mysterybear productions: tag

Aurora (for Kraig Grady)

Posted 15 September 2007, 14:43

Description

Dawn on Mount Meru. Inspired by the work and encouragement of Kraig Grady.

Duration: 3:04

Background & Technical Details

I’ve been listening to music by Kraig Grady recently, and decided that I wanted to start exploring some of the scales he’s been using, in particular the family of tunings he calls “meta-slendro”. At Kraig’s suggestion, I started with his article An Introduction To The Scales Of Mt Meru And Other Recurrent Sequence Scales. The meta-slendro scales are derived from numeric sequences found in Pascal’s Triangle, specifically the one Kraig refers to as Meru #3.

In this piece, I use a 7-note scale and a 5-note scale, which I built using Scala. I started with a 12-note “chromatic” scale built from harmonics 9 through 200 in the Meru #3 sequence, as Kraig recommends in his article. Then I used Scala’s “mos” command to derive various subsets. Of these, I chose a 7-note scale and a 5-note scale that both used generator 7. Of the two only the latter can be called meta-slendro, since slendro is a pentatonic scale. But I like the way they sound together.

For each scale, I wrote lines that consist of permutations of two-note chords, or dyads, within an octave. These lines are played by instruments that simulate the sound of Tibetan bells (using these handy tables of modal frequency ratios). The 5-note scale uses a sequence of 19 notes, played twice (once forward and once retrograde) for a long phrase of 38 beats. The 7-notes scale uses a sequence of 41 notes, played once forward. Played together, these phrases make a rhythmic ratio of 38:41.

Underneath are droney loops made mostly from notes that are present in the original 12-note scale but not in the 5- and 7-note scales, along with a chord build up from combination tones based on the interval 1.324717957/1 (1.324717957 is the number towards which the Meru #3 sequence converges).

Update #1, 16 Sep 2007:

I’d like to thanks Steven Yi again, not just for blue, which has become indispensable, but also for his Mode 6 and Horner/Ayers horn Csound instrument designs, both of which I adapted for use in this piece. Please listen to his music too, it’s wonderful stuff.

Update #2, 16 Sep 2007:

Thanks to some very constructive comments from Carl Lumma and Rick McGowan on the Making Microtonal Music list, I have added more gain to the sound files and re-uploaded them.

Copyright & Licensing

Files/Downloads

MP3 (7.3MB, 48K/16-bit, 320kpbs)
OGG (4.7MB, 44.1K/16-bit, 207kbps)
blue & Csound project files, Scala files (23KB)

Tags

bells, drones, horns, just intonation, meta-slendro, mount meru

Palimpsest

Posted 13 May 2007, 10:58

Description

A meditation on remembrance, breath, stasis and change.

Duration: 10:58

Background & Technical Details

Palimpsest is the second in a series of works that began with Owllight (although it remains to be seen whether or not the series will continue). While the pieces have very different moods, they both employ cellular automata as a kind of structural template, and both are built from very simple materials: sine waves, some reverb, and very few notes.

Rule 57, width 68, height 100 As in Owllight, the harmonic spectrum of every note is determined by the successive states of a simple one-dimensional cellular automaton (in this case, Rule 57) as shown on the right. The states start at the top of the image, with one state per row. A row consists of a series of “cells”, each of which is either “alive” (black) or “dead” (white). I treat each cell as a harmonic (i.e., an integral multiple of the base tone), so the more cells that are “alive”, the richer the sound. Each harmonic is made by an individual sine wave tone.

Palimpsest consists entirely of two two-note chords: 60Hz + 90hz (3/2, a just perfect fifth) and 67.5Hz + 90Hz (4/3, a just perfect fourth). Each chord proceeds through the series of spectral transformations represented by the diagram, but the chords are offset by the exact duration of a single state (the perfect fifth starts, and the perfect fourth follows), so that the chords alternate throughout the piece. In addition to the spectral changes, change occurs at two other levels. The length of the state (the “beat” of the piece) continually decreases at a slow rate, which provides an almost imperceptible sense of acceleration. Also, with every successive “beat”, the individual tones that make the harmonics are arpeggiated at a slightly greater rate, so that the chords get progressively more “smeared” over time; you can hear this most clearly on the very last chord in the piece.

This piece is dedicated to Carter Scholz, whose album Eight Pieces continues to inspire me. (Scholz co-wrote a very interesting sci-fi novel called Palimpsests that was published in 1984, but I had already named the piece before I remembered the book.)

Copyright & Licensing

Files/Downloads

MP3 (25MB, 48K/16-bit, 320kpbs)
OGG (20MB, 44.1K/16-bit, 221kbps)
blue & Csound project files (102KB)

Tags

cellular automata, just intonation

Owllight

Posted 10 April 2007, 10:58

Description

An ambient piece in a dark and mysterious mood.

Duration: 7 minutes.

