JonathanBowen

It usually won't help much to create a smaller version & then scale it up. To maximize the smoothness of the smaller versions, about all you can do is try to avoid diagonals & curves that would partially fill a pixel if that was possible, & possibly to use colors along edges that don't contrast so much that the characteristic stair-step effect (known as the jaggies) is not too noticeable.
 
Basically, for best results each version needs to be designed separately, adding no more detail to each one than looks good when viewed at its actual size. That often requires beginning with a simple design containing only the most important & largest thematic elements, & adding details sparingly so all the sizes look enough alike that your logo is recognizable for what it is in all of them.
 
It isn't easy to begin with & gets progressively harder as the size decreases. 

You did nothing wrong, other than maybe expecting the smaller versions to look as good as the large one.
 
What's happening is when you reduce the number of pixels, you reduce the amount of detail the image can contain. That's because a pixel is the smallest possible unit of color information in an image -- you can't shrink pixels, only add or (in this case) remove them to change the image size.
 
If that still seems unclear, imagine designing your logo on a piece of graph paper. Draw a square box around 1201 x 1201 grid divisions, & fill in each of the grid's little boxes in it with any color you want. That represents how your largest version would look in pixels. Now do the same thing, but inside a box only 400 x 400 grid divisions & again in one 150 x 150 divisions. You can't half-fill any of the little boxes -- they can only be completely filled with one color or empty.
 
See the problem? There just are not enough grid squares to show everything in the large version in the smaller ones, so they can never look as good.

I appreciate your work on that Peter. I've mostly given up on the monogram idea. The "R" is frying my brain.