Purity multiplies the base stats of items, increasing their stats.
|Purity Multiplier||Arts & Crafts||Frontier & Wilderness||Hunting & Gathering||Mines & Mountains||Natural Philosophy|
As you can see, this is pretty straight forward for Inspirationals, simply multiplying the amount of proficiency given.
|Elements||Blood||Phlegm||Yellow Bile||Black Bile|
But for food it gets more interesting. The amount healed and gluttonied by food is multiplied by the purity multiplier (just like with Inspirationals), but the composition of the elements affects Gluttony. Taking a special food like Oakworth, the composition of the elements is very important during Gluttony. When it's 25/25/25/25, there is a 25% chance to get any of the Humours to increase by 3.0. But if the area you found it in has a 0/0/50/50 composition, you can only get get 3.0 for Yellow Bile and Black Bile (both have a 50% chance).
So while the values do increase for Gluttony (Oakworth with purity 2.0 will give 6.0 and 3x 0.8), the composition of the elements have a big impact too. So while 100/0/0/0 gives 10 purity, it can only gluttony for 30/4/4/4, while 0/0/50/50 only has 4 purity, it can give either 1.6/1.6/12/1.6 or 1.6/1.6/1.6/12, which can be better if you want Yellow or Black Bile.
Using this, it's very easy to calculate the base stats (purity multiplier 1.0) for Inspirationals and Food. Simply divide the stats gives by the purity multiplier value (shown in Ender's custom client as 'Purity', or calculated using the elements). Remember that the elements are rounded down in-game to two decimals, and that most values are simple and round, like the smooth stone and oakworth examples.
Purity affects items in dramatic ways, multiplying their effect on study, eating, and such. Living in a high purity zone (or on a "HQ node" as it is sometimes called) will therefore make everything vastly easier as you will be studying with fewer items and filling your humors with less time foraging. This multiplier is very apparent at higher levels of study and gluttony.
Purity is predicted to be a strong incentive for both trade and warfare. As high purity zones are found and fortified they will become more and more scarce, and their desirability for those more inclined to battle will grow.
<mightyagrippa> so, what's the salem analog to sqrt(quality/10)?
<loftar> It's basically the sum of the square of the individual elements (as represented from 0.0 to 1.0).
<loftar> But linearly normalized to the range 0.0-1.0 rather than 0.25-1.0.
<mightyagrippa> so, after you have the quality number in (0,1), how does it translate to humor/skill gain multiplication?
<loftar> Usually, but not necessarily, by using it to generate a multiplier from 1-10.
To calculate the raw purity, a number between 0 and 1, use [(Salt^2 + Merc^2 + Sulp^2 + Lead^2)-.25]*(4/3).
To calculate the purity multiplier for humors and skills, use (Salt^2 + Merc^2 + Sulp^2 + Lead^2)*12-2.
For example, a waxing mushroom with 20% salt, 50% mercury, 15% sulphur, and 15% lead would have
[(.2^2+.5^2+.15^2+.15^2)-.25]*(4/3) = .1133 raw purity
(.2^2+.5^2+.15^2+.15^2)*12-2 = 2.02 purity multiplier