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This is a piece I’m working on that relies on several different Drunkard’s Walk chains, some sequential, some that skip over every other note. I’m not convinced it has hidden it’s algorithmic nature well enough. But this gives me a chance to listen to several different runs through the randomizer.

The title is the weather term for the frost that forms on the windward side of trees in the mountains caused by freezing fog and snow.

It’s scored for Alto Flute, French Horn, Trombone, Tuba, Finger Piano, Baritone Guitar, and Balloon Drums. The primary key is F Major otonoality from the Partch Tonality Diamond. Where the notes in relation to the F in 72 EDO are 30 42 53 63 0 16 8 23 30. In ratios that’s 1:1 9:8 5:4 11:8 3:2 13:8 7:4 15:8 2:1, if you assume F is 1:1.

The bridge includes a sort of circle of fifths:

• E-maj
• A-min
• Dbmin
• Gnmin
• Cnmaj
• Fnmaj

The bridge sometimes only uses the last three, four, five, or all six of the chords. I’ve used this bridge before in some pieces. It has a nice cadence at the end, G minor, C major, F major. The chords before those are pretty far off from a real circle of fifths. More like a broken wagon wheel of 5ths. In the chart below, the column ideal is the number of steps in 72-EDO that the note should be. Next to it are the notes actually used, and the difference between the number of steps between one note and the next. 30 is what it should be, a fourth up the scale in 72 EDO. Ignore the first one, 64. The rest are close but not quite 30 steps up.

or download here:
Hard Rime #1
Hard Rime #2
Hard Rime #3

Different runs through the randomizer. #17:

key Cn-Maj dur 48 dur 40 dur 40 dur 48 dur 40
key Cn-Maj dur 40 dur 40 dur 48 dur 40 dur 48
key Cn-min dur 24
key A--min dur 16
key Fn-min dur 24
key E--Maj dur 16
key F+-Maj dur 24
key A+-Maj dur 16
key F+-Maj dur 24
key A+-Maj dur 16
key Cn-Maj dur 48 dur 48 dur 40 dur 40 dur 40
key Cn-Maj dur 48 dur 40 dur 40 dur 48 dur 40
key D+-Maj dur 24
key A+-Maj dur 16
key F+-Maj dur 24
key E--Maj dur 16
key F+-Maj dur 24
key A+-Maj dur 16
key D+-Maj dur 24
key A+-Maj dur 16
key Cn-Maj dur 48 dur 48 dur 40 dur 40 dur 40
key Cn-Maj dur 48 dur 40 dur 40 dur 48 dur 40
key D+-Maj dur 24
key A+-Maj dur 16
key D+-Maj dur 24
key Fn-Maj dur 16
key D+-Maj dur 24
key Fn-Maj dur 16
key D+-Maj dur 24
key A+-Maj dur 16
key Cn-Maj dur 40 dur 40 dur 48 dur 40 dur 48
key Cn-Maj dur 48 dur 40 dur 40 dur 48 dur 40
key D+-Maj dur 24
key A+-Maj dur 16
key F+-Maj dur 24
key A+-Maj dur 16
key D+-Maj dur 24
key Fn-Maj dur 16
key D+-Maj dur 24
key A+-Maj dur 16
key Cn-Maj dur 48 dur 48 dur 40 dur 40 dur 40
key Cn-Maj dur 40 dur 40 dur 48 dur 40 dur 48
key D+-Maj dur 24
key A+-Maj dur 16
key D+-Maj dur 24
key A+-Maj dur 16
key F+-Maj dur 24
key E--Maj dur 16
key Fn-min dur 24
key E--Maj dur 16
key Cn-Maj dur 48 dur 40 dur 40 dur 48 dur 40
key Cn-Maj dur 48 dur 48 dur 40 dur 40 dur 40
key F+-Maj dur 24
key E--Maj dur 16
key Fn-min dur 24
key A--min dur 16
key Cn-min dur 24
key A--min dur 16
key Cn-min dur 24
key D+-min dur 16
key Cn-Maj dur 40 dur 40 dur 48 dur 40 dur 48
key Cn-Maj dur 48 dur 48 dur 40 dur 40 dur 40
key Gn-min dur 24
key Db-min dur 16
key Eb-min dur 24
key Db-min dur 16
key Eb-min dur 24
key Ab-Maj dur 16
key Fn-Maj dur 24
key D+-Maj dur 16
key Cn-Maj dur 48 dur 40 dur 40 dur 48 dur 40
key Cn-Maj dur 48 dur 48 dur 40 dur 40 dur 40
key A+-Maj dur 24
key F+-Maj dur 16
key A+-Maj dur 24
key F+-Maj dur 16
key A+-Maj dur 24
key D+-Maj dur 16
key A+-Maj dur 24
key F+-Maj dur 16 dur 48 dur 40 dur 48 dur 40
key E--Maj dur 24
key Fn-min dur 16
key A--min dur 24
key Cn-min dur 16
key A--min dur 24
key Cn-min dur 16
key A--min dur 24
key Fn-min dur 16 dur 40


