mysterybear: tag

I’ve long been fascinated by the psychoacoustic phenomena known as binaural beats, and I have employed this effect in previous pieces, particularly The Gemini Nebula. I wanted to make another piece where binaural beats were integral to the music, and the result is Gyre.

Gyre consists of a single 14-note chord whose pitches are introduced in high-to-low order and eventually removed in the reverse order. I used La Monte Young’s Magic Opening Chord, which I have worked with previously. Each tone is produced using two sine waves: one tuned very slightly higher than the target pitch and the other tuned slightly lower, panned to opposite stereo channels. The difference in pitch between any given pair of tones ranges from a bit over 4 Hz to a bit over 11 Hz. These are all within the range that causes binaural beating to occur in the listener’s perception.

The trick here is that I made the beating proportional to the pitch. In other words, the highest note beats at the fastest rate, and the beating is slower with successively lower pitches. The chord is tuned in just intonation, meaning that each interval can be expressed as a rational number (e.g., 3/2, which a perfect fifth). Each tone beats at its own rate which is similarly related to the beats of the other pitches. Thus, as the chord is built, the listener perceives a progressively complex structure of interlocking rhythms. In fact there are two layers of rhythm: one from the binaural beating, and the other from the tonal relationships of the notes in the chord.

The piece is buiilt from nothing but sine waves, with no effects or additional processing. I made it with blue and Csound. You can get the blue project file here.

IMPORTANT: To get the full benefit of the binaural beating, listen to this with headphones. It will also work with speakers, but in that case do your best to place yourself as closely as possible to the center of the stereo field.

Gyre by mysterybear (click the down-arrow to download the track)

Gyre by Dave Seidel is licensed under a Creative Commons Attribution-Noncommercial 3.0 Unported License.

Tags

binaural beats, drones, just intonation, la monte young

Elegy, for Jon

Posted 18 November 2009, 19:40

Jon playing his Guild, 1966

Jon Gams, my closest friend (aside from my wife) for the past 34 years, passed away 11 days ago. It was a complete shock — he got the flu, and he was gone. He was one month short of his 58th birthday.

Jon and I met in 1975, when I was 17 and he was 24, in Great Barrington, MA where I was going to college and he was living. He was looking for someone to play guitar with. We were musical partners, friends and brothers from our first meeting. We had a band in NYC called People Falling from the late ’70’s through the ’80’s and continued to collaborate well into the ’90’s. In the past few years we continued to work together sporadically, but we were too busy with other things and lived too far apart to be productive, a reality that we were finally able to acknowledge to each other only this past September.

(You can hear the last completed piece that we wrote and recorded together, called “Fascists Call Beauty A Joke”, using the music player on the front page of this site, or you can download it. It was published on a CD that accompanied issue #5 of Lingo, the arts magazine that Jon edited and published in the ’90’s.)

“Elegy, for Jon” is a variant of “Solar Midnight”, the second track of my Complex Silence 4 release. I had wanted to make a version that was tuned in just intonation; the original uses an “irrational” tuning based on the Golden Ratio. It is a very slow three-voice mensuration canon in a simple scale, first played at the same starting pitch and then with three different starting pitches.

As I worked on this rearrangement/retuning I realized that it was taking on a strongly elegiac quality. I completed it on Saturday, November 7, 2009 in the early afternoon. Then I went out to make some field recordings of a river. The following morning I learned that it had been Jon’s last day on Earth. It was a week before I could think about this music again and realized what it was for.

Download MP3

Copyright 2009 by Dave Seidel, some rights reserved.

Elegy, for Jon by Dave Seidel is licensed under a Creative Commons Attribution-Noncommercial 3.0 Unported License.

Tags

canons, drones, jon gams, just intonation

New release: Complex Silence 4

Posted 22 October 2009, 10:11

I am pleased to announce the release of Complex Silence 4, my contribution to Phillip Wilkerson’s Complex Silence series, distributed on the Timetheory netlabel.

The release consists of two pieces, Meridian Transit and Solar Midnight, both of which derive musical materials in various ways from the Golden Ratio. This is microtonal music, but (unusually for me) does not employ just or rational intonation. I made both tracks with blue and Csound.

To get the release (including graphics, a PDF with liner notes, and
MP3s), please visit http://www.archive.org/details/tmth06A

When time permits, I will post technical notes and source code to both pieces on this site.

Tags

canons, complex silence, drones, golden ratio, timetheory

A Door Into Spring

Posted 26 April 2009, 00:07

Description

A rhapsody in distressed metal.

