1 2 1 3 1 2 1 4 1 2 1 3 1 2 1 5 1 2 etc.

[Henry Gould]

Jeremy Gardiner sent us the following program

100 rem fractal music
110 rem written for iMac in Chipmunk BASIC
120 rem copyright (c) 2000 J. C. Gardiner
130 cls
140 call wintitle,"Fractal Music"
150 rem graphics window  x, y, width, height
160 graphics window 30,280,530,150
170 x = 10
180 y = 140
190 moveto x,y
200 dim scale(8)
210 scale(1) = 261.6
220 scale(2) = 293.7
230 scale(3) = 329.6
240 scale(4) = 349.2
250 scale(5) = 392
260 scale(6) = 440
270 scale(7) = 493.9
280 scale(8) = 523.3
290 g(8)
300 print ""
310 stop
320 function g(n)
330 if n > 1 then g(n-1)
340 rem plot fractal in graphics window
350 lineto x,y-15*n
360 x = x+2
370 moveto x,y
380 rem sound frequency, duration, volume
390 print n;
400 sound 1*scale(n),0.4,100
410 if n > 1 then g(n-1)
420 return
430 end
I downloaded his Chipmunk Basic, and just entered RUN and got the ruler
printing out and the sequence
1 2 1 3 1 2 1 4 1 2 1 3 1 2 1 5 1 2 1 3 1 2 1 4 1 2 1 3 1 2 1 6 1 2 1 3 1 2
1 4 1 2 1 3 1 2 1 5 1 2 1 3 1 2 1 4 1 2 1 3 1 2 1 7 1 2 1 3 1 2 1 4 1 2 1 3
1 2 1 5 1 2 1 3 1 2 1 4 1 2 1 3 1 2 1 6 1 2 1 3 1 2 1 4 1 2 1 3 1 2 1 5 1 2
1 3 1 2 1 4 1 2 1 3 1 2 1 8 1 2 1 3 1 2 1 4 1 2 1 3 1 2 1 5 1 2 1 3 1 2 1 4
1 2 1 3 1 2 1 6 1 2 1 3 1 2 1 4 1 2 1 3 1 2 1 5 1 2 1 3 1 2 1 4 1 2 1 3 1 2
1 7 1 2 1 3 1 2 1 4 1 2 1 3 1 2 1 5 1 2 1 3 1 2 1 4 1 2 1 3 1 2 1 6 1 2 1 3
1 2 1 4 1 2 1 3 1 2 1 5 1 2 1 3 1 2 1 4 1 2 1 3 1 2 1
about which I had asked. So it is INDEED MUSIC and Jeremy Gardiner himself
verified this today. Now how about a Sloane Symphony No.1 in C major? Or
maybe Cesar Fibonacci in D minor? I actually do some composing of my own
with two programs I have in my computers here. Next to mathematics music
offers a sequence of pleasure. I have written my best research papers in
number theory and combinatorics while listening to Mozart's symphonies 39,
40, 42, K.199 (bassoon concerto), and Eine Kleine Nachtmusik. Mozart forms a
sequence for the mind. . . . Oh . . . and J. S. Bach also!!! Overtures
anyone? Can we get interesting sequences from these guys' work?