Purity
About
Purity affects items in dramatic ways, multiplying their effect on study, eating, and such. 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.
Every item is composed of the 4 alchemical elements of Salt, Mercury, Sulfur, and Lead. Depending on the relative amounts of each element, an item will have a certain level of "Purity". The more concentrated one particular element is, the higher its purity and the more potent it becomes.
Purity effects multipliers for Food and Inspirationals. (High purity food give more humour points, and Inspirationals give more inspiration points)
Purity Multiplier
For determining the bonus multiplier for a Food or Inspirational, you take the Sum of the Squares of each element. Items that are high in one particular element have a higher potency for the same reason that (32+ 12) is more than (22+ 22). Each element is expressed as a fraction of 1, 41.33 salt is 0.4133.
The "Sum of Squares" yields a raw value that is always between 0.25 and 1.00 The formulas for the Purity Percentage and Purity Multiplier thus contain modifying numbers which will make the values span the range from 0-100% or 1-10x.
Purity Percent = ( (Salt2+ Mercury2+ Sulfur2+ Lead2- 0.25) *4/3 )
- Subtracting 0.25 changes makes the range 0.00 to 0.75. Multiplying by 4/3 Makes it 0.00 to 1.00, or 0% to 100%.
Purity Multiplier = ( (Salt2+ Mercury2+ Sulfur2+ Lead2) *12 ) - 2
- Multiplying by 12 makes the range 3.00 to 12.00, and subtracting 2 makes it 1.00 to 10.00.
The purity Percent and Multiplier can be easily inter-converted by this formula: Multiplier = (9 * Percent) + 1
An item with 33% purity has a 4x multiplier.
Purity Table
Here's a table showing the approximate Purity effects based on the Highest element. These values assume that the remaining elements are all equal, and thus it represents a MINIMUM value.
| Element | Percent | Multiplier |
|---|---|---|
| 25.00 | 0% | 1.00 |
| 30.00 | 0% | 1.04 |
| 35.00 | 1% | 1.16 |
| 40.00 | 4% | 1.36 |
| 45.00 | 7% | 1.64 |
| 50.00 | 11% | 2.00 |
| 55.00 | 16% | 2.44 |
| 60.00 | 22% | 2.96 |
| 65.00 | 28% | 3.56 |
| 70.00 | 36% | 4.24 |
| 75.00 | 44% | 5.00 |
| 80.00 | 54% | 5.84 |
| 85.00 | 64% | 6.76 |
| 90.00 | 75% | 7.76 |
| 95.00 | 87% | 8.84 |
| 100.00 | 100% | 10.00 |
Increasing the value of the highest element by 25 will roughly Double the value of an item.
Purity% forms a steady quadratic progression as the Element increases, and the Multiplier is 1 + Quadratic. This can most easily be seen by subtracting 1 from the Multiplier value.
- 3.56 - 1.00 = 2.56 = 1.602
- 4.24 - 1.00 = 3.24 = 1.802
Source Information
<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
