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Hard sync in it's simplest terms: The phase of one oscillator is synchronized to the phase of another oscillator. The wave "resets" to zero every time it receives a pulse from another oscillator. At audio rates we perceive this resetting as harmonic content.

You'll recognize this synth sound from really bad early 00s "hardstyle" kind of like that famous track "zombie nation."

We're going to listen to just the saw output of the DPO. The first channel of DPO is prewired to sync to the second channel of DPO.

Push the black button under channel 1 twice until a little purple light that says "sync" is lit.

Ch. 1 of maths is configured as an LFO because the cycle button is lit. We plug it into the EXPO input of ch. 1 and
now the rising and falling of maths is controlling the pitch of the first oscillator.

Ch. 2 of DPO is the "root" or "tonic" note that we hear - it's the pitch that is constantly being emitted. Ch. 1 is now the control for Timbre in this patch.

Ch. 2 is resetting the phase of Ch. 1, so think of it as sort of superimposing itself onto Ch. 1.

Hard & Soft Sync explained:

EDITED Jul 17th 2016, 00:07

We going to listen to just the Final output of the DPO. The final output of the DPO takes the second oscillator and feeds it through what is known as a waveshaper. Our closest relation to waveshaping outside of the modular environment would be distortion/overdrive/fuzz. A waveshaper does exactly what it sounds like it does: it reshapes the wave from a simple waveform into a more complex shape.

On the DPO we have three controls over our wave shape:
1. FOLD: the number of folds the wave makes back onto itself. We percieve this as volume + distortion.
2. SHAPE: the shape the new waveform becomes. There are three little images next to the shape knob that show you what the incoming sine wave gets morphed into.
3. ANGLE: the angle the new waveform is slanted at.

Maths is configured as two LFOs in this patch. Ch. 1 is controlling the shape of the final output and Ch. 2 is controlling the angle of the final output.

DPO Final output (fast forward to 0:38):

Waveshaping explained:

A saw wave is fed into a filter which then goes into an amplifier. The saw wave is the pitch of the sound, the filter the timbre of the sound, and the amplifier the volume of the sound.

Both the timbre and volume are being controlled by Maths. Ch. 1 of maths when looping is making the filter open and close giving us the feeling that the sound is "going underwater" or "getting muffled."

Ch. 2 of maths when looping is making the volume of the sound open and close giving us the feeling that the sound is "fading in and out" or "pinging" based on the rise and fall settings.

Treat maths like two LFOs in this patch.

Subtractive synthesis explained:

Use Maths ch. 2 to adjust speed and envelope of FM voice. As the voltage rises and falls, the volume of DPO oscillator two adjusts accordingly. Changing the pitch of both oscillators causes timbral & harmonic shifts in the signal.

DPO Oscillator 1 is modulator

DPO Oscillator 2 is carrier

DPO is already hardwired so that Oscillator 1 is already patched into Oscillator 2 and vice versa.

FM explained:
http://www.innovativesynthesis.com/fm-synthesis-made-easy/

AM explained:
https://www.keithmcmillen.com/blog/simple-synthesis-part-9-amplitude-modulation/

DPO Explained:

Maths explained:

FM/AM explained:

EDITED Jul 16th 2016, 23:29