Slow Dance #3b

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Slow Dance #3

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This is a palette cleanser for between two tracks of more complex material. Same scales as Winding out to the Pacific, but in thirds.

Winding out to the Pacific - take 17

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This piece is pretty much finished now.

Winding out to the Pacific is the second to last piece in the Music of the Hoh River Valley series. This one is scored for vibraphone, marimba, harp, finger piano, and sine waves. The intonation system is 72 equal divisions of the octave. There are four chords derived from four scales used throughout the piece, and they are played in succession:

• Subminor with a root on the 26th tone in 72 EDO
• Minor on 23
• Major on 19
• Super Major on 16
• Major on 19
• Minor on 23

This sequence is repeated three times. These four scales are derived from the Partch tonality diamond to the 15th limit. Click on the images below to make them bigger.

In the diamond above, purple is the major scale, 4:5:6:7:9:11:13:15. Green is the minor scale: 12/8:10:12:7:9:11:13:15. Subminor is a mode of the major scale, shown in pink, and yellow is the supermajor, a mode of the minor. Laid out as vertical scales, they look like this:

The orange rows are the primary notes of the scale, making the major or minor sounding chords. Green is for the alternative chords, and white are the really strange ones. I construct fourth chords from these scales, and either play the chord outright, or arpeggiate it up and down. The fourths are constructed starting at the 7th note of the chord in the bass, and going up by approximately 30 steps of the 72 EDO, attempting to go up 60 steps every other note until it repeats. Here are the scale degrees of the fourth chords for each scale.

sub 726 158 473
min 736 251 473
maj 736 251 472
sup 726 148 372


The piece uses indeterminacy heavily. Each instrument has a set of choices for what to play. In this version, the choices random, but weighted towards not picking a choice if it has already been played before.

This version is the 17th run through the algorithm. The 12th and 13th are nice as well, and I might post them some time.

The length of time to stay on one of the four chords is variable from one to eight measures, also chosen with a weighted random selection method.

The tempo is continuously variable, but it tends to go faster on those chords that are played more measures, and slower when the number of measures is low. The transition from one tempo to another is gradual. Here's a nice picture of the mouth of the Hoh River as it enters the ocean, about 56 miles from its source.

Winding out to the Pacific

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I'm at the stage of generating multiple runs through the piece and picking the one to save as the final version. This one is take 12 of 18.

Winding out to the Pacific 8

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So I took the time this morning while my wife and daughter were out shopping to code the tempo as a continuously variable speed that can be set inside the piece, instead of imposed externally with a hand coded Csound tempo command. Now, every note or phrase can have its own tempo. The speed gradually changes from one tempo to another in this version.

I can't believe I waited this long to implement such a simple function. In this version, I let the program choose from among 5 possible tempos. The choice is made when it chooses to play a measure of 96 to 240 beats, so that longer sections have faster tempo and shorter ones play slower.

Winding out to the Pacific 7

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Playing with the tempo. I'd really like the ability to set the overall tempo the way I set the overall volume: as a continuously variable speed that can change with each note. Csound allows that, I just need to code the preprocessor to support it. Today I hand code it thusly:
t0 480 200 840 300 1280 600 800 700 240 900 1200 2000 1300
Where starting at time zero the tempo is 480 beats per minute, until time 200, when it reaches 840 bpm, then speeds up to 1280 at beat 300, then slows down to 800 at beat 600, and so on.
But that means I have to know when the tempo change is supposed to happen, and that varies depending on the chosen route through the piece. Simple matter of programming...

Winding out to the Pacific 7

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Trimmed the algorithm down to fit in 60 seconds. I still need to work on showing the drift from sub-minor, minor, major, supermajor.

Winding out to the Pacific 6

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Winding out to the Pacific 5

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Here we have an intermix of the minor scale with the subminor. I can't hear the difference with this set of instruments and patterns. I may have to go back to the drawing board. My goal is to showcase the movement from subminor to minor to major to supermajor. But this musical material may not be appropriate for that idea. Oh well. It sounds good anyway.

@ play them
@
&all-t23min-48-*. &all-t23min-48-*. &all-t23min-48-*. &all-t23min-48-*.
.vel-vel a235
&all-t23min-48-*. &all-t23min-48-*. &all-t23min-48-*. &all-t23min-48-*.
.vel-vel a200
&all-t26sub-48-*. &all-t26sub-48-*. &all-t26sub-48-*. &all-t26sub-48-*.
.vel-vel a100
&all-t26sub-48-*. &all-t26sub-48-*. &all-t26sub-48-*. &all-t26sub-48-*.
.vel-vel a230
&all-t23min-48-*. &all-t23min-48-*. &all-t23min-48-*. &all-t23min-48-*.
.vel-vel a255


Winding Out to the Pacific 4

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Adding some complexity, but this will diminish later.

Winding out to the Pacific 3

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I've added some new instruments and backed off to just the subminor fourths for now.

Winding out to the Pacific 2

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Sub-minor to minor to major to supermajor in fourths. Click to enlarge.

Winding out to the Pacific

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Fourths based on a sub-minor scale.

Through Western Bog Laurel - take 20

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This is the last version for now, I think. I slow the piece down by a small amount every 40 seconds until it is running around 11% slower at the end. Each of the 12 tempo reductions are done by the ratio of 2^(1/72), which is the 72nd root of two (1.0096735332). The beats per minute are divided by that number 12 times. Coincidentally, that's the same as the ratio of one note to the next in 72-EDO, the tuning the piece is realized in. I can't figure out how that happened, but there it is.

