WiFi in the 2.4 GHz range is usually fairly congested in urban environments. The 5 GHz band used to be better, but an increasing number of routers now support it and so it has become fairly busy as well. It turns out that there are a number of channels on that band that nobody appears to be using despite being legal in my region.

Why are the middle channels unused?

I'm not entirely sure why these channels are completely empty in my area, but I would speculate that access point manufacturers don't want to deal with the extra complexity of the middle channels. Indeed these channels are not entirely unlicensed. They are also used by weather radars, for example. If you look at the regulatory rules that ship with your OS:

$ iw reg get
global
country CA: DFS-FCC
    (2402 - 2472 @ 40), (N/A, 30), (N/A)
    (5170 - 5250 @ 80), (N/A, 17), (N/A), AUTO-BW
    (5250 - 5330 @ 80), (N/A, 24), (0 ms), DFS, AUTO-BW
    (5490 - 5600 @ 80), (N/A, 24), (0 ms), DFS
    (5650 - 5730 @ 80), (N/A, 24), (0 ms), DFS
    (5735 - 5835 @ 80), (N/A, 30), (N/A)

you will see that these channels are flagged with "DFS". That stands for Dynamic Frequency Selection and it means that WiFi equipment needs to be able to detect when the frequency is used by radars (by detecting their pulses) and automaticaly switch to a different channel for a few minutes.

So an access point needs extra hardware and extra code to avoid interfering with priority users. Additionally, different channels have different bandwidth limits so that's something else to consider if you want to use 40/80 MHz at once.

The first time I tried setting my access point channel to one of the middle 5 GHz channels, the SSID wouldn't show up in scans and the channel was still empty in WiFi Analyzer.

I tried changing the channel again, but this time, I ssh'd into my router and looked at the errors messages using this command:

logread -f

I found a number of errors claiming that these channels were not authorized for the "world" regulatory authority.

Because Gargoyle is based on OpenWRT, there are a lot more nnwireless configuration options available than what's exposed in the Web UI.

In this case, the solution was to explicitly set my country in the wireless options by putting:

country 'CA'

(where CA is the country code where the router is physically located) in the 5 GHz radio section of /etc/config/wireless on the router.

Then I rebooted and I was able to set the channel successfully via the Web UI.

If you are interested, there is a lot more information about how all of this works in the kernel documentation for the wireless stack.