Formally Speaking
This piece is construced of five (5) distinct patterns. The patterns were created by the fractal equation known as the Mandelbrot set. The equation looks like this:
Z => Z ^ 2 + C
The equation requires an initial value for the variable C which is a complex number. I used the following two seeds for the initial value of C.
C = -0.745454545454545
and,
Ci = 0.435897435897436
Then...the equation is calculated to produce new values for the variable Z (and those new values are then used in the next iteration(s) of the equation recursively).
The value of Z approaches infinity at the eigth iteration -- hence the title of the piece. In other words, after calculating the values of Z seven times then our mathematical tools (like numbers) become rather meaningless and modern computers cannot calculate numbers at those depths.
Each pattern was "translated" into musical elements by assigning the values of C and Ci to either MIDI pitch numbers or durations, and the values of Z to velocity. By that I mean that the five (5) unique patterns are derivatives of the exact same set of numbers by assigning those numbers to musical elements as follows:
- Piano 1
- Pitch numbers: Generated by the values of C
- Durations: Generated by the values of Ci
- Piano 2
- Pitch numbers: Generated by the values of Ci
- Durations: Generated by the values of C
- Piano 3
- Pitch numbers: Generated by the values of C
- Durations: Generated by the values of Ci
- Then all vaues were converted to absolute values (no negative numbers!)
- Piano 4
- Pitch numbers: Generated by the values of C
- Durations: Generated by the values of Ci
- Then all vaues were converted by the Sine() function
- Piano 5
- Pitch numbers: Generated by the values of C
- Durations: Generated by the values of Ci
- Then all vaues were converted by the CoSine() function
After the translation of each pattern, three (3 of the patterns became eighty (80) units in length (repeating forever of course), the fourth became twenty-eight (28) units, and the fifth became forty-eight (48) units. If each unit is considered to be an eighth-note (arbitrarily), then three (3) of the patterns are ten (10) measures long (in common time) while the other two (2) patterns are seven (7) and twelve (12) measures respectively.
Therefore, performing the five (5) patterns simoultaneously will create a loop where patterns 1, 2, and 3 repeat twenty-one (21) times while pattern 4 will repeat sixty (60) times while pattern 5 will repeat thirty-five (35) times.
Although I did not choose the pitches the results were limited (normalized) to the 12-note well-tempered scale. As it turned out the patterns oscillate between E-flat and B major.
Comments for Performance
If you have intentions of performing this piece or including this piece in a musical event of any kind then I would love to know about it...and perhaps attend the performance. Currently this piece has only been performed by my computer (and perhaps yours).
On a dissimilar note: I am normally opposed to using computers to emulate acoustic sounds. I believe the computer to be an instrument in and of itself...but it has different faces. Sometimes I feel it's appropriate to consider a computer to be not an instrument but merely a tool by which acoustic pieces are created. Having said that, I consider this piece to be an acoustic piece composed by electronic means and not an electronic piece (and I'm sad that I haven't yet heard the piece with five pianists).