Version 18:

key Cn-Maj dur 48 dur 40 dur 40 dur 48 dur 40
key Cn-Maj dur 40 dur 40 dur 48 dur 40 dur 48
key Eb-min dur 16
key Ab-Maj dur 24
key Fn-Maj dur 16
key Ab-Maj dur 24
key Fn-Maj dur 16
key D+-Maj dur 24
key Fn-Maj dur 16
key D+-Maj dur 24
key Cn-Maj dur 48 dur 40 dur 40 dur 48 dur 40
key Cn-Maj dur 40 dur 40 dur 48 dur 40 dur 48
key Fn-Maj dur 16
key Ab-Maj dur 24
key Eb-min dur 16
key Ab-Maj dur 24
key Fn-Maj dur 16
key Ab-Maj dur 24
key Fn-Maj dur 16
key Ab-Maj dur 24
key Cn-Maj dur 48 dur 48 dur 40 dur 40 dur 40
key Cn-Maj dur 40 dur 40 dur 48 dur 40 dur 48
key Eb-min dur 16
key Db-min dur 24
key Eb-min dur 16
key Db-min dur 24
key Eb-min dur 16
key Db-min dur 24
key Eb-min dur 16
key Ab-Maj dur 24
key Cn-Maj dur 48 dur 48 dur 40 dur 40 dur 40
key Cn-Maj dur 48 dur 40 dur 40 dur 48 dur 40
key Fn-Maj dur 16
key Ab-Maj dur 24
key Eb-min dur 16
key Db-min dur 24
key Eb-min dur 16
key Ab-Maj dur 24
key Fn-Maj dur 16
key D+-Maj dur 24
key Cn-Maj dur 48 dur 48 dur 40 dur 40 dur 40
key Cn-Maj dur 40 dur 40 dur 48 dur 40 dur 48
key Fn-Maj dur 16
key D+-Maj dur 24
key A+-Maj dur 16
key F+-Maj dur 24
key E--Maj dur 16
key F+-Maj dur 24
key A+-Maj dur 16
key F+-Maj dur 24
key Cn-Maj dur 48 dur 40 dur 40 dur 48 dur 40
key Cn-Maj dur 48 dur 48 dur 40 dur 40 dur 40
key E--Maj dur 16
key Fn-min dur 24
key A--min dur 16
key Fn-min dur 24
key A--min dur 16
key Fn-min dur 24
key A--min dur 16
key Cn-min dur 24
key Cn-Maj dur 48 dur 40 dur 40 dur 48 dur 40
key Cn-Maj dur 48 dur 48 dur 40 dur 40 dur 40
key D+-min dur 16
key Cn-min dur 24
key D+-min dur 16
key Gn-min dur 24
key Db-min dur 16
key Gn-min dur 24
key D+-min dur 16
key Gn-min dur 24
key Cn-Maj dur 48 dur 40 dur 40 dur 48 dur 40
key Cn-Maj dur 48 dur 48 dur 40 dur 40 dur 40
key D+-min dur 16
key Cn-min dur 24
key D+-min dur 16
key Gn-min dur 24
key D+-min dur 16
key Cn-min dur 24
key D+-min dur 16
key Cn-min dur 24 dur 48 dur 40 dur 48 dur 40
key D+-min dur 16
key Cn-min dur 24
key D+-min dur 16
key Gn-min dur 24
key Db-min dur 16
key Gn-min dur 24
key D+-min dur 16
key Gn-min dur 24 dur 40