Background & Technical Details

I first encountered the word “owllight” (in hyphenated form) in the Dylan Thomas poem Altarwise by owl-light, which I first read as a teenager. The word hadn’t occurred to me in many years, but as I worked on this piece and searched for a title, I remembered the term and it felt right. I looked it up online and found a great definition from Webster’s 1913 dictionary: “glimmering or imperfect light”. The piece has, to my ears, a somewhat somber, mysterious, and possibly foreboding mood, which seems appropriate given the place the owl occupies in folklore. I’m also reminded of the creepy owls in Twin Peaks, which were apparently based on aspects of Native American mythology. (“The owls are not what they seem.”)

The technical notes that follow may be irrelevant to your experience of listening to the piece, but I present them (as I generally do) in case someone is curious about the compositional process I followed.

This piece is made by varying the harmonic spectra of three tones at 60Hz, 90Hz, and 97.08Hz, which we hear as root (1/1, at stereo center), perfect fifth (3/2 or 1.5/1, at stereo left), and sharp or augmented fifth (1.618/1, which is an approximation of the golden ratio, at stereo right). The ~7Hz difference between the second and third pitches produces a binaural beating effect in the approximate range of the transition between alpha and theta waves. If you listen carefully, you will hear this three-note phrase repeating throughout the piece.

The structure of the piece is governed by the first 97 states of a 1-dimensional cellular automaton known as Rule 150. I treat the center cell in each state as the fundamental and the cells on either side as harmonics (odd-numbered on one side, even-numbered on the other side).

I wrote this using Steven Yi’s fantastic program blue, which is a front end for Csound. This is the first time I used the blue feature that allows one to generate the Csound score from Python code. The code that calculates cellular automata is based on a Python Cookbook entry by Rick Muller. The sounds themselves are entirely made up of individually-generated sine waves with some reverb; I used no other waveforms or effects of any kind.

Copyright & Licensing

Files/Downloads

MP3 (16MB, 44.1K/16-bit, 320kpbs)
OGG (11MB, 44.1K/16-bit, 221kbps)
blue & Csound project files (39KB)

Tags

cellular automata, golden ratio, just intonation

TimeWave Canon

Posted 22 July 2006, 11:58

Description

A mensuration canon in just intonation based on Terence McKenna’s TimeWave Zero. Revised 22 July 2006.

Duration: 4 minutes, 56 seconds.

Background & Technical Details

Terence McKenna was one of the more interesting counter-cultural thinkers to emerge in the Sixties. His novelty theory is largely based on a mathematical construct called the TimeWave, which has its origin in a particular arrangement of the I Ching called the King Wen sequence. While McKenna’s explanation of the TimeWave is interesting, a paper by physicist John Sheliak provides a clearer and more mathematically rigorous account.

I have no opinion on novelty theory per se, but I have for several years been fascinated by the form of the TimeWave that Sheliak calls the Tri-Level Bi-Directional Wave (see Figure 4 in the McKenna article and Figure 10 in the Sheliak article). Without getting into too many details, the essence of it is a sequence of 64 integers, superimposed upon itself. One layer is a single cycle, which defines one period of the overall wave; the next layer is two cycles; the third layer is six cycles. Actually, each layer consists of two sequences: the original sequence and a retrograde-inversion of the original sequence, so there are six lines altogether. It made sense to me to see this object in musical terms, where each integer represents a note in some scale, and each of the three layers represents a two-voice sequence of those pitches in time. So I decided to translated the wave into sound, but first I had to choose an appropriate musical language.

Within any cycle of the TimeWave, the set of integers has a very small range, between 1 and 6. Since seven-note scales or modes are so frequently used in music around the world, I decided that I would limit myself to something in that domain. Something about the “contrapuntal” structure of the wave reminded me of Gamelan, which led me to make my first attempt using a pelog scale and bell- or gong-like timbres. But I don’t have access to convincing gamelan sounds, nor do I have a deep understanding of gamelan, so I abandoned that approach. I eventually settled on a scale similar to the following:

C D E♭ F♯ G A B♭ C

which contains some of my favorite intervals: the minor third, the augmented fourth and the flat seventh. There are a number of ways to express this scale in just intonation, and this is the one I chose:

1/1 9/8 7/6 7/5 3/2 5/3 7/4 2/1

Each two-voice sequence is presented in its own octave, where the slowest single-cycle line is in a lower octave, the two-cycle line is one octave higher in pitch, and the six-cycle line is another octave higher.

I’m a little embarrassed to admit that it didn’t occur to me for quite a while that the structure of the music that emerged can be considered a mensuration canon, which is a type of canon where the different voices play the same music at different speeds. My flimsy excuse for this belated realization is that it’s been 28 years since I studied music in college.

The piece starts (and ends) with a slightly reverb-processed sine-wave choir that plays the minor seventh chord that is implied by the scale. Before the full six-voice canon begins, you hear one complete cycle at the highest octave and speed.

I wrote the piece using Steven Yi’s excellent program blue as a front-end to Csound 5.0. Blue’s Microtonal Piano Roll feature allowed me to work directly with the scale I built in Scala, and the very cool BlueX7 feature made it very easy to use Russell Pinkston’s DX7 emulation instrument designs for Csound.

