[Scilab-users] The sound of mathematical formulas

[Rafael Guerra]

Hi Stephane,

Thanks a lot for the excellent tip.
After digging a bit, it seems that the reference for the cascaded frequency modulation sound synthesis is:

Chowning, J. [1973] The Synthesis of Complex Audio Spectra by Means of Frequency Modulation. JAES

The following course has a comprehensive chapter on it:
https://www.music.mcgill.ca/~gary/307/week8/fm.html

from where one can find the code snippet for a bell sound:

// by Gary Scavone, McGill University, 2004
// Bell-like sound
fs = 22050;
T = 1/fs;
dur = 4;
t = 0:T:dur;
T60 = 0.5;
env = 0.95*exp(-t/T60);
// FM parameters
fc = 200;
fm = 280;
Imax = 10;
I = Imax.*env;
y = env.*sin(2*%pi*fc*t + I.*sin(2*%pi*fm*t));
sound(y, fs);


Kind regards,
Rafael

From: users [mailto:users-bounces at lists.scilab.org] On Behalf Of Stéphane Mottelet
Sent: Saturday, November 05, 2016 2:49 PM
To: Users mailing list for Scilab <users at lists.scilab.org>
Subject: Re: [Scilab-users] The sound of mathematical formulas

Hello,

Cascaded frequency modulation gives nices sounds. For example signals like

sin((w0+a1*sin(w1*t))*t)

w1 itself can also be modulated, and so on. This kind of synthesis was used by the famous Yamaha DX-7 and gave typical sounds (bass guitar, bells, ...)

S.

Le 05/11/2016 à 13:43, Rafael Guerra a écrit :
Dear Scilab'ers,

Are you aware of any good references showing how to produce brief, nice and useful sounds using simple mathematical formulas?
This is primarily out of curiosity but they could well be played using sound() or playsnd() functions, and provide different sound warnings during Scilab code execution/interaction.

E.g., something like but hopefully nicer to listen than the following tests:

--> x=1e2:1e4; b=0.6; y=window('hm',length(x)).*sin(x.^b.*log(x)); sound(y,9944)
or:
--> x=1e2:1e4; b=sqrt(2); y=window('hm',length(x)).*sin(x.^b.*log(x)); sound(y,9944)

Thanks and regards,
Rafael





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