Hi Ralph- just regular white granulated sugar. Basically, I use 5% sugar by weight as per each pound of oils in my batches, which roughly = 2 tablespoons by volume. When I make my honey/beeswax soap, instead of the white sugar, I use 5% honey by weight as per each pound of oils in my batch, which equals out to 1 tablespoon by volume as per pound of my oils (it weighs more than granulated sugar).
For what it's worth, I do my honey soaps differently than many people......I add the honey directly to my cooled-off lye solution before adding it to my oils. Adding the honey to my lye solution first eliminates all the weird drama that can happen to soap when adding honey to it. Fellow member Salted Fig has a great post somewhere on the forum explaining from a chemical standpoint why adding honey to the lye instead of to the batter produces drama-free results. I'll try and see if I can find it and post a link here. Anyway, I had been adding my honey like that for years with awesome drama-free results before Salted Fig came along and explained the why of it.
I looked over your original recipe in SoapCalc and wow- that would be some drying soap....and that's coming from someone whose skin (and whose family's skin) is fine with higher amounts of coconut and PKO than several folks here, even though the climate is crazy dry where I live. Go figure!
For what it's worth, this is how I tweaked your original formula so that it would be quite compatible with me and my family. The fatty acid profile is very much the same as my tallow/lard soap which is a fave of my hubby and son and is super bubbly and non-drying to us, only the tweak is 1 percentage point more conditioning than mine. I normally add .5% tetrasodium EDTA to it as per the total weight of my soap, as well as 2 tablespoons granulated sugar as per each pound of the oils in my batch, and also 2% sodium lactate as per pound of oils:
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Everyone's skin is different in what it likes/hates, but the above fatty acid profile is what we happen to like.
IrishLass
Edited to add: I superfat mine @ 8%