scoville scale vs. human scale

[Hermitian]

I've seen several posts in this "Peppers" forum asking how hot is some pepper on a human scale vs. a scoville scale, so perhaps the following will help some readers on their quest to find the ultimate pepper for their tastes.

Humans are usually endowed with 10 fingers and thus we like to measure things on a linear scale of 0 to 10. The scale of chemical reactivity with the human tongue for chili peppers is "Scovilles" which is a non-linear scale from 0 to billions. Here's a chart that equates the two:



For the general reader, it's worth pointing out: on the human scale of 1 the spiciness is about that of a very mild Anahiem-type chili pepper, on the human scale of 5 the spiciness is about that of a Jalapeno, at the human scale of 7.5 you reach a Serrano, and at the human scale of 9 is an orange habanero.

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For engineers and science-minded people, where does all this come from?

We know that the human sense perceptions are logarithmic with respect to phenomena. Several studies of human taste perception have shown that the lower limit of "spiciness" perception is at 100 scovilles and the upper limit is at 400,000 scovilles (i.e., there is no differentiation between 400,000 scovilles and anything above). Using the variable t as the human scale and variable s as the scoville scale we have:
t = m*log(s) + b
1 = m*log(100) + b
10 = m*log(400000) + b
... and from linear equations the rest falls into place.
The lower limit of s0 approx. 39.79 makes total sense since bell peppers are typically rated with scoville << 40.