Some Sonifications of Problem 1.

First - boot the server and create a really basic sine wave synth:

z = Server.internal;

SynthDef("sine",{ |freq=100, atk=1, rel=1,sus=1, amp=0.005,pan =0,gate=0 |
Out.ar(0,Mix.ar(Pan2.ar(SinOsc.ar( freq * [1,1],0,amp),pan)) * EnvGen.ar(Env.perc(atk,rel,sus),gate, doneAction:2) );
}).load(z);


The first sonification is really basic - just run through the sequence of frequencies returned by the series and if the frequency f is greater than 0, then play the note at that pitch (times 8 so that the lowest notes are audible). The amplitude is scaled back over a pink noise curve (1/f) so that the low freqs are nice and full and the high freqs are not piercing.

(
Routine {
       //generate our numbers
 ({|i|i}!1000).collect({|i|((i%3==0).or(i%5==0)).if({i},{0})}).collect({|f,i|
  var s;
  f.postln;
  (f != 0).if({
          //allocate a sinewave synth
                 s = Synth("sine");
                       //frequency
   s.set(\freq,f*8);
                       //scale back the amplitude
   s.set(\amp,0.001,\atk,0.001,\rel, 1/3 ,\sus,-32,\gate,1, \amp, 1/(f+1) * 1/16);
  },{});
  (1/12).wait;
 }).sum;
}.play;

)

You can hear the 3/5 rhythm really clearly in this example:


1.0 by Backtrace

In the second sonification, I leave the notes on a long release so that many of them play simultaneously, and I lock the pitches to a single octave. As the notes build up, you can hear the same 3/5 rhythm, only this time as a differnce tone between frequencies.

(
Routine {
 ({|i|i}!1000).collect({|i|((i%3==0).or(i%5==0)).if({i},{0})}).collect({|f,i|
  var s, freq;
   freq = f*(512/ (2**f.log2.ceil));
  f.postln;
  (f != 0).if({
   s = Synth("sine");
   s.set(\freq,freq );

   s.set(\amp,0.001,\atk,0.001,\rel,(1000-i)/8,\sus,-32,\gate,1,  \amp,(1/ freq )*1/12);
  },{});
  (1/12).wait;
 }).sum;
}.play;
)

1.1 by Backtrace