Tool #10: Additive Processes

In this post I’d like to go back to an idea referenced in Tools #3 and #3.1: generating a list of techniques for motivic development.  One such technique is actually a technique with a large standalone reputation, especially in more modern/postmodern music.  This technique is the “additive process”.

Some pieces are additive processes alone.  Frederic Rzewski’s Les Moutons de Panurge is a piece in which the players play the notes in additive fashion (eg. note 1, notes 1 & 2, notes 1, 2, &, 3) and then subtract notes once the whole sequence of 65 notes has been played in full (so 1-65, then 2-65, 3-65, etc.).  This is a challenging piece because even though it uses a relatively small pitch class set, it is not fully notated and the rhythms are irregular; all you have is notes 1 through 65, and you make the additive process by moving your eyes back to the first note at each iteration of the sequence.  I have played it before: it can take up to 40+ minutes to play, and is a workout mentally, physically, and on one’s instrument.

However, instead of pieces that are entire processes, now I’d like to discuss additive processes in the form of motivic development.  Here are some ways additive (and subtractive) processes can be used:

  • After having come up with a pitch class set, you can add them one by one, two by two, or at random.  So, if I come up with B-D-A#-F-F#-A-G-E, I could order them as: B, B-D, B-D-A (one note at a time); B-D, B-D-A#-F, B-D-A#-F-F#-A (two notes at a time); or B, B, B-D, B-D-A#, B-D-A#-F-F# (here the number of notes corresponds to the Fibonacci series, which is an additive process in itself: 1, 1, 2, 3, 5, 8…).
  • You can also subtract values in similar ways to the ones above in order to focus on a certain pitch, for example subtracting pitches until you reach B again as the sole note.
  • You can add or subtract rhythmic value to notes.  For example, every D in the examples above could have an added eighth note value to it, and the other notes could be truncated to make it work metrically.  This would make the D stand out more.  Conversely, I could subtract values from the D to make it eventually disappear from the sequence.
  • You can add phrases or larger chunks of music.  Four themes can be added to one another in an order, even if you only use one bar of them.  For example, bar 1 of each of four themes could be ordered: Theme 1 + Theme 2, T1 + T2 +T3, T1 + T2+ T3 + T4.
  • You can add or subtract silence.  In my piece for marimba and drum set I use irregularly timed silence to create tension, space, and uncertainty as to when the next phrase will begin.  I did this by altering the time signature of certain measures of rest.  While I didn’t use an additive process in that section, I could have, and the effect would have been somewhat the same, but a little more comprehensible; the silences would have kept getting longer and longer, instead of having been their seemingly random durations.
  • You can apply additive/subtractive processes to articulations, dynamics, or other markings, for example creating new accents on repeated notes.  If you have a string of eighth-note “A”s, you could apply accents in on A1, A1 & A2, 1-2-4, 1-2-4-8, 1-2-4-8-16, etc. (here I am using an exponent with base 2, so  2 ^0, 2^1, 2^2, 2^3, and 2^4 are ordered in additive fashion).
  • You can add harmonies and intervals to stacked notes.  If you want to slowly build a quartal chord, you could add the root, root+perfect fourth, r+P4+TT, r+P4+TT+P4, r+P4+TT+P4+TT, etc. (here I am alternating added intervals between the Perfect Fourth and Tritone).
  • You can add instruments and voices in orchestration.  This works well for building volume and excitement, and the reverse applies for subtracting instruments and voices in orchestration.

As you can see, there are a myriad of possibilities with additive and subtractive processes, many of which go beyond just adding pitch classes or rhythmic values.  Try it out, and let me know what you think!

Thanks for reading!


One thought on “Tool #10: Additive Processes

  1. Pingback: Zekai Liu – Enigma – Composer's Toolbox

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