Duration: 9:14

Background & Technical Details

I made a recording just under seven seconds long of the sound made by the spring inside my dishwasher door when it’s opened and closed. Then I slowed it down to a bit over nine minutes in duration and played it back in six layers, each at a different pitch. The layers are staggered low to high, making it a canon. Besides being time-stretched and pitch-shifted, the sampled sound has also been filtered, compressed, and reverbed, all in a few lines of Csound code. No other sounds, sampled or otherwise, were added.

(For the sake of completeness, I recorded the sample as a stereo 96K/24-bit WAV file using my Zoom H4 recorder. Then I used Audacity to trim it and convert it to mono before using the sample in Csound.)

Files/Downloads

MP3 (21MB, 320kpbs, 44.1/16)
FLAC (24MB, 359kpbs, 44.1/16)
Original sample and Csound orchestra/score (2MB)

Copyright 2009 by Dave Seidel, some rights reserved.

A Door Into Spring by Dave Seidel is licensed under a Creative Commons Attribution-Noncommercial 3.0 Unported License.

Tags

drones, granular synthesis, metal, spring

Herald of Water, Herald of Air

Posted 25 February 2009, 23:15

Description

Two versions of a tantric fanfare. Dedicated to La Monte Young and Lois V Vierk.

Duration: 16:03 each version, or 32:06 total

Background & Technical Details

A single chord, eleven notes, built up slowly from low to high. Each voice has a regular pulse that starts almost completely still and accelerates to a speed proportional to its pitch — the higher the note, the faster the pulse. From the peak, everything decelerates together, back to near stasis.

The pulses are shaped, dynamically and timbrally, by a random process, a different sequence for each voice. The “Water” version has smooth transitions from one pulse to the next, producing an undulating texture. The “Air” version has abrupt transitions, resulting in a percussive/plucked/struck attack. This is the only difference between the two versions of the piece, except for the random aspect (which makes every rendering or performance somewhat unique). In character, I think “Water” is more ambient and “Air” is more ecstatic.

This chord is built by combining two of La Monte Young’s chords¹, the Opening Chord and the Magic Chord. These are the pitches, expressed as multipliers of the unheard base pitch of 60Hz:

2, 3, 3.5, 4, 4.5, 5.0625, 5.25, 6.75, 10.125, 12, 13.5

The instrument design is derived from Atte André Jensen’s ResonantRhythm, which I tweaked quite a bit for my own purposes, quite different from Atte’s original intention. I’m grateful to Atte for all his work on this and a number of other useful instrument and effect designs for Csound/blue.

Of course, I am deeply indebted to La Monte Young for the Opening Chord and the Magic Chord, as well for his (and Michael Harrison’s) “cloud” technique, which inspired the texture of this piece.

I am also in debt to to Lois V Vierk, in particular her use of logarithmic curves as a key structural element. I was fortunate to have worked with Lois for a while as a player (I participated in the premiere live and recorded performances of her pieces Go Guitars and Red Shift), and being “inside” her music was a profound experience that has had a deep effect on me as a composer. The accelerations and decelerations in this piece are linear rather than logarithmic, but they nonetheless are informed by Lois’ example.

¹ Kyle Gann, “The Outer Edge of Consonance,” in William Duckworth and Richard Fleming (editors), Sound and Light, La Monte Young and Marian Zazeela (Lewisburg, PA: Bucknell University Press, 1996), page 174.

Files/Downloads

MP3 – Herald of Water (37MB, 320kpbs)
MP3 – Herald of Air (37MB, 320kpbs)
blue project and Csound orchestra/score (6KB)

Copyright 2009 by Dave Seidel, some rights reserved.

Herald of Water, Herald of Air by Dave Seidel is licensed under a Creative Commons Attribution-Noncommercial 3.0 Unported License.

Tags

drones, just intonation, la monte young, lois v vierk

Nur

Posted 11 January 2009, 18:44

Description

Ecstatic light: a virtual dhikr.

Duration: 7:50

Background & Technical Details

This is my first SuperCollider (SC) piece. Having just put out a CD-R release, the result of three years or so of working with Csound, it seemed like a good time to try something new. Another excuse for experimentation was provided by an invitation to participate in the first show in the Unique States series. As I prepared for this event, I ported my Csound Risset harmonic arpeggio instrument to SC and started playing around with it in real time (something which is much easier to do in SC than in Csound). This piece is what emerged. I performed it for the first time at the Unique States event at BUOY in Kittery, Maine on Friday, January 9, 2009.

