gradual-ramp-up-volume greeting 

Refers to a non-startling strategy employed whenever you are unable to unobtrusively get someone's attention or make eye-contact with him for whatever reason (maybe he's deep in a book, concentrating hard on a household/carpentry task, or using noisy equipment, and thus he does not look up/around occasionally or hear/observe your presence) and so you start out to say hello by speaking very quietly, and then cautiously raising your voice little-by-little (like some modern-day alarm-clocks do so as to wake you "gently" instead of startling you out of a sound slumber with a full-blast ringer right away) till the previously-oblivious person eventually becomes aware of your proximity and glances up.

I'd wanted to ask my elderly neighbor about my possibly carpooling with him on his grocery-shopping trip the next day, but he was so busy using his riding lawnmower that he never noticed me despite my circling around in front of him several times, so I eventually used the gradual-ramp-up-volume greeting to finally get his attention.

gradual-ramp-up-volume greeting by QuacksO August 22, 2018