There was a channel six in providence ri, but that was back in the analog days. I don't know what it is now.
Many of them now only map to the channel location they were originally at. The reason is that before the shutdown of full power analog, most channels had to have two locations. They had one for their analog channel and one for their digital channel, which then virtually mapped down to their "actual" channel location. In many cases, these channels just simply stayed once full powered analog was shut down.
What is broadcasting on 87.75 FM through an analog channel 6 on television are essentially Low Powered television stations, which weren't forced to transition digital at the same time as full power television channels. Originally, Low Power was to convert to digital in 2015, which was extended indefinitely due to "economic hardships". The new date set for the conversion is now in 2021. Again, if I'm correct, anything broadcasting digitally on channel 6 will not repeat over 87.75 FM. Therefore, it is safe to presume that it is not in a company's best interest to start a new Low Powered analog television station on channel 6, especially for the purpose of having a radio station on 87.7 FM. In about 2.5 to 3 years time, you'll have to convert your television station to digital and won't be able to broadcast on 87.7 after.
Again, for the MeTV station in Chicago, that station had been broadcasting for years. It was initially a TV station, but after moving to channel 6, began to operate as a radio station. It ran formats including smooth jazz, country, alternative, and Sports Talk before being MeTV FM.
My interest began when it was an alternative station, as I had a theory that corporate radio was systematically killing anything rock and alternative. That was before the rejuvenation of the alternative format. Q101 Chicago was sold, became internet only, and the frequency 101.1 FM became FM News. Later, channel 6 became Q87.7 when Cumulus entered a LMA to run the station. Eventually, it moved back to 101.1 after FM News and a follow-up format flopped, and channel 6 became a short lived sports talk station. Therefore, MeTV FM is fairly new, but the operation at channel 6 is over a decade old.
I don't see any new operations starting for the fore mentioned reasons, and still think it's safe me to use my transmitter on 87.9 in my area, as nothing will begin operating on 87.7. Also, if it was to become that I was wrong, my retort to any complaints that I was causing interference would be that essentially, anyone broadcasting on 87.7, is not running a radio station. They are running a TV station that happens to broadcast on a frequency that can be picked up on 87.7 FM. The FCC doesn't license 87.7 FM. They licence channel 6 on TV. So, they wouldn't have any defense in my opinion, as my transmitter isn't interfering with channel 6.