This is a final version of the Games piece I’ve been working on for a while. It’s scored for cellos, finger pianos, baritone guitar, balloon drums, and a small sewer pipe drum. The tuning is Adams, a 12-note scale taken from 72 EDO. Here’s the Scala file:
12 out of 72-TET
The key to this scale is the tremendous variety of step sizes, and the presence of three different major scales. But that leaves some really weird wolfish modes. This piece exploits four of them. I take six notes at a time:
In the chart, the ratios relative to the #1 note, the root of the chord are shows on the left, and the ratios to the #2 note are on the right. Notice that the B- neutral chord third note is neither major nor minor, at a ratio of 27:22. In 72 EDO steps, that’s 21 steps, exactly midway between a 5:4 at 23 steps, and a 6:5 at 19 steps. Notice also that there’s a just C major using steps 2, 4, and 6 buried in the scale. The same is true of the E minor/F major six note scale.
At any given moment, each instrument has a wide variety of choices for what to play next, or remain silent. The choices are random, but in this piece, in honor of the “Games” title, I’ve made sure that the choices follow a Markov chain “drunkard’s walk”. From the wiki:
A famous Markov chain is the so-called “drunkard’s walk”, a random walk on the number line where, at each step, the position may change by +1 or −1 with equal probability. From any position there are two possible transitions, to the next or previous integer.
In many cases, the instruments are constrained to pick either the next alternative in their list, or the previous one. Sometimes the actual scale follows the drunkard’s walk, going up by one degree or down by one, no more. But much of the melody is composed. The hitch is that the melody has seven different ways it can be played:
- straight composed melody on the six notes in the mode
- each note is trilled to the next note in the scale
- glissando to the next note in the melody
- play the note 2 steps above the straight choice
- play the note 2 steps below the straight choice
- be silent
This introduces a good deal of indeterminacy. If one instrument is playing the “straight” melody, then the Markov Chain would constrain the next instrument to play the melody with trills, or the note 2 steps below the straight choice. With four cellos picking their way through their seven choices, you never know what you’re going to get next.
The rhythm has a kind of drunken walk to it as well. It’s either in 4/4 with 9 microbeats per quarter note or 4/4 with 6 microbeats per quarter note. So it kind of sounds like slow four, fast four. It’s as if he were staggering around the dance floor and almost falling down at times, but recovering to continue.
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Or download here: Games.