = 127 (180°) for Square wave

We will be emulating a one envelope monosynth sound so all 3 Envelopes (Mod, Filter & Amp) will have the same settings. The Env Decay will be the main modulator of Phase. Note that Env. Sustain has to be low so that the Decay has a good range to move across; but Sustain can't be zero or else the Amp Env just dies out too quickly. Let's use Sustain= 31 (a quarter). We'll do Decay last, so just set Decay at 63 for the moment.

● Mod Env: A= 0, D= 63, S= 31, R=31

● Filter Env: A= 0, D= 63, S= 31, R=31

● Amp Env: A= 0, D= 63, S= 31, R=31

For the Filter, let's use the "½ Freq & ½ Env" style sound. Set both the same at halfway.

● Filter-1: Type= LP24, Freq= 63

● Filter Env: Amount= 63

For Mod Env Amount (Gain), we want a wide range of modulation but, near the max. (0°), it sounds very thin. Let's go three-quarters.

● Mod Env: Amount (Gain)= 95

And now to set the Decay (for all 3 Envs). To me, the Decay is good between 45 and 60. Play around and see what you like. Let's use Decay= 55 to put it in the 80s league.

● Mod Env: D= 55 ● Filter Env: D= 55 ● Amp Env: D= 55

Finish off with some Vibrato.

● LFO-2: Dest= Osc 1&2, Rate= 70, Amount= 15, Delay= 30

Save this generic Bass patch as we will use it later.

Note: Using Pulse= 127 and Mod Env Amount= 95, the modulation sweep (Decay) is from 315° to 180°.

Roland Juno-60 front panel [source- WikiCommons]

These diagrams below show the waveforms for 0°, 45°, 90°, 135° & 180° {going anti-clockwise by convention}.

Saw-wave: Subtract emulates PWM

Early 80s monosynth with one oscillator, PWM & one envelope generator.

Roland SH-09 front panel [source- Pintrest]

- - e. Saw: Multiply - A generic Synth Brass using Osc.Sync - -

Let's look at the waveforms from Multiplication of Saw, Square and Tri.

Saw: Multiply set-up

● OSC-1: Mode = [x] multiply

● OSC-1: Wave = Saw

As mentioned before, the Saw: Multiply waveforms has similarities to Osc.Sync (Hard Sync). Typically, the Sync Oscillator is continuously being reset sync to the pitch frequency while itself would be having Pitch Mod Env applied using perhaps a 4-octave fast-dive to create a raw raspy rude sound. Subtractor was not designed with this in mind. Also, a normal Saw Sync starts off with a Saw wave, with it's rich timbre. We're starting with a U-shaped horn, which should be like a dog-tooth equivalent. We shall do our best with what we've got.

Load the generic Strings patch.

Change the OSC-1: Mode = [x] multiply -&- OSC-1: Wave= Saw.

Turn off the LFO-1 Amount and have a listen by rotating the Phase knob!

● LFO-1: Amount= 0 (off)

The ends with U-shape at Phase= 0 and W-shape at 127 sound pretty dull. But around Phase= 35 (±30), it's very rich with a brassy quality. Let's make some synth brass {BTW this is not a typical brass}.

● OSC-1: Phase= 35

Next, we make a slow Filter Envelope to make it brassy which we'll apply to the Phase as well as Filter.

● Mod Env: Dest= Phase

● Mod Env: A= 63, D= 73, S= 0, R=50

● Mod Env: Amount= 60

● Filter Env: A= 63, D= 73, S= 0, R=50

● Filter-1: Freq= 41

Finish off with some of that Phase wobble but after the brassy envelope (use LFO-2's delay).

● LFO-2: Dest= Phase

● LFO-2: Rate= 60

● LFO-2: Amount= 60

● LFO-2: Delay= 35

Part 2:-

Load the generic Bass patch. Change the OSC-1: Mode = [x] multiply -&- OSC-1: Wave= Saw.

That sounds pretty good! A bit raspy bright but okay with me.

Saw-wave: Multiply

Late 70s polyphonic synthesizer with Oscillator Sync

SCI Prophet 5 front panel [source- Great Synthesizers]