The piano work under construction started with randomly permuted notes in the lowest register of the instrument played with an even 16th-note rhythm. It then used this material to transition from the lowest to middle register with an accompanying crescendo from piano to fortissimo. Now in the middle register it needs something new.
The new in a piece can be discovered through the old, through seeing what is established and imagining potential contrasts, which can serve as next steps in a piece. In this piano work, the even 16th rhythm is well established. Contrasts to this would be an uneven rhythm or a different pulse, perhaps triplets, for instance. Texture is well established. The original randomly permuted line is monophonic that, with the addition of the right hand, becomes a kind of accompaniment. (I'm reluctant to call it a contrapuntal voice since both right and left hands play the same notes, but it does have this quality as well.) A change in the relationship between the music in each hand would contrast established textures. Variation is well established. While it seems that we've repeated something 12 times so far, through the creation of a randomly permuted series, each result yields something distinct. There has been no exact repetition in the work. Register is well established. Everything until this point in the work has taken place in the lower registers of the instrument. Exploring the upper registers would be a contrast to this. The challenges with this aspect of the compositional process are threefold. First, while as many established presumptions as possible need to be discovered, this can be difficult since they are presumptions and by definition go unquestioned. Second, for each, a composer needs to think about what potential contrast looks like. If there has been a lot of repetition, for example, it's clear that using variation or a series of new materials would be contrasting. But what do the variations or new materials look like? Finally, the composer can't employ all potential contrasts. Instead, certain ones need to be selected. This selection process is a kind of discernment that needs practice. It's a precarious act because the choice can influence what comes later on, that is, the contrasts that will be necessary to these contrasts being selected, which the composer often can't yet see or hasn't yet imagined.
I'll challenge the following established dimensions of the work:
1. Instead of even 16th notes, I will use triplets and the rhythm will not be even.
2. Dynamics will not be consistent, as in part 1, or gradual, as in part 2, but instead contrasting with abrupt changes.
3. There will be 2 types of material rather than 1. This will also abruptly change like the dynamics.
4. Everything will take place between middle C and two octaves above it.
5. I will add pedal and change the resonance of the instrument.
Ironically, these contrasts will result from a substantial reuse of previously written code. But the reuse of code is sensible because it is not typically a composer's goal to change everything in the music, but instead a few aspects of it. For instance, to change from 16th notes to triplets, this familiar code,
(length-legato (position-replace l '1/16 (make-list 12 :initial-element '-1/16)))which was used to generate a rhythmic grid for the melodies in the previous post, becomes:
(length-legato (position-replace l '1/12 (make-list 12 :initial-element '-1/12)))The only difference is that the value 1/16 has been changed to 1/12. (A 12th of a 4/4 bar is the length of a triplet, which is how this note value is expressed in the programming environment I use.)
(setf sers-3 (loop repeat 6 collecting (rnd-order '(0 1 2 3 4 5 6 7 8 9 10 11))))By now, you can probably read this and know what it means. We set a variable called sers-3 and assign to it a list of 6 sublists, each of which is a random permutation of the values 0 to 11. Again, this was used previously. There's no need to change it for this new section but we will use it differently.
4-6 index values will be selected. Half will be used to "filter-first" values from a randomly permuted series of values from 0 to 11, the other half will be used to "filter-last" from the same series. The filter-first values will be assigned as index values to the right hand pitches, and the filter-last ones to the left hand pitches. Below is an example to illustrate.
In the first bar of the example, the randomly permuted series is played in rhythmic unison in both hands, with the right hand placed an octave above the left. In the second bar, a different randomly permuted series indicates index values. The first 3 are used as index values for the right hand, selecting which pitches will remain. The last 3 are used in the same way for the left hand. In the final bar, rests have been replaced with ties to make the passage legato. What results in a contrapuntal texture. While I won't share the code for this here, you can imagine that it has a great deal of similarity to what you've seen previously since the processes are very similar.
To build this section of the piece, there will be 5 events of this contrapuntal music. Each will be separated by a very contrasting bit of music. This contrasting bit of music will always be the same, that is, it will be an exact repetition, yet its character will be derived directly from the original material of the composition. Note that it contrasts with the contrapuntal music in articulation and resonance - no pedal will be used in this bar - as well as speed and dynamic.
The 5 contrapuntal events will incorporate a transformation through an increase in the number of bars. While first event will be 6 bars long, the following events will be 2, 3, 5, and 8 bars, respectively. These are Fibonacci numbers, a series of numbers that result from adding the previous two values together, [1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ...]. Fibonacci numbers work well in transformations where neither the evenness of a geometric series, e.g., 2, 4, 6, 8 nor the expanse growth of an exponential series, e.g., 2, 4, 8, 16, 32, is desired.
The Fibonacci series is also used to determine where ff attacks occur within the more general pp environment. The distances of 13, 8, 5, 3, 2, and 1 attacks are used to place the fortissimo.