The piano piece is nearly complete. I'd like to add one last section, which will offer a new material. In a previous post, I mentioned that identifying presumptions in a composition is difficult because presumptions are by definition unquestioned. There is one aspect of this work that has not been questioned, which when I mention it, might surprise you and illustrate why presumptions are sometimes difficult to see. Everything up to this point in the piece has been built from melodic lines of single notes. There are no chords. A component considered essential to music making has been absent all along and it wasn't missed. Hence, the last section will shift to chords.
Keeping with the goal of generating everything from random permutation, it would be sensible to randomly permute a list of values from 0-11, then assign the first 6 to one hand and the last 6 to the other. That would look something like the following:
(setf ser (rnd-order '(0 1 2 3 4 5 6 7 8 9 10 11)))
(setf rh-chord (filter-first 6 ser))
(setf lh-chord (filter-last 6 ser))This would be fine if humans had 6 fingers on each hand, or better still, 7, just to be safe. While there are many 6-note configurations within an octave that can be played by a single hand, there are many that cannot be. One could devise an algorithm that would ensure that the chord could be played by a single hand, but I won't explore that here. Instead, I will limit each hand to 4 notes. That is almost guaranteed to work.
(setf ser (filter-first 8 (rnd-order '(0 1 2 3 4 5 6 7 8 9 10 11))))
(setf rh-chord (loop for p in (filter-first 4 ser) collecting (+ 96 p)))
(setf lh-chord (loop for p in (filter-last 4 ser) collecting (+ 84 p)))The variable ser returns the first 8 values in a randomly permuted list. The variable rh-chord take the first 4 values of ser and iterates through them, adding 96 to each, thus placing them in the highest octave of the piano. The variable lh-chord takes the last 4 values of ser and iterates through them, adding 84 to each, placing them in the second highest octave of the piano. Repeating this 10 times and applying the same rhythm to each chord yields the following:
After about 5 chords I feel the music needs an added dimension. Since this is the end of the work, I will add in a small transformation that slows the music down. Starting with the sixth chord, the lowest note in the left hand is repeated, first at a 1/8 note pulse, and then gradually slower. Since the original pulse results in 13 repetitions, this will be the number of repetitions with each new chord. But because the pulse slows with each new chord, the duration of that chord increases. This is one of the adjustments I made when assembling the 5 parts of the work into a final piece. Other adjustments were as follwings:
I felt the 6 repetitions of a randomly permuted series at the very beginning was a bit too long. I used the last two to insert a melody in the right hand, only the melody in these 2 bars is not doubled at the octave and the 2 beats of rest is maintained.
I took a moment at the end of section 2 to invert the behavior of its 2 materials. This occurs in the score in mm. 41-49. Here the randomly permuted series that has been repeated at ff is played pp and the pedal is held rather than being released. The last note of the contrapuntal material, a F#, is repeated at ff. The finished piece can be heard below.