gauss

gauss — Gaussian distribution random number generator.

Description

Gaussian distribution random number generator. This is an x-class noise generator.

Syntax

ares gauss krange
ires gauss krange
kres gauss krange

Performance

krange -- the range of the random numbers (-krange to +krange). Outputs both positive and negative numbers.

gauss returns random numbers following a normal distribution centered around 0.0 (mu = 0.0) with a variance (sigma) of krange / 3.83. Thus more than 99.99% of the random values generated are in the range -krange to +krange. If a mean value different of 0.0 is desired, this mean value has to be added to the generated numbers (see example below).

For more detailed explanation of these distributions, see:

  1. C. Dodge - T.A. Jerse 1985. Computer music. Schirmer books. pp.265 - 286

  2. D. Lorrain. A panoply of stochastic cannons. In C. Roads, ed. 1989. Music machine . Cambridge, Massachusetts: MIT press, pp. 351 - 379.

Examples

Here is an example of the gauss opcode. It uses the file gauss.csd.

Example 330. Example of the gauss opcode.

See the sections Real-time Audio and Command Line Flags for more information on using command line flags.

<CsoundSynthesizer>
<CsOptions>
  -d -o dac
</CsOptions>
<CsInstruments>
instr 1
irange   = p4
imu      = p5
isamples = p6
indx     = 0
icount   = 1
ix       = 0.0
ix2      = 0.0

loop:
i1       gauss   irange
i1       =       i1 + imu
ix       =       ix + i1
ix2      =       ix2 + i1*i1
if i1 >= -(irange+imu) && i1 <= (irange+imu) then
  icount = icount+1
endif
         loop_lt indx, 1, isamples, loop
        
imean    =       ix / isamples                         ;mean value
istd     =       sqrt(ix2/isamples - imean*imean)      ;standard deviation
         prints "mean = %3.3f, std = %3.3f, ", imean, istd
         prints "samples inside the given range: %3.3f\%\n", icount*100.0/isamples
endin
</CsInstruments>
<CsScore>
i 1 0   0.1 1.0   0   100000  ; range = 1, mu = 0.0, sigma = 1/3.83 = 0.261
i 1 0.1 0.1 3.83  0   100000  ; range = 3.83, mu = 0.0, sigma = 1
i 1 0.2 0.1 5.745 2.7 100000  ; range = 5.745, mu = 2.7, sigma = 5.745/3.83 = 1.5
</CsScore>
</CsoundSynthesizer>


Its output should include lines like this:

mean = 0.000, std = 0.260, samples inside the given range: 99.993%
mean = 0.005, std = 0.999, samples inside the given range: 99.998%
mean = 2.700, std = 1.497, samples inside the given range: 100.000%

See Also

seed, betarand, bexprnd, cauchy, exprand, linrand, pcauchy, poisson, trirand, unirand, weibull

Credits

Author: Paris Smaragdis
MIT, Cambridge
1995

Precisions about mu and sigma added by François Pinot after a discussion with Joachim Heintz on the Csound List, December 2010.

Example written by François Pinot, adapted from a csd file by Joachim Heintz, December 2010.

Existed in 3.30