EVOL – The Chord Catalogue for Eight-O-Eight

I made some charts for EVOL’s latest album. The Chord Catalogue for Eight-O-Eight is inspired by Tom Johnson’s The Chord Catalogue which entails playing on a piano every possible chord for every combination of notes in an octave from 2 to 13 notes. EVOL have done a similar thing with the 16 notes on a TR-808 drum machine. The small difference between Johnson’s maximum of 13 notes and EVOL’s maximum of 16 notes leads to a large difference in the total number of chord combinations: 8,178 vs. 65,519. Whatever the maximum number of notes, as the number of notes per chord increases the number of possible combinations first increases and then decreases, with the final chord that contains all notes having just one possible configuration. Here’s the number of combinations for 2 to 16 notes:
{120, 560, 1820, 4368, 8008, 11440, 12870, 11440, 8008, 4368, 1820, 560, 120, 16, 1}
The chart below shows those numbers plotted. You might notice that it’s almost symmetrical, which it would be if counting the number of combinations for 0 to 16 notes:
{1, 16, 120, 560, 1820, 4368, 8008, 11440, 12870, 11440, 8008, 4368, 1820, 560, 120, 16, 1}

Instead of analysing the data that EVOL actually used, I recreated it in Mathematica code using the function ‘Subsets’ which gives a list of all possible subsets of a given list and a given number of elements. For example, here’s all subsets for 2 note chords from a possible 16 notes (‘Range[16]’ is just a short way of writing the full list of numbers 1 to 16):

In[32]:= Subsets[Range[16],{2}]
Out[32]= {{1,2},{1,3},{1,4},{1,5},{1,6},{1,7},{1,8},{1,9},{1,10},{1,11},{1,12},{1,13},{1,14},{1,15},{1,16},{2,3},{2,4},{2,5},{2,6},{2,7},{2,8},{2,9},{2,10},{2,11},{2,12},{2,13},{2,14},{2,15},{2,16},{3,4},{3,5},{3,6},{3,7},{3,8},{3,9},{3,10},{3,11},{3,12},{3,13},{3,14},{3,15},{3,16},{4,5},{4,6},{4,7},{4,8},{4,9},{4,10},{4,11},{4,12},{4,13},{4,14},{4,15},{4,16},{5,6},{5,7},{5,8},{5,9},{5,10},{5,11},{5,12},{5,13},{5,14},{5,15},{5,16},{6,7},{6,8},{6,9},{6,10},{6,11},{6,12},{6,13},{6,14},{6,15},{6,16},{7,8},{7,9},{7,10},{7,11},{7,12},{7,13},{7,14},{7,15},{7,16},{8,9},{8,10},{8,11},{8,12},{8,13},{8,14},{8,15},{8,16},{9,10},{9,11},{9,12},{9,13},{9,14},{9,15},{9,16},{10,11},{10,12},{10,13},{10,14},{10,15},{10,16},{11,12},{11,13},{11,14},{11,15},{11,16},{12,13},{12,14},{12,15},{12,16},{13,14},{13,15},{13,16},{14,15},{14,16},{15,16}}

The challenge was how to visualize the whole dataset that varies greatly in the the size of its parts. After some trial and error, what worked quite well was using simple line or point plots while keeping the charts to the same size, which has the effect of cramming in the data points for the larger sets. While this makes it impossible to read the detail in the larger sets, this approach shows the overall structure and how the sets change as the number of notes increases. The final charts used a colouring system based on note order (1st, 2nd, etc.) rather than note name (i.e. pitch on a piano / instrument on the 808). Here’s the final two charts:

You may notice that these show 16 sets each, more than the 15 sets that EVOL actually play. I included the set for 1 note chords to get an even number of plots. I also made a couple of GIFs from the individual plots:

As I’d recently made a spectrogram showing the whole of Cristian Vogel’s album Eselsbrücke, I thought it would be good to see what EVOL’s album looks like. The longest track is just under 26 minutes and the shortest is 4 seconds:

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