Liquid castille soap like Dr Bronner's unscented. Any mild castille bar soap. Notice it is soap, not detergent, being spoken of.
Someone suggested Ivory Flakes. I mean to see what it is made of next time I go to the store. If soap, fine, it's a good idea.
Mild detergent as in shampoo would be second to soap.
Silk Warning:
In any case, when washing pearls strung with silk, follow all the precautions so the silk won't stretch. Even so, you may end up with stretched silk, because it it the very nature of silk to stretch. I think stretched silk looks bad. Gaps between the knots and the pearls- ick. That is why I like to say, if your pearls are dirty enough to be washed, they should be restrung as well.
In spite of what our esteemed Bernadette said once in a post- silk is highly absorbent of body oils and grime, far more than nylon or other man made materials. Just google "silk properties" -or "silk qualities" to get plenty of references from the manufacturers as to how highly absorbent it is. Google up on beading thread to see that nylon is absorbent-resistant.
I think we need a separate thread on the subject of silk, what it is, what it does and does not do and its innate properties. If someone else does not want to start it, I'll get around to it soon.
The Thread Thread