The piece is dedicated to the memory of Terence McKenna, whom I wish I had met, and also to John Sheliak, with gratitude for his willingness to discuss the TimeWave through an email conversation.

Revised, 22 July 2006: In the process of preparing an eight-channel version of the piece, I made a new stereo version that makes a much better use of space relative to the orginal version. Each sequence now starts with the two voices on separate sides of the stereo field, which then cross-pan to swap places. The cross-pan recurs for each repetition of the sequence.

Update, 23 September 2006: The eight-channel version of TimeWave Canon was played last night (22 September 2006) as part of the final concert of the third annual Mid-Autumn Harvest Moon Festival at Concordia University in Montreal. Thanks to Kevin Austin at Concordia for encouraging me to participate, and also to Mark Corwin, Yves Chigon, the students, and everyone else who made this event so collegial and congenial.

Copyright & Licensing

Files

MP3 (4MB)
OGG (8MB)
blue & Csound project files (19KB)

Tags

bells, canons, just intonation, timewave

Drift Dhikr II

Posted 2 April 2006, 11:26

Description

Or, “Heraclitus Takes It to the Bridge.” Ambient but intense. Should be played loud.

Duration: 5 minutes.

Background & Technical Details

I was inspired by a pair of Csound instruments designed by Anthony Kozar as seen in a recent post of his, where the output of several oscillators is accumulated and used to frequency-modulate a carrier wave.

Among other changes, I modified Anthony’s carrier instrument so that it glides from a starting pitch to an ending pitch along an exponential curve, and made two instances: one that glides from 2/1 (the octave) down to 3/2 (a perfect fifth), and one that glides from 1/1 (the “root”) up to 3/2. For each carrier I used a set of eleven modulators, tuned to a sequence of prime harmonics starting with 3.

The end result, like the first Drift Dhikr, is a complex resonant drone that is simultaneously static and constantly changing. The timbre in this piece is more intense than in the earlier piece because of the use of FM synthesis, and I have made it a “hotter” mix as well. I’ve tried to approach the intensity of good old electric guitar feedback, though (alas) with fewer of the chaotic elements that occur when vibrating metal wires in a magnetic field are sympathetically excited by a bath of high volume sound waves from a Marshall amp turned up to 11.

Copyright & Licensing

Files

MP3 (11MB)
OGG (14MB)
Csound unified score file (7KB)

Tags

drones, just intonation

Threnody

Posted 24 March 2006, 13:18

Description

In memory of the civilian casualties of the war in Iraq and all other victims of political violence around the world.

Update: I’ve replaced the sound files with a version that improves the balance and equalization.

Duration: 5 minutes, 30 seconds

Background & Technical Details

This piece began as a couple of experiments. I had been playing with a pair of complex sawtooth-like waveforms and found that I liked the sound they made when arranged according to the first ten pitches in the harmonic series and spread out across the stereo image. I had separately been playing with a Csound instrument design that added a jitter value to the pitch where the amplitude of the jitter was proportional to the frequency. Applying the jittering to the drone using a small amount of variation (3% of the frequency for each note) made it much richer.

I also tried multiplying the frequency with the jitter rather than adding or subtracting. This resulted in a much wilder sound, since the resulting pitch variations are so broad that the original pitch is replaced by a range of pitches connected in a continuous glissando. I did this with the same chord as the drone, but two octaves higher and with simple sine waves rather then the harmonically-rich waves I used for the drone. The result sounded almost like voices to me (albeit non-human ones).

Then I combined the drone with the “voices”, along with some fairly heavy reverb, and got a dark and somewhat spooky sound where the vocal-like sounds are partially buried in the all-encompassing drone (they start in the low part of the spectrum at about 1:15 and expand into higher registers over the next 4 minutes, but remain somewhat subliminal throughout).

Note: this piece is best experienced using headphones.

As the piece started to come together, the visual image that emerged was that of vast aerial beings in a deep atmosphere — I’ve been entranced for a long time by the idea that we live at the bottom of an ocean of air. However, as it developed further, the piece took on a darker, more somber quality, and the “voices” began to sound like wailing. I thought of the high number of non-combatant lives lost in Iraq over the past three years; some estimates put the number as high as 37,000 or more, and growing. Also, as it happens, I finished this piece on March 11, the second anniversary of the Madrid train bombings. Thus, the title and dedication of the piece.

Copyright & Licensing

Files

MP3 (12MB)
OGG (19MB)
Csound unified score file (8KB)

Tags

drones, just intonation

Sublimation (Realtime Version)

Posted 11 March 2006, 12:52

Description

A live performance version of my piece Sublimation, as arranged by Art Hunkins. Requires Csound 5.0 and a MIDI controller with 6-8 sliders or rotary pots.

Duration: 12 minutes.

