The most direct way to convert one range of numbers into a different range of numbers is a process called linear mapping. For each number in a source (input) range, find the corresponding number in a destination (output) range. The process is to multiply the input value by the size of the destination range (destination maximum minus destination minimum) divided by the source range (source maximum minus source minimum), then add the destination minimum to that.
This patch shows examples of linear mapping and linear interpolation, using the lmap abstraction described in the “Linear mapping equation” example. One could substitute the built-in Max object scale in place of lmap with the same results.
The term "mapping" refers to making a map of correspondences between a source domain and some other "target" range. (Think of the game where you are given words in one category and are challenged to try to find an appropriate correspondence in another category, as in "Kitten is to cat as puppy is to ...".) The simplest kind of numerical mapping is called "linear mapping". That's when a one-to-one correspondence is drawn from every value in a source range X to a value that holds an exactly comparable position in a target range Y.
A linear fade-in or fade-out of audio is okay for quick changes that take place in a fraction of a second, but for slower fades one should generally take into account that our subjective sense of loudness more closely conforms to an exponential change in amplitude. This patch allows you to use the slider (or the mod wheel from a MIDI controller) to control the amplitude of white noise in one of three different ways: with straight linear mapping, exponentially (with an exponent of 4), or using a range of 60 decibels.
The slider object has some attributes that have a significant effect on its output: floatoutput, size, min[imum] and mult[iplier]. By default slider uses only integer values, with a size of 128 (i.e., ranging from 0 to 127). For an integer slider, the range will be size different integers from 0 to size-1, whereas for a float slider the input range will be the full range from 0. to size., inclusive.