Here is another version of Games, this one with a better implementation of the Markov Chain Drunkard’s Walk randomization method. The previous one had a bug that failed to allow choice across the entire list of alternatives. I regret the error.
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This is a work in progress. I’ve been noodling around more with the Markov Chain Drunkard’s Walk. This version is a more explicit implementation of that random algorithm. The finger piano and guitar parts are strict followers of the chain, while the bass part is composed. This is just a vamp at this point. I plan to add alto flute and English horn next, then the balloon drum and tube drums. The rhythm is a nice jumpy 4:4, with 9 microbeats per quarter note. It starts out as 9 6 3 3 9 6 = 36 microbeats per measure.
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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-Adams.scl
!
12 out of 72-TET
12
!
200.000
266.667
383.333
433.333
500.000
550.000
700.000
883.333
966.667
1050.000
1083.333
1200.000
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:
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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This is a work in progress. This week I’ve been adding more variations to the melody.
As of now, it has the following choices:
There are two melodies now, one in B- Neutral, and one in D Minor. The first has all the variations implemented, the second does not yet. It’s time consuming to make all the variations. For example, here are the variations in the second measure melody part.
.mel-36a2a d9h10e8&pre-&n6.. &pred-&n6.-&n5.. &preu-&n5.-&n1.. d3h4&preu-&n1.-&n2.. &preu-&n2.-&n3.. &preu-&n3.-&n4..
.mel-36a2b d9h16e39&pre-&n6..&tril-&n6.-&n1.. &pred-&n6.-&n5..&tril-&n5.-&n6.. &preu-&n5.-&n1..&tril-&n1.-&n2.. d3h16e37&preu-&n1.-&n2..&tril-&n2.-&n3.. &preu-&n2.-&n3..&tril-&n3.-&n4.. &preu-&n3.-&n4..&tril-&n4.-&n5..
.mel-36a2c d18h19e8&pre-&n6..&slidd-&n6.-&n5.. d9h10&preu-&n6.-&n1..&slidu-&n1.-&n2.. &preu-&n1.-&n2..&slidu-&n2.-&n4..
.mel-36a2d d9h10e8&pre-&n6..&trem-9*. &pred-&n6.-&n5..&trem-9*. &preu-&n5.-&n1..&trem-9*. d3h4&preu-&n1.-&n2..&trem-3*. &preu-&n2.-&n3..&trem-3*. &preu-&n3.-&n4..&trem-3*.
.mel-36a2e d9h10e8&pre-&n2.. &pred-&n2.-&n1.. &preu-&n1.-&n3.. d3h4&preu-&n3.-&n4.. &preu-&n4.-&n5.. &preu-&n5.-&n6..
.mel-36a2f d9h10e8&pre-&n4.. &pred-&n4.-&n3.. &preu-&n3.-&n5.. d3h4&preu-&n5.-&n6.. &preu-&n6.-&n1.. &preu-&n1.-&n2..
.mel-60a2a d9h10e8&pre-&n6.. &pred-&n6.-&n5.. &preu-&n5.-&n1..d33h27 d3h4&preu-&n1.-&n2.. &preu-&n2.-&n3.. &preu-&n3.-&n4..
mel-36a2a is the straight melody. a2b is with trills added. a2c is the slide. a2d is the tremulo. a2e is up a third/fourth. a2f is another third/fourth.
You just never know who will play what at any given time.
I am never happy with the viola or violin samples in the McGill University Master Sample set. Nor any others I’ve tried. So all four are now the cello martele set from McGill. I always come back to that one. Whoever made them was really dramatic that day. Must have had an extra few cups of coffee that cold day in Montreal. Masterful. I’ll have to boost the volume some more in that part in the next mix.
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This is a work in progress. I’ve added a counter melody in D minor to the B- neutral. And the rhythm was modified. It was originally in 4/4, with 9 microbeats per quarter note, for a total of 36 microbeats per measure. Now it also has some with 60 microbeats, divided into six nine beat quarter notes plus an extra 6 beat in the middle of each measure. It’s more like a dance in which the dancers stop in the middle of each measure before moving on.
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This is a work in process. Today’s entry is a new song in the Second of July series using the Adams 12 non-equal tuning. This one uses a mode with a seriously neutral third. It has kind of a funeral vibe. The ratios of the six notes in the mode are:
1:1 12:11 27:22 15:11 3:2 18:11
Note the 27/22 third. In my 72-EDO tuning, that is 21 steps above the root, compared to a normal just major third ratio (5:4) at 23 steps, and a typical 6:5 minor third at 19. So it’s just two 72-EDO steps above minor, and two steps below major. Definitely funereal.
I’m working on a melody that can be played in unison by several instruments. But each can choose either a straight version of the simple melody, or one with trills, or one that slides from note to note. Each instrument picks one of the three, and there is a high likelihood that each will pick a different one. This way I end up with a mix of the three difference versions by the cello, violin, finger piano, and baritone guitar.
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This is a piece scored for baritone guitars, finger pianos, flutes, and vibraphone. It uses a 12 note scale taken from 72-EDO.
Each instrument has a very wide variety of phrases it can play at any given moment, including the option to play another instrument’s phrase in unison. There are a wide variety of ways I can move from one mode to another, and back again. Some of the sliding is within the scale, some is from one mode of the scale to the next, or the previous. The length of the piece depends on some of the paths through the chosen phrases, but almost all take about four minutes. The tempo varies from slow to fast and back to very slow at the end. The rhythm is mostly two against three.
There is no particular melody, just triademonium in the hexads:
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There is more indeterminacy in this piece than most, so I’m having trouble picking the version I want to keep. Here are two iterations for your listening pleasure. There is no particular melody, just triademonium in the hexads:
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This is a work in progress. I’ve made four versions at this point and will listen to see which one to keep. Here is the fifth pass through the algorithm with different degrees of randomness vs repetition. There is no particular melody, just triademonium in the hexads:
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This is a work in progress. Now each instrument can also play the other’s parts as well as its own. They move through these chords, spending a random amount of time in each:
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