Background & Technical Details

This is Art’s fourth realtime arrangement of one of my pieces. This one pushes the envelope — the sheer number of simultaneous oscillators along with the reverb processing makes this a very processor-intensive piece. Art made two variations, one using precision oscillators (as in my original version) and one using lower-precision interpolating oscillators, and also explains how to adjust the sampling rate if necessary to achieve a smooth performance; this is all explained in his performance notes.

Thanks again to Art for his dedication, time and energy. I appreciate his hard work not only on a selfish level, but also because of his tireless efforts to promote Csound as a viable and powerful tool for cross-platform realtime musical performance. To other Csound composers, I recommend reading and studying his code to learn some great techniques. Please visit Art’s site to check out his own beautiful and contemplative music.

Files

Performance notes (9KB)
CSD files and performance notes, as a zip archive (9KB)

Tags

art hunkins, collaborations, combination tones, just intonation, la monte young, midi

Sublimation

Posted 18 January 2006, 12:13

Description

A drone of varying densities built from layers of complex justly-intoned chords with scintillating harmonics.

Duration: 12 minutes.

Background & Technical Details

My primary motivation for this piece was to continue working with chords built from combination tones (see Combination Study 1, Cloud Dragon, Drift Dhikr, and Drift Dhikr Interactive) but to start exploring denser, more complex sonorities.

I continue to be fascinated and inspired by La Monte Young’s work, in this case three specific chords from The Well-Tuned Piano and various sine-tone installations: the Opening Chord, the Magic Chord, and the Magic Opening Chord. I didn’t use Young’s chords literally, but instead made five new chords whose pitches I derived based on the combination tones (summation, difference, and periodicity pitch) implied by his chords. The piece was built by combining these five chords in various layers.

Sine waves are the only sound materials used in this piece, but they are processed using a type of reverberation. I used this particular reverb opcode in Csound because it not only provides the sense of spaciousness one would expect, but also has the side-effect of creating a kind of randomized arpeggiation in the higher harmonics that evokes for me the visual phenomenon that astronomers call scintillation. If the resulting timbres seem to be more complex than simple sine waves, it’s because of the number of sine oscillators that sound simultaneously (from a minimum of 35 to a maximum of 209), and because the precise mathematical relationships between the tones creates the impression of complex composite waveforms. The “rhythms” in the middle of the piece are examples of the acoustical phenomenon of beating, which I worked with previously in The Gemini Nebula.

In the title, I’m using the word sublimation based on its meaning in the physical realm, inspired by recent conditions here in the New Hampshire countryside where the snow fields have been covered with dense white mist.

It’s important to mention that I couldn’t have made this piece (or my other La Monte Young-related pieces) without the help of Kyle Gann’s article The Outer Edge of Consonance: Snapshots from the Evolution of La Monte Young’s Tuning Installations in the book Sound and Light, which is essential to any serious study of Young’s music.

Update: A belated “thank you” to Kyle Gann for adding Sublimation to the playlist for his PostClassic Radio show!

Update 2 (15 June 2006): I am pleased to note that Tim Rutherford-Johnson (see the comments section) has been kind enough to include Sublimation in a very cool avant-classical mix Thanks, Tim!

Copyright & Licensing

Files

MP3 (28MB)
OGG (5MB)
Csound unified score file (7KB)

Tags

combination tones, drones, just intonation, la monte young

Drift Dhikr Interactive

Posted 26 July 2005, 17:55

Description

A live performance version of my piece Drift Dhikr, as arranged by Art Hunkins. For realtime versions of Csound, with or without MIDI controllers.

Background & Technical Details

See the Drift Dhikr page for background. Art’s arrangements (there are actually twelve different variants) make it possible for the performer to control several aspects of the piece, including the duration, the choice of starting interval, and more. Several of the variants are designed specifically for people with hardware MIDI controllers. See Art’s performance notes for all the details.

This is the third collaboration so far for Art and me, and as before I thank him for his interest and his energy. Please be sure to check out Art’s own music. It’s great stuff.

Copyright & Licensing

Files

Performance notes (10KB)
CSD files and performance notes, as a zip archive (44KB)

Tags

art hunkins, collaborations, combination tones, just intonation, midi

Drift Dhikr

Posted 8 July 2005, 09:53

Description

Alternate title: Combination Study 2

Pitches start at the perfect fifth and simultaneously glide up to the octave and down to tonic, and an ever-changing chord emerges from the reinforced difference and summation tones. A slowly changing ambient landscape of relative consonance and dissonance.

Duration: 9 minutes 3 seconds.

Background & Technical Details

In an earlier piece, Combination Study 1, I made a Csound instrument that, given a two pitches, played a chord consisting of that interval plus six derived pitches: first, second, and third-order difference tones; first and second-order summation tones; and periodicity pitch. I have now extended this idea to intervals that are not fixed, but change over time in a glissando. As one or both of the primary tones glide from one pitch to another, combination tones are continuously computed and played, making a chord built from several simultaneous glissandi.

This piece has three layers:

starting with the interval formed by a pitch at 1/1 and a pitch at 3/2, where the 3/2 glides down to 1/2 and the 1/1 remains constant (the conbination tones come from the moving pitch in relation to the fixed pitch);
starting with the interval formed by a pitch at 1/1 and a pitch at 3/2, where the 3/2 glides to 2/1 and the 1/1 remains constant (the conbination tones come from the moving pitch in relation to the fixed pitch);
starting with a unison — both pitches at 3/2 — where one pitch glides down to 1/1 and the other pitch glides up to 2/1 (the combination tones come from the two moving pitches in relation to each other).

Heard together, the three layers form a single chord that is constantly changing. The length of the piece is in a sense arbitrary — at shorter durations, you can hear the glissandi, but at longer duractions, the effect is much more subtle. I chose a nine minute duration for this rendition because I prefer the slower pace, but it’s short enough to make a reasonable download. If I ever put it on a CD or some other media, I will probably make it at least twice as long.

All glissandi follow exponential curves. Sine tones are the only sonic material, post-processed with some reverb.

The word drift in the title is a reference to La Monte Young’s Drift Studies. These were a series of drone pieces for sine tones that Young made in the days before he had access to the very stable sine wave oscillators he now uses; the tones would “drift” in and out of phase and pitch, hence the name.

Dhikr (Arabic for “remembrance”) is a Sufi spiritual practice that has the goal of maintaining in the participant an awareness of the presence of God. It is characterized by the rhythmic repetition (silent or aloud) of certain words or phrases, sometimes with instrumental accompaniment. This piece is not meant to sound like any kind of traditional dhikr, but it is possible to listen to it in a meditational context as a metaphor for the journey from oneness to Oneness, which corresponds to one of the aims of dhikr.

Drift Dhikr is dedicated to Lois V Vierk.

Copyright & Licensing

Files

Tags

combination tones, just intonation

Resonant Palindrome

Posted 12 March 2005, 22:45

Description

A variation on La Monte Young’s 1989 sine-tone installation The Romantic Symmetry (over a 60 cycle base) in Prime Time from 144 to 112 with 119. An electronic piece written and realized with Csound.

This is a revision of a piece called Symmetrical Melodic Variation on the Romantic Symmetry, originally published on 6 January 2005.

Dedicated to La Monte Young in his 70th year.

Duration: 9 minutes.

Background & Technical Details

La Monte Young’s Romantic Symmetry is a piece consisting of a chord of 22 sustained tones that express a specific set of harmonics of a 7.5 Hz fundamental frequency. All of these harmonics are prime or octaves of primes, except for 119. It is one of Young’s sine-tone installations, intended to run continuously for extended periods of time. The frequencies in the piece range from 60 Hz up to 8.64 kHz.

I have never actually heard Young’s piece as originally rendered, as it has not been recorded (or if recorded, not released) and I have had no opportunity to experience an installation of it, but I’ve been fascinated by this entire family of works as described by Kyle Gann in his article “The Outer Edge of Consonance” from the book Sound and Light: La Monte Young and Marian Zazeela (Bucknell University Press, Lewisburg 1996, ISBN 0-8387-5346-9). Gann provides a detailed analysis of the piece, including a complete list of the harmonics employed. From this I was able to easily produce a rendering of the Romantic Symmetry using Csound. Once I was able to actually hear it, I was inspired to write something that would explore some of the intervallic combinations embodied in the material of the piece. I wanted to refract the multicolored light of Young’s chord into a revolving mobile, to provide an additional way of hearing it. The result is the work presented here.

In the title Symmetrical Melodic Variation, I’m using the term “melodic” in the sense that matches my understanding of Young’s use of the term, in that the tonal materials are used horizontally rather than vertically. By “symmetrical,” I mean that I am deliberately working with the intervallic/registral symmetry inherent in Young’s arrangement of pitches. The drone note, the 127th harmonic, is the axis of symmetry in Young’s chord. I divided the remaining pitches into three “registers”. Of the four moving voices, the bottom one uses the lower seven pitches, the middle two voices use the central nine pitches minus the 127 axis, and the top voice uses the upper six pitches. Each voice uses step-wise motion, beginning and ending at the same pitch within its series. Each voice uses notes of equal duration, but each register is at a slightly different speed, so that they all start and end at the same time. The end result is that each voice, and thus the entire piece, is melodically and rhythmically symmetrical — in fact, each voice is a palindrome, which is reflected in the new title. All of the pitches used in the Romantic Symmetry are present in this piece, and there are no additional pitches added.

For the original version of the piece, I made an instrument that combines a simulation of a plucked string (using Csound’s pluck opcode) with a simple oscillator tone. I did not use a pure sine wave except for the central drone, but the other tones use relatively pure waveforms consisting of the first partial with different strengths of the 2nd, 4th, and 8th partials; since these are all octaves of the fundamental, the pitch ratios remain unmuddied.

