Several dense red dyes were used in period, including madder, and brazilwood. With madder dyebaths, the same pot of coloured water would be used until it was nearly colourless. Thus the first few fabrics dyed would be a brilliant dark red, and the last few a pale pink colour. As such, dark/dense reds were for the richer people (or at least the more expensive clothes of the poor), while pink was a colour for cheaper fabrics (mostly).
To dye wooll red, from A Profitable Booke ...
Ye shall put too four pound of woollen yarne, tenne ounces of Allom, and seeth it with branne water so much as ye shall thinke good, then take your yarne out, and put that water out of that Kettle, and put therein againe three parts of fresh branne water, and one part of faire cleere water, and warme it a little on the fire, then put therein two pound of grening weede, and let it so warme a while, then put therin your wooll, and stirre it wel with a sticke the space of three houres, but let it not seeth in any wise, so done, then take out your wooll againe, and put it againe into your Kettle, and put thereto halfe a glassefull of unsleakt lime, with as much of common ashes, and thereto put your wooll againe, and stirre it with a staffe sixe or seuen Paternoster whiles, than take foorth your wooll, and ye shall haue a faire colour. But if yee will haue it yet a more sanguine colour, then must you put into your Kettle halfe a little glasse full of more lime, and a little glasse full of common ashes, and thereto put your wooll againe, and stirre it well still foure or fiue Paternoster whiles, then take foorth your wooll and wash it, and so ye shall haue a verie faire colour.