James Wyness

I'm fairly new to Max. I want to output floating point numbers with a Cauchy distribution which has lower and upper boundaries of 0.25 and 2.0 respectively, the mean being 1. I know 1 isn't the mean but I want the numbers to spread around 1 and create those boundaries. It's to randomise playback speed values into sig~ then groove~ objects. I'm looking at the ccauchydist object but can't figure out if this will do the job or how to scale it to my needs. Any suggestions or is there an easier solution?

cacauchy-dist-object-how-to-scale-the-output

a simple gaussian distribution will give you the same effect, but make sure if that is really what you want, because for "speed" you will need different curves for below x1. and above x1.

[expr (sqrt(-2.0*ln(1-((random(0\,32767))*(1./32768.)))))*(cos(((random(0\,32767))*(1./32768.))*6.283185307))]

you might want to add a multiplier to control the range:

or why not all in one line (unavoidable version of the patch):

[expr exp(.057762265*((((sqrt(-2.0*ln(1-((random(0\,32767))*(1./32768.)))))*(cos(((random(0\,32767))*(1./32768.))*6.283185307)))-1.)*$f2))]

you might want to add a multiplier to control the range:
[expr exp(.057762265*(($f1-1.)*$f2))]

or why not all in one line (unavoidable  version of the patch):

[expr exp(.057762265*((((sqrt(-2.0*ln(1-((random(0\,32767))*(1./32768.)))))*(cos(((random(0\,32767))*(1./32768.))*6.283185307)))-1.)*$f2))]


Thanks for pointing out the need for different curves and also forsaking time to provide the maths. As a relative beginner I don't know where or how to plumb in those functions to a patch. To explain more simply - if my boundaries or limits are, say, -0.5 and 2, the mean is 0.75. Let's say then that I have most of my values cluster around 0.75 with far less chance of values near the limits, hence the Cauchy or Gaussian distribution. Then can I offset the mean by +0.25 to make it 1.0 and (somehow) eliminate 0 and any unwanted values which result because of the offset? Or is this too ambitious?

the gaussian noise generator from above will provide you with an output centered around 0., and with a range of somewhat between - 1.5. and 1.5. (in a real live situation, you dont want to have the full range of a gauss distribution; so we should just cut it off somewhere.)

you said your desired range is between 0.25 and 4, right? lets redefine that to something more useful.

you could have two ranges from *1 - *4, one for "slower" and one for "faster". or you could have range of "/4" - "*4." as you might know, record players and CD players show percentage, that is also a nice option. or you could translate it to relative pitches (e.g. "*2.0" = "+ 1 octave").

(this is what the exp() thing does. it is basically the same math what you would use to convert midi to hertz, just with another offset, center, and range.)

i wanted to post you an example patch, but as it seems there is something wrong with the math ;)

you said your desired range is between 0.25 and 4, right? lets redefine that to something more useful.
you could have two ranges from *1 - *4, one for "slower" and one for "faster". or you could have range of "/4" - "*4." as you might know, record players and CD players show percentage, that is also a nice option. or you could translate it to relative pitches (e.g. "*2.0" = "+ 1 octave").
(this is what the exp() thing does. it is basically the same math what you would use to convert midi to hertz, just with another offset, center, and range.)

i wanted to post you an example patch, but as it seems there is something wrong with the math ;)


ah, found it, the -1. in exp(.057762265*(($f1-1.) is wrong, as 0 must become 1 anyway. :)

the noise generator produces a linear range of -n to n with 0. as center, and we want to output pitch up and pitch down between 1/m and 1*m with 1. as the center. this is what exp() kinda does by default.

"randomspeed.pat: Sorry, this file type is not permitted for security reasons."

it is probably too random for this forum.

"randomspeed.mxb: Sorry, this file type is not permitted for security reasons."

see what happens when you move the "adjust range" to 17 or so.

I'll get on the case and report back. Thanks so much for taking time to help.

cacauchy dist object - how to scale the output?