In the revised version of the piece, I removed the pluck sound and used a simple oscillator tone. All the voices are now pure sines, except for the lowest voice, in which I added a bit of the second partial to balance it better against the higher-pitched voices. The other big change was to use a different type of reverb, using the Csound babo (“BAll-within-the-BOx”) opcode. The cool thing about this reverb is that it allows one to specify the exact dimensions of the virtual room, and well as the three-dimensional placement, within that room, of the sound source. I decided to use a room size that was a multiple of the wavelength of the fundamental frequency (7.5 Hz), to get a “tuned” resonant reverberation. I also chose to make a two-stage reverberator, where the output of the first fed into input of the second.

I am indebted to Kyle Gann, without whose writings I could not have even begun to study and explore areas of La Monte Young’s work which would otherwise have been inaccessible to me.

Notes on the Revision

I decided to revise this piece for two reasons.

First, I wasn’t really satisfied with the sound of the piece (the plucked sound was too harsh, and there was not enough “spaciousness” in the overall sound). I made the individual timbres simpler but took a different approach to overall texture over time by putting the sound within a much more resonant (virtual) space — see the penultimate paragraph in the previous section for details.

Second, I wrote this before I realized that it would become part of a series (it is the first of three, continuing with The Gemini Nebula and concluding with Passacaglia and Fugue State). After completing the other two, I felt the need to go back and make this one more consistent with the others. More specifically, I wanted simpler timbres and a greater emphasis on beating patterns and combination tones from massed sonorities. The new title is more consistent with the other pieces as well, in that it is hopefully a little more evocative and less prosaic.

Thanks to Torsten Anders for his comments.

Copyright & Licensing

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Tags

just intonation, la monte young

Passacaglia and Fugue State

Posted 6 March 2005, 21:56

Description

An electronic work inspired by La Monte Young’s sine-tone installation The Base 9:7:4 Symmetry in Prime Time When Centered above and below The Lowest Term Primes in The Range 288 to 224 with The Addition of 279 and 261 in Which The Half of The Symmetric Division Mapped above and Including 288 Consists of The Powers of 2 Multiplied by The Primes within The Ranges of 144 to 128, 72 to 64 and 36 to 32 Which Are Symmetrical to Those Primes in Lowest Terms in The Half of The Symmetric Division Mapped below and Including 224 within The Ranges 126 to 112, 63 to 56 and 31.5 to 28 with The Addition of 119.

Written and realized with Scala, blue, and Csound.

Dedicated to La Monte Young in his 70th year.

Duration: 10 minutes 45 seconds.

Background & Technical Details

This is the third and final piece in what has become a series inspired by La Monte Young’s sine-tone installations, following Symmetrical Melodic Variation on the Romantic Symmetry and The Gemini Nebula.

I used Scala to build a 31-note microtonal “scale” based on the complete set of unique pitches in Young’s The Base 9:7:4 Symmetry, in essence recasting Young’s carefully-selected group of prime-numbered harmonics as generalized interval ratios rather than absolute multiples of a fundamental. This allowed me to use the pitches in any register — similar to the strategy I used in The Gemini Nebula. However, whereas in the latter piece I kept everything constrained to the range of a single octave, in this piece I use a broader registral pallette (though not as broad as Young’s).

The piece consists of four layers:

a set of five drones on 1/1, 9/8 and 7/4, using the Risset harmonic arpeggio effect to sound slightly tamboura-like;
a sort of obbligato built from two complex waveforms that together encode the cluster of harmonics at the registral “center” of Young’s piece, using a much slower version of the Risset effect to create a sort of looping cascade that sounds almost like intersecting glissandi;
a repeating three-note bass motif: 1/1, 7/4, 9/8, …;
a sine-wave “chorale” on 12 pitches within the range of an octave, starting as two voices diverging in pitch, then slowly gathering into a cluster containing all 12 notes plus two more, creating complex binaural beating patterns.

The piece starts with the drone, then adds the obbligato, then the bass motif, and finally the chorale, which builds in intensity and density almost until the end, when suddenly only the done remains to fade out.

The title comes from the repeating bass motif, which reminded me of one of my favorite musical forms, the passacaglia. The rest of the title is, of course, a joke. At the same time, I hope that the piece has a kind of ambient hallucinatory quality, so the phrase fugue state seemed appropriate.

Thanks yet again to Kyle Gann for his article in Sound and Light, without which I could not have embarked on this project.

Copyright & Licensing

Files

MP3 audio (23MB)
Ogg-Vorbis audio (10MB)
Archive containing blue project file, Csound unified score file generated by blue, and Scala Base974 scale (7KB)

Tags

drones, just intonation, la monte young

The Gemini Nebula

Posted 31 January 2005, 06:38

Description

A variation on La Monte Young’s The Prime Time Twins in the Ranges 576 to 448; 144 to 112; 72 to 56; 36 to 28; with the Range Limits 576, 448, 288, 224, 144, 56, and 28. An electronic piece written and realized with Scala, blue, and Csound.

