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: