Some members may be interested in this video . . . .
Joe does a nice job in this video of showing the lighting effect created by a beauty dish and how it can be replicated with a shoot through umbrella.
I have some additional thoughts. Instead of using a black cardboard disc, you can simply cut black material in a circular pattern and sew it to the outside of the umbrella for a permanent shoot through umbrella beauty dish. I think I will do that. It should make the lightest and easiest to transport "beauty dish."
Finally, I have some of these I use with monolights. http://www.ebay.com/itm/2-x-Umbrella-Softbox-Soft-Brolly-Box-Reflector-Studio-40-Flash-Light-Reflective-/361097365784?hash=item5413148918:g:WhcAAOSwSypY9QvM I like to use them instead of a traditional soft box for on-location shoots because they are easier to transport and set up than a traditional soft box and they balance better on a light stand to reduce tip over risk. When you use one of these brolly boxes with a monolight, guess what? That monolight creates the dark center circle in the catch-light like a beauty dish. One difference is that you can see a line going down from the black spot created by your light stand. A thinner light stand will create a thinner line but looking for that line in the catch-light is something no one other than a photographer will do.
I am going to have to haul some gear half-way across the country to make portraits of old folks in a nursing home and was experimenting with the lightest and smallest equipment I could use for the task. I settled on using two of these with light weight light stands, a D500 and two SB-5000s. http://www.ebay.com/itm/Godox-60x90cm-Softbox-Umbrella-Reflector-Softbox-for-Flash-Speedlight-/162273264929?hash=item25c83d8521:g:8E4AAOSwal5YNWEo By cutting a six inch slit in the bottom (and side) of the white diffuser through which I pass the light stand I am able to angle the softbox down more. By using the clip on diffuser which comes with the SB-5000 speedlight I am able to achieve nice diffused and even lighting. The wireless lighting system in the D500 with the SB-5000 creates an easy way to adjust lighting ratios from the camera menu system. I am not going to need a beauty dish as these folks will want diffuse lighting to hide wrinkles!