Wolfram Science Group
Phoenix, AZ USA
Registered: Aug 2003
Listening to the ECAs & the Tones Interface
While the Wolfram Tones site allows all sorts of complicated mappings to mimic various styles, it can also be used with minimalist mappings to "hear" the structure in CAs. In this post I'll explain how to look through the ECAs this way, using the Tones site interface.
Here is a good starting point -
Right click that link and "open in new window".
That is rule 30 playing. Pick "create your own", and you will keep all those settings while going to the "generate a composition" page. Ignore for now the style options in the middle of the page, and focus on the bottom set of four buttons, under the banner "composition controls". Press the leftmost button, labeled "generator". This expands the composition controls window, with the four buttons now acting as tabs, each bringing up a different portion of the controls.
I'll explain the settings on each of the tabs, and how one can use them to listen to the ECAs in particular.
Right now we should be on the "generator" tab - go back to it if you browsed around in the meantime. This is the place we specify the rule being used, and other details of the underlying CA. We have a number of controls here.
The rule type is set in a drop down menu. Right now it should show "7 (r=1)" Those are the range 1, 2 color ECAs - don't worry about the numbering scheme for now. If you click on the drop down you will see an entry for "31 (r=2)" - those are the range 2, 2 color, general CAs, a much larger rule space that you might want to explore after the ECAs.
Next is a text entry field labeled "rule". That is the rule number in the standard Wolfram and Mathematica numbering scheme. As you can see, right now it reads "30". You can type right in that field. Backspace over the 30 and type in 110. Note that the change does not take effect until you hit "return". The graphic above will change and rule 110 will start playing, its periodic background taking over pretty rapidly.
The next field is labeled "seed" and specifies the initial condition. You can hit "vary" a few times to hear how different initials affect the sound. You should find a few with longer notes. Try seed 12897 if you haven't found one yet, to see what I mean. But the overall sound will be characteristic. Sometimes you will get a narrower pattern that does not fill the whole graphic. That happens because rule 110 grows only on the left, and some initials will have the "highest" 1 away from the top.
Now, while making sure the "width" is still set to 13 as I had it, put the number 8193 in the "seed" field. You should get a pattern starting from a single 1 on the top. 8193 is 13^2 + 1. Put in 8192 and you get a blank pattern with no notes at all! That is because that initial is all 0s. Now try 8321, which is 8192 (all zeros) plus 1 plus 128 = 2^7. You get 2 initial 1s, in the top position and 7th or middle position. To hear rule 30 from a single black cell with width 13, change the rule to 30 and the initial condition to 8193.
Next, try entering rule 45 and try a few seeds for it. You should find some of the liveliness of rule 30 and some of the note length variation of 110, even more at times. Be sure to try it with seed 8320, which is a single 1 in the middle (7th) position.
Next there is a slider control that determines the height, that is the width of the CA evolution returned in NKS terms. With the rule still set on 45, try changing the height to 17. You will hear some higher notes over the previous style, which sound pretty nice. Notice that the number in the "seed" field increased, while the initial pattern on the graphic remained the same. The numbering scheme for initial conditions depends on the overall width, so it has to go up to accomodate the greater width. One 1 in the 7th position is now seed number 133120, for example.
Now try lowering the height to something really low, like 6. The "pipe" through the CA narrows and the notes are all low. Notice how much smaller the "seed" number is - there aren't nearly as many possible initial conditions for a region only 6 cells width. (Note that narrow pipes with cyclic boundary - see below - force repetition for the "systems of limited size" reason discussed in the book. They are suitable for "signalling" style tones). Set the width back to 17, and vary the seed a bit, to get a feel for the variety present in just rule 45.
Now trying changing to rule 54, which is much more repetitive. Enter seed 199716, and listen to the changes in those periods as the small background defects move across the pattern.
The last field you see is a little checkbox marked "cyclic boundaries". With the rule on 54 and the seed on 199716, check it. Hit stop up above when you get tired of the resulting repetition. What changed? Now we are "wrapping" the CA array around, with info leaving the bottom of the piece reappearing on the top. Before we were in effect taking a narrow slice through a wider CA evolution. Now we are getting the evolution through a narrow cylinder. Change the seed to 198180. While still repetitive, that is much more pleasant. A few persistent structures are moving across the pattern, and you hear the resulting "hole" in the pattern of notes, as variation in the chords being sounded.
Change the rule back to 45. Explore a few other rules, like 18, wrapped and unwrapped. Sometimes there can be considerable quiet periods in this one when not cyclic boundary, as the slice is through a large white triangle in the underlying CA evolution.
You can see a typical whole evolution of the selected rule, from wide random initial conditions, by hitting the "show evolution" button on the upper right of the "generator" tab. You must allow pop ups to see this. You get a black and white pop up window showing that CA's typical behavior. Close the pop up window by clicking on its upper right box as you would any other window. End back on rule 45, non-cyclic, 17 wide.
Next hit the instrumentation tab. You can see we are using a single instrument, electric piano 1, with a role listed as polyphonic.
Try changing the instrument to Vibraphone. Now try Guitar (nylon). Harp. Tubular bells. Back to piano, but grand rather than electric. Go back to the "generator" tab and change the rule to 110, the width to 13, cyclic boundary checked, and set the seed to 12897. Now go to the instrument tab and change the instrument to Strings (Legato).
There is a lot more about "roles" on that tab, more relevant for trying to find styled music. Let's instead go on to the "pitch mapping" tab. You see the scale listed there, "Scottish Penatonic". This is a particularly forgiving scale with most transitions "allowed", which works well with dense underlying data and a polyphonic role. Take that a step further by changing the scale to "Bi Yu (China)" - a scale with only 4 notes. Sounds particularly good with strings in my opinion. The musical pitch slider can be used to raise or lower the whole composition by changing the base note.
Back on the generator page, switch back to rule 45 17 wide non-cyclic, and change the instrument page to our original electric piano. Now change the scale to mixolydian hexatonic, which allows more distinct transitions but is still pretty forgiving.
The last tab is "time controls". You see we have been playing 100 beats per minute and 4 notes per beat, and have used 200 steps of CA evolution each time. Try slowing it down to only 60 beats per minute. Try the Strings (Legato) at that speed.
By now you should have the hang of it. Look at rule family 31 (r=2) and explore. I hope this is helpful, and have fun.
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