For the past two weeks I’ve been part of the less-than-1% — the ranks of Americans who live in areas where local TV stations can’t be picked up no matter how much Dad fiddles with the digital antenna on the roof. For these viewers, the concept of free over-the-air TV has gone the way of the horse and buggy.

A little background: My husband and I recently bought a summer place near beautiful Lake Chautauqua in western New York state. Since we’ll be there only for limited stays, we decided that it made no sense to pay for cable or Internet service.

I confidently predicted that we’d have fun surfing the local broadcast fare, and we’d still keep up with our summer reality faves “Hell’s Kitchen” and “MasterChef” through the Fox affil in Buffalo. But as Gordon Ramsay would shout — wrong!

We got nothing after we unpacked our new digital TV set and scanned for local signals. Our broadcast black hole was confirmed by a search (via smartphone, our only Internet access) on AntennaWeb.org, the website sponsored by the Consumer Electronics Assn. and the National Assn. of Broadcasters to help viewers determine the optimum digital antenna for their geographic location, right down to the street address.

AntennaWeb’s verdict was harsh: “Due to factors such as terrain and distance to broadcasting towers, signal strength calculations have predicted no television stations may be reliably received at this location.”

It seemed downright unconstitutional. Although more than 90% of households pay for subscription TV service these days, we still prize the safety net of being able to pull the Big Four out of the air for free if all else fails.

The area wasn’t always so barren, our neighbors confirmed. Before the transition from analog to all-digital broadcasting took effect in June 2009, rooftop antennas would bring in stations from Buffalo (about 60 miles away) and Erie, Pa. (about 30 miles in the other direction).The picture quality could be hit and miss, depending on the weather, but you could get something. The agriculture-rich region is dotted by gently rolling hills, not the kind of peaks you’d expect to smack down an HDTV signal.

But with digital broadcasting, it’s all or nothing — you either latch on to a signal or you get that infernal blue screen. And that means plenty of people in Chautauqua County have no choice but to pay for cable or satellite service if they want any TV at all. It all adds up to a gift to Time Warner Cable (the local provider), satcasters DirecTV and Dish Network. (AT&T’s U-Verse and Verizon’s Fios aren’t available in the area yet.)

The over-the-air blackout phenomenon isn’t exclusive to one bucolic pocket of the Empire State. Hard numbers are hard to come by, but the FCC acknowledges that a small percentage of U.S. TV households got the short end of the stick in the digital transition.

While the vast majority of the nation’s nearly 1,800 full-power TV stations increased their overall coverage area by flipping the switch to digital, there were at least 401 stations, by the FCC’s count, that lost the ability to reach at least 2% of homes they had previously covered.

Most of those stations (including the major Buffalo outlets) still wound up gaining greater reach in other areas of their markets than they lost on the fringes. Until stations serving far-flung areas invest in signal-amplifying services — and until advertisers demand they do so — there will be clusters of digital TV left-behinds scattered around the country. That helps explain why the level of TV penetration has actually dropped, to 96.7% of U.S. households in 2012 from 98.9% in 2011, per Nielsen.

For my family, the happy upshot of a fortnight with no TV and limited Internet access was more time spent with books (finally, I’ve plunged into Thackeray’s “Vanity Fair”), playing Scrabble and getting to know our seasonal neighbors. As if to add contrast to our 21st century media dilemma, the local color is enhanced by the sizable number of Amish families who still clop-clop-clop around town in their horse-drawn buggies.