ran

[Function]: (ran {keyword value}*)

Generates random numbers in a variety of distributions according to its keyword arguments.

ran supports the following keyword arguments:

:below number

Sets the exclusive upper bounds for random number generation. Defaults to a value specific to the type of distribution specified, usually 1.0.

:from number

Sets the inclusive upper bounds for random number generation. Defaults to a value specific to the type of distribution, usually 0.0.

:type

Sets the distribution for random number generation to type specified as a symbol or keyword. Defaults to :uniform.

ran supports the following distribution types:

:uniform: Equal probability distribution.
:low-pass: Likelihood of lower numbers is greater then higher numbers. Density is f(x)=2*(1-x) for {x 0<1} and mean is .2929.
:high-pass: Likelihood if higher numbers is greater than lower numbers. Density is f(x)=2*(1-x) for {x 0<1} and mean is .2929.
:mean: Likelihood of mid-range numbers is greater than lower or higher numbers. Mean is n/2.
:beta: The :a and :b parameters determine the shape of the distribution. When a=b=1 the distribution is uniform. When a=b, the distribution is symmetric around .5. When a<1 and b<1 then the density of larger and smaller numbers increases. When a>1 and b>1, density is similar to the gaussian distribution.
:exponential: Returns a floating point value greater than zero. The :a parameter is a stretching factor; increasing its value "prefers" smaller numbers. The distribution is unbounded but when a=1 then %99.9 of the time the value returned will be than 6.9077554, i.e. -log(.001). The distribution density is f(x)=(exp -x) with a mean of 1.0.
:gaussian: Gaussian (normal) distribution returns an unbounded value. The spread (standard deviation) is 1.0 centered at 0, so 68.26% of the results are between -1 and 1 inclusive and 99.74% of the results are between -3 and 3 inclusive.
:cauchy: Returns an unbounded value. The density function is a bell shaped curve centered at 0 similar to a normal distribution but with more values at the extremes. The mean and standard deviation of the Cauchy distribution are undefined. If parameter :a is true then only positive values are returned. Density is f(x)=1/(pi(1 + x^2)).
:poisson: A discrete distribution: returns positive integer values, theoretically unbounded but practically limited by the shape parameter. Parameter :a controls the distribution's shape and must be positive: the mean is a and the standard deviation is sqrt(a).
:gamma: Returns a floating point value greater than 0. Parameter :a controls the distribution's shape and should be a positive integer (if a non-integer is provided, the value is rounded.) When a=1, the distribution is the same as exponential. As its value increases, the probability density function becomes a curve with mean=a and standard deviation = sqrt(a)

:a number

A control parameter whose interpretation depends on the distribution type.

:b number

A control parameter whose interpretation depends on the distribution type.

:state state

The random state object. The value defaults to *random-state*.

Examples:

Example 1. The ran function.

(define (play-ran type len rate key1 key2)
  (process repeat len
           for r = (ran :type type)
           for k = (rescale r 0.0 1.0 key1 key2)
           output (new midi :time (now)
                       :keynum k
                       :duration (* rate 1.5))
           wait rate))

;;; Playing uniform distribution.
(events (play-ran ':uniform 100 .1 20 100)
        "test.mid" :channel-tuning 4)
⇒ "test.mid"
;;; Playing the low pass distribution.
(events (play-ran ':low 50 .1 20 100)
        "test.mid" :channel-tuning 4)
⇒ "test.mid"
;;; Playing the high pass distribution.
(events (play-ran :high 50 .1 20 100)
        "test.mid" :channel-tuning 4)
⇒ "test.mid"

Example 2. The beta distribution.

(define (rain len rate env key1 key2 amp)
  (process for i below len
           for e = (interpl (/ i len) env)
           for v = (vary rate e :above)
           ;; rescale e to control shape of beta distribution
           ;; when e=0 z=.4, and when e=1 z=1.
           for z = (rescale e 0 1 1 .4)
           for b = (ran :type ':beta :a z :b z)
           output (new midi :time (+ (now) v)
                       :duration v
                       :keynum (between key1 key2)
                       :amplitude (rescale b 0 1 .1 amp))
           wait rate))

(define rain-env '(0 1 .4 0 .6 0 1 1))

(events (list (rain 80 .5 rain-env 70 90 .8)
              (rain 40 1 rain-env 40 60 .8)
              (rain 20 2 rain-env 20 40 .9))
        "test.mid")
⇒ "test.mid"

Examples:

See also: