Madder is one of the main dyes in the medieval period. It can give orange and pink tones as well as beautiful reds. I have dyed several times with madder and the thing that strikes me is that many modern sources give different recipes for the bright red. These often contradict each other.

The groot plantaardig verfboek by Iet van de Vrande suggests to warm the water till 100 degrees Celsius, whilst wild colours by Jenny Dean recommends alkaline water and prerinsing the madder wit boiling water to get the orange and brown dyestuffs out. She also mentions that alkaline water is good, so people with hard water will have it easy.

None of these methods have given me bright reds. So I guess some other factor must have a hand in getting bright reds. And I suspect it might be the hardness of the water. My latest experiments only involved presoaking, pH and temperature and although some were brighter than others there was no bright red among them. I used tap water and it is high in calcium-ions. Some people add soda to their dyebath which seems to work. Proper soda is Na₂CO₃ and the carbonate ions precipitate with calcium ions to make the insoluble calciumcarbonate (CaCO₃), thus getting the calcium-ions out of solution. This invorces my idea that hardness of the water has a big influence. 

Another factor that might be usefull is a bit of fermentation. I once made a madder dye bath and it smelled off. As if the madder was a bit rotten. The silk got a very nice dark red, so something might be in here as well. 

I bought some distilled water from the store and started soaking some madder in it. So in a few days I will hopefully show some results with bright reds. If this works I will be examining if it is the fermentation or the distilled water or both.Very curious for now