'Is there a certain call you've heard the dads use to calm startled chicks?'
To calm the chicks? Not that I've noticed. But to assure 'lost' chicks that 'I'm here'? Indeed yes. It's the basic grunt.
And if you sit patiently, you'll hear regular 'conversations,' and very often the meanings of these are, from context, crystal clear. The model you're asking about goes like this:
'Dad Plus' moves as a unit. The age of the chicks dictates how far from Dad they will wander. Now, if food is involved -- 'OMG I'm missing out!!' -- the chicks will vocalise piteously. (And they all vocalise as they eat, which is a mystery . . . ) Otherwise they tend to silence.
But what will happen is that a chick investigating something -- the fig tree or the grape bush -- will get a bit left behind. It will then cheep in distress, and six or eight cheeps later, Dad will grunt, to re-establish communication.
And overall:
there is a range of vocalisations. I don't understand them all, but a good few. Context is the all. That is, chicks and Dad talk -- unless there's danger, in which case they are deathly still and quiet as they listen.
Breeding-pairs talk. Mobs on the move talk. But small groups grazing do not. A bird or birds reconnoitring an occupied pasture will vocalise as a form of psyops. Females vocalise 'territorially' at night. Sometimes they talk to males at night. (This is most unusual though.)
And conflicts involve vocalisations.
SE