Dedicated to La Monte Young in his 70th year.

Duration: 7 minutes 30 seconds.

Background & Technical Details

Young’s Prime Time Twins is one of his continuous sine-tone installations. The twins of the title refer to pairs of numbers called “twin primes”: prime numbers that have a difference of two, such as 137 and 139. Young treats the set of twin primes listed in his title as overtones above a subsonic fundamental at 7.5 Hz. The piece consists of these ten pairs of pitches, which cover a five octave range, combined with seven other pitches (multiples of the seventh and ninth partials, the “range limits” of the title). The fundamental does not appear in any octave, but is implied by the resulting combination tones.

In preparing for my piece, I converted the PTT numbers into ratios, essentially reducing them to intervals within a single octave. Then I used Scala to gather these ratios, along with 9/8 and 7/4, into a “scale” (linked below). The fascinating thing when one considers the notes in this way is that it reveals very clearly that the PTTs are grouped into two tight clusters or ranges at the high and low ends of an octave: five pairs are located between 1/1 and 9/8, and the other five pairs are located between 7/4 and 2/1. Here is a table of the PTT “scale”, in ascending pitch order:

Ratio	Cents	Interval
1/1	0.000	unison
521/512	30.167	521-523 twins
523/512	36.801	521-523 twins
269/256	85.755	269-271 twins
271/256	98.579	269-271 twins
137/128	117.638	137-139 twins
139/128	142.729	137-139 twins
281/256	161.312	281-283 twins
283/256	173.590	281-283 twins
569/512	182.742	569-571 twins
571/512	188.816	569-571 twins
9/8	203.910	major whole tone
7/4	968.826	harmonic seventh
227/128	991.858	227-229 twins
229/128	1007.045	227-229 twins
461/256	1018.348	461-463 twins
463/256	1025.842	461-463 twins
29/16	1029.577	bottom of 29-31 twins
59/32	1059.172	bottom of 59-61 twins
239/128	1081.040	239-241 twins
241/128	1095.467	239-241 twins
61/32	1116.885	top of 59-61 twins
31/16	1145.036	top of 29-31 twins
2/1	1200.000	octave

In my piece, I use all of these pitches within the octave that starts at 240 Hz. The 1/1 and 2/1 are used as drones, as are 9/8 and 7/4, together serving as what Young calls range limits. The other tones enter gradually from low to high within the limits, and then gradually leave. As the texture thickens, the beating between tones forms a complex rhythmic pattern. Each pair of twins is played in stereo, with the pair members on opposite sides, which adds the element of binaural beating. All of the tones are simple sine waves, and no effects are used. The piece was composed using Steven Yi’s excellent program blue, which allowed me to work directly with the PTT scale I made in Scala.

The title The Gemini Nebula has several derivations. Gemini, of course, is a reference to twins. I used the word nebula because one of the effects produced by the piece reminds me of the “clouds” in the piano music of Young and Michael Harrison, but since I recently used the word “cloud” for another piece, I decided to use a related word. (By the way, it turns out that there really is an astronomical object called the Gemini Nebula.)

As with my previous piece that takes off from one of La Monte Young’s sine-tone works, I relied on Kyle Gann’s article “The Outer Edge of Consonance: Snapshots from the Evolution of La Monte Young’s Tuning Installations”.

Copyright & Licensing

Files

MP3 (18MB)
OGG (2MB)
blue project (text, 11KB)
Csound unified score file (text, 2KB)
Scala Prime Time Twins scale (text, 307B)

Tags

drones, just intonation, la monte young

Cloud Dragon

Posted 7 December 2004, 17:56

Description

A live electronic piece; a series of swelling sustained chords built from the combination tones resulting from just-tuned dyads, over an optional drone.

Duration: variable. Requires a performer, a PC, one or two banks of eight continuous MIDI controllers (optional) and certain versions of Csound (see below for details).

Realized for live performance by Art Hunkins.

Background & Technical Details

This is a live-performance (i.e., real-time) Csound piece based on Combination Study 1, made in collaboration with Art Hunkins. It was Art’s idea to transform CS1 into a live piece. I did a little work on the visual appearance, and came up with some ideas for opening up the possibilities of the piece, but Art is responsible for all the hard work of designing and coding the performance arrangements, as well as writing the performance notes — he really drove this project. There are several different versions of the piece included, as explained in the performance notes, excerpted below:

There are three major versions of Cloud Dragon – indicated as v1, v2, and v3. They differ by performance instrumentation: v1 uses only computer mouse and monitor; v2 requires a bank of 8 MIDI (continuous) controllers – either pots or sliders; v3 requires 12 (or 14) controllers, configured as a bank of 8 and a bank of 4 (or 6).

There are three variants of each version as well – indicated as a, b, and c. Variant a is the most basic, offering preset Chord Ratios; its fixed six-chord sequence (and suggested performance order) is 8/5, 7/5, 6/5, 7/6, 9/8 and 5/4; eight-chord sequences add a final 4/3 and 3/2.

