Hmmmm .... maybe you were rounding off a bit too much one way and then the other. Let's see ...
OK. Flash has guide number of 120. Have no flash meter.
If distance from object to flash is 10 feet and guide number is 120, at 100ISO the optimal aperture is around f11.
OK - let's buy into this - it actually would be f/12
If distance form object to flash is 5 feet and guide number is 120, at 100 ISO the optimal aperture is around f16.
Nope ... 120 divided by 5 is equal to 24 so the rounded-off aperture would be f/22.
If diffuser cuts out one stop, aperture at 5 feet returns to f11 - right?
So, then if a diffuser cut off only one stop the aperture now would be f/16.
If film speed goes up to 200ISO aperture goes to f16 - right?
based on starting at f/16 (with diffuser on) going to 200 speed film would make the aperture f/22.
Changes in distance are modified according to the "inverse square or squared law" - although this applies strictly only to point sources of light and not flashes that have their light sources encased in reflectors. Changes in film speed affect "calculations" in an inverse linear manner - double the speed allows you to use an aperture that is twice as small (one f stop difference for doubling or halving the speed). A TWO stop difference for doubling or cutting distance in half. I think I need a nap.
adios, andy
Andrew Davidhazy, School of Photographic Arts & Sciences/RIT - andpph@rit.edu