Version #19

key Cn-Maj dur 48 dur 40 dur 40 dur 48 dur 40
key Cn-Maj dur 40 dur 40 dur 48 dur 40 dur 48
key D+-min dur 16
key Cn-min dur 24
key D+-min dur 16
key Cn-min dur 24
key D+-min dur 16
key Cn-min dur 24
key A--min dur 16
key Fn-min dur 24
key Cn-Maj dur 48 dur 40 dur 40 dur 48 dur 40
key Cn-Maj dur 48 dur 48 dur 40 dur 40 dur 40
key E--Maj dur 16
key F+-Maj dur 24
key E--Maj dur 16
key Fn-min dur 24
key E--Maj dur 16
key Fn-min dur 24
key E--Maj dur 16
key Fn-min dur 24
key Cn-Maj dur 48 dur 40 dur 40 dur 48 dur 40
key Cn-Maj dur 40 dur 40 dur 48 dur 40 dur 48
key A--min dur 16
key Fn-min dur 24
key E--Maj dur 16
key Fn-min dur 24
key A--min dur 16
key Cn-min dur 24
key D+-min dur 16
key Gn-min dur 24
key Cn-Maj dur 48 dur 40 dur 40 dur 48 dur 40
key Cn-Maj dur 48 dur 48 dur 40 dur 40 dur 40
key Db-min dur 16
key Gn-min dur 24
key D+-min dur 16
key Cn-min dur 24
key D+-min dur 16
key Cn-min dur 24
key A--min dur 16
key Cn-min dur 24
key Cn-Maj dur 40 dur 40 dur 48 dur 40 dur 48
key Cn-Maj dur 48 dur 40 dur 40 dur 48 dur 40
key A--min dur 16
key Fn-min dur 24
key E--Maj dur 16
key F+-Maj dur 24
key A+-Maj dur 16
key F+-Maj dur 24
key A+-Maj dur 16
key D+-Maj dur 24
key Cn-Maj dur 40 dur 40 dur 48 dur 40 dur 48
key Cn-Maj dur 48 dur 40 dur 40 dur 48 dur 40
key Fn-Maj dur 16
key D+-Maj dur 24
key Fn-Maj dur 16
key Ab-Maj dur 24
key Eb-min dur 16
key Ab-Maj dur 24
key Eb-min dur 16
key Db-min dur 24
key Cn-Maj dur 48 dur 48 dur 40 dur 40 dur 40
key Cn-Maj dur 40 dur 40 dur 48 dur 40 dur 48
key Eb-min dur 16
key Db-min dur 24
key Eb-min dur 16
key Ab-Maj dur 24
key Fn-Maj dur 16
key Ab-Maj dur 24
key Eb-min dur 16
key Db-min dur 24
key Cn-Maj dur 48 dur 40 dur 40 dur 48 dur 40
key Cn-Maj dur 48 dur 48 dur 40 dur 40 dur 40
key Eb-min dur 16
key Ab-Maj dur 24
key Eb-min dur 16
key Ab-Maj dur 24
key Eb-min dur 16
key Ab-Maj dur 24
key Fn-Maj dur 16
key Ab-Maj dur 24 dur 48 dur 40 dur 48 dur 40
key Eb-min dur 16
key Ab-Maj dur 24
key Fn-Maj dur 16
key D+-Maj dur 24
key A+-Maj dur 16
key D+-Maj dur 24
key Fn-Maj dur 16
key D+-Maj dur 24 dur 40


I’ve made a few small modifications to increase the variety of the rhythm and chord changes. It’s still mostly in C major otonolity to the 15 limit in 72 EDO, with a bridge that wanders through the Partch tonality diamond of o- and u-tonality using the Markov Chain Random Walk. It can move up and to the right, or down and to the left in the diamond, but only one step at a time.

Version 12 takes this path, with the chorus in C major, and the bridge wandering:

