Hello and welcome!
It looks like you have a lot of translator stations to your east. Do you know what network is being carried on each one?
The reason I ask is because all of your nearby channels come from three directions. Most of them are at compass heading 77 degrees (just east of Medford), and a few are coming from compass heading 317 degrees (King Mountain). There is one other "stray" channel at compass heading 126 degrees (Mt. Ashland).
The transmitters on King Mountain include KOBI, KSYS, and KDRV, which are NBC, PBS, and ABC affiliates, respectively. The transmitter on Mt. Ashland is KTVL, a CBS affiliate.
If the content of KOBI, KSYS, KDRV, and KTVL is already being re-broadcast on the translator stations out of Medford, then all you need to do is go after the Medford stations. This would make life simple since these stations are pretty strong and all coming from the same direction. You should be able to get by with a smaller antenna.
If some of the stations you want are missing from the set of translators, then you'll need to either get a second antenna to fetch the off-axis station(s), or install an antenna rotator to point your antenna to the other directions. Since these other stations are on VHF and further away, you will either need to add a somewhat large VHF-only antenna (if joining two antennas) or get a combo antenna that has a fairly large VHF section on it (if using a rotator).
Having said all that, here are three possible setups, depending on what channels you need to get:
1) If all you need are the Medford translators, then get a Winegard HD7695P on your roof pointing at compass heading 77 degrees.
2) If you need the Medford stations and ONE of the other transmitter groups (King Mountain or Mt. Ashford, but not both), then get two antennas. Get a UHF-only antenna like the Channel Master 4221HD pointing at compass heading 77. Get a VHF-only antenna pointed at the other channel group you want (compass heading 317 or 126 degrees). Join the two antenna feeds using a diplexer like the Pico Macom UVSJ (do not just use an ordinary splitter). The choice of VHF antenna depends on whether or not you need channel 5 (KOBI, NBC). If you don't need channel 5, then a high-VHF antenna like the Winegard YA-1713 should be good enough. If you also need to pick up channel 5, you'll need to go with something larger like the Winegard HD-5030.
3) If you need ALL THREE groups of channels, then you should get one slightly larger antenna and put it on an antenna rotator like the Channel Master 9521A. Again, the choice of antenna depends on whether or not you need to pick up channel 5. If you do not need channel 5, you can use an antenna like the Winegard HD7696P (narrower antenna because it does not support low VHF). If you need channel 5, then you can use something like the Winegard HD7084P (a wider, full band antenna).
The Stacker antenna from Denny's may or may not work for you. There are anecdotal reports of this antenna working well for some people, but there is very little hard data on this antenna (gain specs, radiation pattern, impedance match, etc.). Without a detailed computer model of the antenna or measurements against calibrated reference signals in an RF controlled lab environment, it is difficult to tell whether or not this antenna has any hidden weaknesses (i.e., lower raw gain on some channels, unusual positioning of lobes/nulls in the radiation pattern, impedance mismatches that lead to lower realized gain, etc.).
My gut feel is that the UHF (on bottom) and VHF (on top) sections of that antenna are too close together. While either part alone may be a very good standalone antenna, when you place them so close to each other, I would expect there to be some undesirable interaction between the two. Since this alters the radiation pattern, gain, and characteristic impedance of each antenna, you can end up with something that performs very different than the two antennas you started out with. That is why in most cases, when you combine multiple antennas, you want to make sure there is plenty of space (often several feet) around each of the antennas you are joining together.
Unfortunately, at this point in time, there is not enough independent analysis to tell where the strengths and weaknesses of this antenna are.
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