Some time ago I found a Ford Media Relations pdf that described it but can't find it now. However, do a search on the transmission with variations of "6-speed" or "6 gears" and you'll find info.
Here's some from Wikipedia's page on the Super Duty: "The TorqShift design in fact has six forward ratios, but only five are advertised, with the 'hidden' gear only used in extreme cold weather. The TorqShift 1st to 5th gear ratios are 3.11, 2.22, 1.55, 1.00, and 0.71:1. It also utilizes an alternate 4th gear, overdrive on 2nd gear of the 3-speed automatic component (0.72 x 1.55), that is 1.10:1 that is used under cold start conditions to aid engine and transmission warm up."
Here's some other info from Powerstroke Nation:
Mark Kovalsky 01:15 PM 02-23-2015
First, you need to understand how the TorqShift was built. It is a two speed transmission in front of a three speed transmission.
You can get six ratios by combining the two times three ratios. The problem is that two of the ratios are nearly identical.
The two speed has ratios of 1:1 and 0.71:1.
The three speed has ratios of 3.1:1, 1.54:1, and 1:1.
By combining them you get:
3.1:1
2.2:1
1.54:1
1.09:1
1:1
0.71:1
The 1:1 and 1.09:1 ratios are nearly the same." He also stated this was a more economical design than one with 6 actual gears, but I'm sure part of that also had to do with compatability with other components, with assembly plant components, etc. Everything's a compromise, of course.
The close ratios of 1.0:1 and about 1.10:1 would allow either to be used depending on temperature and it'd never feel like a gear had been skipped above or below it when upshifting. One may also feel torque converter lockup to add to the things one would feel while driving.