Gradual-ramp-up-volume greeting
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Refers to a non-startling strategy employed whenever you are unable to unobtrusively get someones attention or make eye-contact with him for whatever reason (maybe hes 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.
Gradual-ramp-up-volume greeting meaning & definition 1 of Gradual-ramp-up-volume greeting.