// title: Series of numbers
// author: Henk Lasschuit
// description:
// In his book "Schema's voor programmeren" (Diagrams for programming, Kluwer, Deventer, 1988) Andree Hollander introduces a simple algorithm for generating a series of numbers: pick a number, if it is even, divide by 2, else multiply by 3 and add 1. Repeat until the value 1 is reached (or else 4,2,1,4,2,1 will be repeated endlessly). Use the numbers as sound parameters and you have, well, music!
// I generated 100 series, starting with 1 to 100. Of the sound in the middle the pitch is controlled by the numbers within a series and the timbre by the starting number. The sound in the left channel is the length of a series (pitch) and the longest series up until now determines the timbre. The sound in the right channel is controlled by the maximum value within a series and the highest value up until now determines the timbre.
// code:
//series of numbers
Server.default.boot;
(
SynthDef(\beep, { |freq=440, cutoff=1000, pan=0|
Out.ar(0, Pan2.ar(LPF.ar(Saw.ar(freq), cutoff), pan)) }).send(s);
)
//from 1 to 100
//while number>1
//if even: divide by 2, else multiply by 3 and add 1
//remember highest value, remember longest series, both with their startnumber
//startnumber->cutoff, number-> frequency, pan mid
//startnumber->cutoff, highest value -> frequency, pan right
//startnumber->cutoff, longest series -> cutoff, pan left
(
var highest=1, longest=1, starthighest=1, startlongest=1;
var numberbeep, highestbeep, longestbeep;
numberbeep=Synth(\beep, [\freq, 200, \cutoff, 200, \pan, 0]);
longestbeep=Synth(\beep, [\freq, 200, \cutoff, 200, \pan, -1]);
highestbeep=Synth(\beep, [\freq, 200, \cutoff, 200, \pan, 1]);
Routine({
for (1, 100, { arg startnumber;
var number, length=1, maximum;
number=startnumber;
maximum=startnumber;
(number.asString+" ").post;
numberbeep.set(\cutoff, 100*startnumber);
while ( {number>1},{
if (number.asInteger.even, {number=(number/2)}, {number=3*number+1});
length=length+1;
if (number>maximum, {maximum=number});
numberbeep.set(\freq, 30+number);
longestbeep.set(\freq, 75*length);
highestbeep.set(\freq, 30+maximum);
0.1.wait;
});
if(length>longest, {longest=length; startlongest=startnumber});
if (maximum>highest, {highest=maximum; starthighest=startnumber});
longestbeep.set(\cutoff, 100*longest);
highestbeep.set(\cutoff, highest*2);
("length: "+length.asString).post;
(" maximum: " + maximum.asString).postln;
});
postf("longest series % at % \n", longest, startlongest);
postf("highest value % at % \n", highest, starthighest);
numberbeep.set(\freq, 30, \cutoff, 10000);
longestbeep.set(\freq, 75*longest, \cutoff, 100*startlongest);
highestbeep.set(\freq, 30+highest, \cutoff, 100*starthighest);
10.wait;
numberbeep.free;
highestbeep.free;
longestbeep.free;
}).play;
)