key Cn-Maj dur 48
dur 48
dur 40
dur 40
dur 40
key Cn-Maj dur 48
dur 40
dur 40
dur 48
dur 40
key Cn-min dur 24
key A--min dur 16
key Fn-min dur 24
key A--min dur 16
key Fn-min dur 24
key A--min dur 16
key Cn-min dur 24
key D+-min dur 16
key Cn-Maj dur 40
dur 40
dur 48
dur 40
dur 48
key Cn-Maj dur 48
dur 40
dur 40
dur 48
dur 40
key Cn-min dur 24
key A--min dur 16
key Fn-min dur 24
key A--min dur 16
key Fn-min dur 24
key E--Maj dur 16
key F+-Maj dur 24
key E--Maj dur 16
key Cn-Maj dur 48
dur 48
dur 40
dur 40
dur 40
key Cn-Maj dur 48
dur 40
dur 40
dur 48
dur 40
key F+-Maj dur 24
key A+-Maj dur 16
key D+-Maj dur 24
key Fn-Maj dur 16
key D+-Maj dur 24
key Fn-Maj dur 16
key D+-Maj dur 24
key Fn-Maj dur 16
key Cn-Maj dur 48
dur 48
dur 40
dur 40
dur 40
key Cn-Maj dur 40
dur 40
dur 48
dur 40
dur 48
key D+-Maj dur 24
key A+-Maj dur 16
key F+-Maj dur 24
key E--Maj dur 16
key Fn-min dur 24
key A--min dur 16
key Cn-min dur 24
key A--min dur 16
key Cn-Maj dur 48
dur 48
dur 40
dur 40
dur 40
key Cn-Maj dur 48
dur 40
dur 40
dur 48
dur 40
key Fn-min dur 24
key A--min dur 16
key Fn-min dur 24
key E--Maj dur 16
key Fn-min dur 24
key A--min dur 16
key Cn-min dur 24
key A--min dur 16
key Cn-Maj dur 40
dur 40
dur 48
dur 40
dur 48
key Cn-Maj dur 48
dur 40
dur 40
dur 48
dur 40
key Cn-min dur 24
key D+-min dur 16
key Gn-min dur 24
key D+-min dur 16
key Cn-min dur 24
key A--min dur 16
key Fn-min dur 24
key A--min dur 16
key Cn-Maj dur 48
dur 48
dur 40
dur 40
dur 40
key Cn-Maj dur 40
dur 40
dur 48
dur 40
dur 48
key Fn-min dur 24
key A--min dur 16
key Fn-min dur 24
key A--min dur 16
key Fn-min dur 24
key E--Maj dur 16
key F+-Maj dur 24
key E--Maj dur 16
key Cn-Maj dur 48
dur 40
dur 40
dur 48
dur 40
key Cn-Maj dur 40
dur 40
dur 48
dur 40
dur 48
key Fn-min dur 24
key E--Maj dur 16
key F+-Maj dur 24
key E--Maj dur 16
key F+-Maj dur 24
key E--Maj dur 16
key F+-Maj dur 24
key E--Maj dur 16
dur 48
dur 40
dur 48
dur 40
key Fn-min dur 24
key A--min dur 16
key Cn-min dur 24
key A--min dur 16
key Cn-min dur 24
key D+-min dur 16
key Gn-min dur 24
key D+-min dur 16
dur 40


These are some of the ones I’m listening to now. I’ve been replacing the versions on the web each day as I try to refine the approach. Version 9 uses the following keys for a bridge.
In the following table, the first column is the number of times it is played. The second is the key, and the last the duration; 24 is 3 beats, 16 is two. This version uses more keys than the other two.

# Key dur
2 Fnmaj 24
4 D+maj 16
5 A+maj 24
4 F+maj 16
3 E-maj 24
6 Fnmin 16
8 A-min 24
6 Cnmin 16
4 D+min 24
4 Gnmin 16
4 Dbmin 24
4 Ebmin 16
5 Abmaj 24
7 Fnmaj 16
5 D+maj 24
1 A+maj 16


Version 10 looks like this. For some reason, he picked a lot of A Minor and C Minor. No idea why.

# Key dur
2 Abmaj 16
3 Fnmaj 24
2 D+maj 16
3 A+maj 24
3 F+maj 16
2 E-maj 24
9 Fnmin 16
16 A-min 24
10 Cnmin 16
6 D+min 24
4 Gnmin 16
2 Dbmin 24
3 Ebmin 16
3 Abmaj 24
3 Fnmaj 16
1 D+maj 24


Finally, here is what version 11 looks like. Far fewer alternatives made it into the final mix.

# Key dur
3 Ebmin 16
8 Abmaj 24
14 Fnmaj 16
19 D+maj 24
13 A+maj 16
7 F+maj 24
5 E-maj 16
2 Fnmin 24
1 A-min 16


The drunkard’s walk tends to make the results cluster near each other. In this case, around Db Minor, near the C Major of the primary key of the piece. It could just as easily cluster somewhere else. I don’t keep the history of where they clustered in versions 9 & 10.

Still working out the mix and the tempo and chord changes. But this sounds interesting.

Or download here: Windstorm/Snowfall #7.

