IMHO - as stated above, a mother sauce can diversify into a myriad of other sauces, a base so to speak, not unlike primary colors in art.
Rather than focus on specific sauces, it is probably easier to remember them as what they are (type) rather than what they should be (actual sauce)
So that out of the way, from how i perceive them to be:
Brown Sauces based on brown stocks
White sauces based on white stocks
White sauces based on milk/cream and roux
Cold Emulsion Sauces i.e. mayonnaise
Hot Emulsion Sauces i.e hollandaise
Even though a Beurre Blanc is a sauce, generally speaking, the end product is still a Beurre Blanc. As opposed to a mayonnaise and its derivatives, sauce tartare or mixed with aspic to make a chaud froid. Or making a demiglas from stocks etc.
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