Variant b allows the performer to select his/her own Chord Ratios; the choices (numerator and denominator) are integers between 1 and 1500. Default settings are the fixed ones indicated above. In addition, the performer can select a single Chord-to-Drone Root Ratio – a kind of global transposition factor for all chords. (Default is 1/1 – no transposition.) Again, integers up to 1500 are allowed in numerator and denominator. All these ratios may be varied during performance, but doing so is not encouraged. Any change takes place with the following chord.

Variant c permits the performer, in addition to the above, to specify Chord-to-Drone Root Ratios independently for each chord (all defaults, 1/1). This variant encourages you to explore the wide-open possibilities of tuning systems referenced by Dave Seidel on his Combination Study 1 webpage (see above).

Versions 3b and 3c have the highest degree of flexibility and will hopefully be interesting and fun for anyone who would like to experiment in realtime with complex ratios that are not necessarily anchored to the “root” (1/1) established by the drone.

Because this is a live performance piece that employs a graphical user interface, only certain versions of Csound are suitable. See the performance notes (available below as a separate download) for details.

For more information on the underlying musical/acoustical concepts, see the notes for Combination Study 1. The title comes from an image I get when listening to the piece: a winged serpent weaving in and out of the tops of the clouds, sinuous and gleaming in the sun.

My sincere thanks to Art Hunkins for envisioning this project and making it happen. “Cloud Dragon” is also listed on his site, along with some of Art’s other compositions (electronic and otherwise, most of them realtime), which are lovely and well worth checking out.

Copyright & Licensing

Files

Performance notes (text, 8KB)
Csound unified score files and performance notes (zip, 42KB)

Tags

art hunkins, collaborations, combination tones, just intonation, midi

Combination Study 1

Posted 24 October 2004, 11:23

Description

Over a bed of sruti-box-like drones, a slow chord sequence plays through twice, first in closed voicing, then in open voicing. Best listened to with headphones.

Duration: 8 minutes, 5 seconds.

Background & Technical Details

This piece was inspired by a section of David B. Doty’s excellent book The Just Intonation Primer. Chapter 2, “Acoustic and Psychoacoustic Background”, pages 17-19, discusses the phenomena of difference tones, summation tones (collectively referred to as “combination tones”) and the periodicity pitch. I won’t get into a detailed description of these terms, but essentially they describe pitches that are synthesized by our ears and/or by our higher-order neural processing in response to hearing a set of two or more simultaneous tones. These tones are not always perceivable by the listener, but are theoretically always present, or at least potential.

When I read this part of the book, I was fascinated by Figures 2.10 (page 17) and 2.11 (page 18) which show in musical notation the chords that emerge from certain simple-ratio intervals when these combination tones are perceived. I decided to make a Csound instrument that, given an interval, would produce a chord consisting of the original dyad plus its derived combination tones. My initial motivation was to simply make these chords audible with properly-tuned intervals (not possible on my equal-tempered keyboard), but when I heard the results, I decided to write something using these materials.

The instrument I eventually came up with (instr 2 in the Csound score), takes as input a starting pitch and a ratio (which together describe the base dyad) and computes an eight-note chord consisting of the dyad plus three difference tones (first-, second-, and third-order), two summation tones (first- and second-order), and the periodicity pitch. Of course, for a given dyad, the resulting combinations tones are not always unique, so there are not always eight distinct pitches. A chord based on an interval smaller than an octave will generally cover a wide range (i.e., it’s in an open voicing), but I wanted to be able to hear what a close voicing version would sound like, so I added the capability of “reducing” the chord such that all the tones could be transposed as necessary to be restricted to a given interval, such as an octave. The chord sequence in this piece is played in close voicing the first time, and in open (or natural) voicing the second time. I also added a little flanging to “fatten” the sound.

The chord sequence in the piece is based on a series of simple-ratio intervals, all except one (9/8) taken directly from the Doty figures. The complete set of ratios used (in the order in which they appear) are 8/5, 7/5, 6/5, 7/6, 9/8, and 5/4.

The drone in the background is based on an instrument I found in the Amsterdam Catalog of Csound Computer Instruments v1.2, which implements Risset’s design for a harmonic arpeggio. The drone consists of four instances of this instrument on the pitches 1/1, 3/2, 2/1, 2/1 (tonic, fifth, tonic+8ve).

The entire piece is based on a root frequency of 60Hz. If I were to make a “European” version, I would base it on 50Hz (you can do this yourself by commented out line 256 in the score, and uncommenting line 259).

I wrote the piece with Csound version 4.23f12 (the “canonical” version), using the 64-bit Windows executable. The piece renders fine in real time, at least on my machine (try this yourself by uncommenting line 19 and commenting out line 20 in the score).

Copyright & Licensing

Files

Score in Csound unified file format (10KB)
MP3 soundfile (8:05, 19MB)
Ogg Vorbis soundfile (8:05, 5MB)

Tags

combination tones, drones, just intonation