I’ve added some new instruments to make some more variety. The piece is now scored for French Horn, Alto Flute, Trombone, Tuba, Finger Piano (2 kinds), Marimba, Baritone Guitar, and Balloon Drum. The Finger Pianos, Baritone Guitar, and Balloon Drum samples are my own, the rest came from the McGill University Master Samples. The slides are added using Csound. Lots of slides.

Here are the instrument definitions. Every time one plays, the pre-processor chooses loudness, stereo location, audio envelope, chance of actually playing or being silent, a “z” factor that displaces a few milliseconds in time, the randomness algorithm, and the octave.

.frnh c2a0u0&wind-vel*.&sid*.&wind-env*.&frnh-ran*.g0&horn-z*.&all-pva.&ver-oct*.
.alto c3a0u0&wind-vel*.&sid*.&wind-env*.v+9&alto-ran*.g0&horn-z*.&all-pva.&alt-oct*.
.trom c4a0u0&wind-vel*.&sid*.&wind-env*.&trom-ran*.g0&horn-z*.&all-pva.&ver-oct*.o-1
.bass c5a0u0&wind-vel*.v+10&sid*.&wind-env*.&bass-ran*.g0&horn-z*.&all-pva.&bass-oct*.
.finb c7a0u0&fin-vel*.&sid*.&arp-env*.&finb-ran*.g0&arp-z*.&all-pva.&fnb-oct*.
.mari c8a0u0&fin-vel*.&sid*.&arp-env*.&mari-ran*.g0&arp-z*.&all-pva.&arp-oct*.
.guit c9a0u0&gui-vel*.&sid*.&arp-env*.&guit-ran*.g0&arp-z*.&all-pva.&gui-oct*.
.fing c10a0u0&fin-vel*.&sid*.&arp-env*.&fing-ran*.g0&arp-z*.&all-pva.&arp-oct*.
.bal1 c13a0u0&ball-vel*.&sid*.&ball-env*.&bal1-ran*.g0&ball-z*.&all-pva.

There is extensive use of the Drunkard’s Walk, and more will follow soon as I extend the piece out over time. Imagine a drunk walking on a snowy walkway with ice under the snow and wind gusts. We had 18″ at Snoqualmie Pass in the last 24 hours. That’s almost an inch an hour.

Or download here: Windstorm/Snowfall.

I’m just noodling around with a 15 limit tonality diamond in 72-EDO. In most traditional classical music there is a heavy reliance on the circle of fifths to build towards a satisfying conclusion. In the tonality diamond, I find the same sense of inevitability in the circle of utonality or otonolity.

Here we go down the diamond from the C Major in the center to the lower right with otonality on each of the following:
C Major, Ab Major, F Major, D+ Major, A+ Major, F+ Major, E- Major back to C Major.
Then we go up the diamond from the F Minor in the center to the upper right, with utonality on each of the following:
F minor, A- Minor, C Minor, D+ Minor, G Minor, Db Minor, Eb Minor back to C Major.

&Cnmajx.&all-ver48. &all-ver48. &all-ver48. &all-ver48. &vel.d48d*4
&Abmajx.&all-ver48. &vel.d48
&Fnmajx.&all-ver48. &vel.d48
&D+majx.&all-ver48. &vel.d48
&A+majx.&all-ver48. &vel.d48
&F+majx.&all-ver48. &vel.d48
&E-majx.&all-ver48. &vel.d48
&Cnmajx.&all-ver48. &all-ver48. &all-ver48. &all-ver48. &vel.d48d*4
&Fnminx.&all-ver48. &vel.d48
&A-minx.&all-ver48. &vel.d48
&Cnminx.&all-ver48. &vel.d48
&D+minx.&all-ver48. &vel.d48
&Gnminx.&all-ver48. &vel.d48
&Dbminx.&all-ver48. &vel.d48
&Ebminx.&all-ver48. &vel.d48
&Cnmajx.&all-ver48. &all-ver48. &all-ver48. &all-ver48. &vel.d48d*4


Or download here: Windstorm/Snowfall.

This version includes a coda with much slower chords. I had a bad file link in previously, but I think it’s fixed now.

Or download here: Herzliebster Jesu.

Here’s another version with a better choice of chords and measures to wander through.

Or download here: Herzliebster Jesu.

Here’s a version with some Drunkard Walk wanderings for finger piano, horns, and tuba. Tempo is a drunkard walk through the golden ratio of tempi. Still thinking through how to make this work.

Or download here: Herzliebster Jesu.