Csound takes care of tempo with the t tempo statement.

t0 1200 800 1200 896 1188 1592 1188 1688 1176 2376 1176 2472 1164 3152 1164 3248 1152 3920 1152 4016 1140 4680 1140 4776 1129 5432 1129 5528
1118 6177 1118 6273 1107 6915 1107 7011 1096 7645 1096 7741 1085 8368 1085 8464 1074 9084 1074 9180 1063 9792 1063 9888 1052 10493 1052 10589

The t0 makes it a tempo statement. The next number is the beats per minute, in this case 1200. A quarter note is about 8 beats when there are 1200 beats a minute. The next number after beats per minute is the number of beats where the next tempo marker is found, in this case 1200. So it stays at 1200 beats a minute for 800 beats, about 100 eighth notes. The next number 896 is the beat marker, and 1188 is the beats per minute. 1200 / 1.0096735332 is 1188, approximately. Over the next 96 beats or 12 eighth notes, it slows down from 1200 to 1188 beats per minute. Then at beat 1592 it starts to slow down to 1176 beats per minute, arriving at that speed at beat 1688. The overall effect is a gradual slowing down, sometimes noticably, sometimes imperceptively, until it stops.

Through Western Bog Laurel - take 19

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This is another take on the same piece I've been working on for a while. This version includes adjustments to the tuning of the samples. There were some intonation problems with the marimba, harp, vibes, flute, and balloon drum. To determine pitch I used Cooledit (now called Adobe Audition) and its FFT option. You basically load a sample file and select Analyze-FFT and it puts up a Fast Fourier Transfer window showing the most prominent frequencies, with the pitch in note/cents from 12-EDO for the most prominent frequency. For most non-bass notes that is the fundamental. Here's one for the harp D#6, 4 cents flat at a point about half a second into the harp sample.

My Csound preprocessor allows me to put -4 into a list of samples, and Csound adjusts the sample when it's used in the synthesis instrument. Four cents is not noticiable, for the most part. Anything over 10 is not good.

Most of these samples, from the McGill University Master Samples CDROM library, are not very in tune, and they don't necessarily hold the same pitch for the whole note. Many go up and down by a few cents from the start to finish.

This is the first time I have systematically used the Cooledit frequency analysis to fine tune the samples. I previously tuned them by ear to a reference sine wave. It was a time consuming process, and error prone. The harp sample was particularly out tune, with one note 43 cents off, and others 10-20 off. The flute was also way out of tune, with the highest note 31 cents sharp. Here's C6 31 cents sharp one second into the sample. Typical flute player getting excited that he can hit such a high note. I back that sample down by 31 cents and we are good to go.

Through Western Bog Laurel - take 11

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This is a version of the finished work. It is scored for flutes, marimba, vibe, finger piano, harp, balloon drums, and a percussion board with a contact microphone. The latter instrument includes several rocks, toothbrushes, and pieces of wood, glass, and rocks glued to the surface of a piece of sitka spruce. If you hear something that sounds like a monkey chant, it's probably the percussion board.

The intonation is 72-equal divisions of the octave (72-EDO) approximating the Partch tonality diamond to the 15 limit. There are many glissandi and trills employed. The marimba and vibe are given many opportunities to trill and slide around their pitches. The triad is the basic melodic element, either 4:5:6 or 7:9:11 or their inversions in the major scale, and comparable chords in the sub-minor and minor modes.

The piece starts out in B 16/9, with a scale based on the overtone series. As shown on the chart below, it modulates around the tonality diamond from there. Click on the chart for a larger version. The yellow colored blocks are the B 16/9 major scale. The subminor D 12/11 is in orange, the subminor G 3/2 is in pink, the C 1/1 minor is green, and the F 4/3 major is in blue. I use glissandi to slide from one chord to another.

As with all my works, there is a great deal of indeterminacy. Each instrument has many choices to make, subject to constraints about repeatability and change. Imagine a band improvising from a set of approved riffs.

Fridge over Bob Launer

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Another time through with a different mix of patterns for the instruments to choose from.

The Bridge over Western Bog Laurel

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The bridge has the changes referred to earlier.

Another Sketch for TWBL

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Here's another step along the way towards the Western Bog Laurel piece. Today's sketch uses semi-unison lines in the harp, finger piano, vibe, marimba, bass finger piano, and balloon drums. I say semi-unison because each instrument can change alter his line by a few notes. There is a variable randomness setting in the software. The balloon drum part has more notes than the others, but that's because his sustain is so limited.

Each chord can have a variety of alterations: straight, trill, or slide. The trills and slides move each note in a triad up or down by a step in the otonality scale. Bb 16/9 can go up a 9:8 to C 1/1 or down a 7:8 to Ab 14/9. The D 10/9, which is a 5:4 above the Bb 16/9 can go up an 11:10 to Eb 11/9 or down a 9:10 to C 1/1. And the F 4/3 a 3:2 above Bb 16/9 can go up a 7:6 to Gb 13/9 or down a 11:12 to an Eb 11/9. The slides are nice and sweet. Here is the glissando up a 12:11 in Csound:

f 323 0 256 -7 1 64 1 128 1.0905077 64 1.0905077 ; 12:11 22 up 9

And here it is graphically, as rendered by Csound to a PDF file:

Sketch for Western Bog Laurel

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The subminor scale is my name for a minor scale built from overtones, but with the root of the scale starting on the 3:2 instead of the 1:1. For example, consider an overtone series on F. The 3:2 above F is C. If the scale is based on a mode starting on C, as shown in the graph above, you have the subminor scale.

As with all overtone series, a cluster of notes above a certain pitch will always generate a difference tone. But even though the scale designed to favor the root at C, the difference tone will always be F. I will have to take that into consideration when I add low notes. They will have to resolve that F to C, and choose notes carefully to minimize the difference tone prominence.