While it is intended to be performed live, I have included a rendering of the piece (available below) for people who just want to listen. If you use SuperCollider, and would like to try this, the source file (also available below) contains comments that explain how to play it; you should find it quite straight-forward. (Please note, if you are an SC aficionado: I know that the piece could have been written more compactly, but I am still a newbie, and I chose to err in the direction of directness, simplicity and readability as opposed to elegance. Plenty of time to get fancy later.)

The piece itself is no radical departure from my previous work, but continues to explore some of the things I find interesting, in particular the use of interference patterns to create subtle rhythms, the tension between stasis and constant change, and the power of perfectly tuned consonance.

If you listen to this on speakers (as opposed to headphones), please turn it up — the sound should fill the room.

Files/Downloads

MP3 (18MB, 320kpbs)
SuperCollider code (5KB)

Copyright 2009 by Dave Seidel, some rights reserved.

Nur by Dave Seidel is licensed under a Creative Commons Attribution-Noncommercial 3.0 Unported License.

Tags

drones, just intonation, supercollider

Unstill Light

Posted 27 October 2008, 20:19

Description

Epimoric dream music. For Greg Schiemer and Warren Burt.

Duration: 7:49

Background & Technical Details

The initial spark for “Unstill Light” was a piece by Greg Schiemer called Tempered Dekanies and his related article Tempered Dekanies: Chorus effect using microtonal intervals based on just intonation. As described in the paper, and heard in the piece, Greg came up with an Csound instrument design that is based on the Risset harmonic glissandi. This was intriguing, as I have used a similar instrument in several of my pieces; however, Greg added a couple of new wrinkles, once of which is particularly interesting: using superparticular (or epimoric) ratios to determine the frequency differences between the stacked oscillator tones that together produce the output of the instrument. I immediately wanted to explore that idea, and I ended up writing something that is entirely based on epimoric ratios and uses a version of Greg’s Risset instrument (modified to produce a different effect from the one he used in his piece).

Fundamentally, the piece is based on the superparticular series 3/2, 4/3, 5/4, 6/5, 7/6, 9/8. If you treat these numbers as musical intervals relative to a “root” (1/1) pitch, they get progressively narrower as one moves through the series (3/2 is a just perfect fifth, 9/8 is a just major second, and the others fail in between). Then for each number in the series I computed the ratio that is the “harmonic mean” between that number and 1/1, giving the series 5/4, 7/6, 9/8, 11/10, 13/12, 15/14, 17/16 (note that these are all superparticular as well). Finally, I made two more series that consist of the the reciprocals of the two original series. If we stack up all four series, add in the 1/1 pitch, and look at it in table form, the columns form the chords that are the harmonic basis of the piece (top-to-bottom = high-to-low pitch):

3/2	4/3	5/4	6/5	7/6	8/7	9/8
5/4	7/6	9/8	11/10	13/12	15/14	17/16
1/1	1/1	1/1	1/1	1/1	1/1	1/1
4/5	6/7	8/9	10/11	12/13	14/15	16/17
2/3	3/4	4/5	5/6	6/7	7/8	8/9

The chords get narrower and more closely-voiced as they progress, converging on the central root pitch.

However, the chords are not simply played as blocks. Except for the central 1/1 pitch, which remains constant, the horizontal voices are offset from one another, so that the chords change gradually, one note at a time.

Getting back my modified Schiemer/Risset instrument, I didn’t employ Greg’s use of envelopes to vary the pitch offsets, using constant offsets instead. I also decided to use much smaller ratios (based on twin primes 1021 and 1023) for the oscillator offsets, resulting in a 2:1 beating pattern (DAH-dit, DAH-dit). Since the duration of the beats depends on the pitch, two or more voices at different pitches played together creates a rhythmic counterpoint. Different lines come in and out of sync with one another, sounding at times like arpeggios.

The chords played on the pulsating Scheimer/Risset instrument have no added effects, but they are backed with a reverb-processed drone. The only sound source used is a precision sine wave generator.

Thanks very much to Greg Schiemer for his music, for corresponding with me about his work, and for allowing me to study his Csound code. I also dedicate “Unstill Light” to Warren Burt, another source of inspiration.

Copyright & Licensing

Files/Downloads

MP3 (17.8MB, 320kpbs)
blue project (35KB)

Tags

drones, epimores, greg schiemer, just intonation, superparticular numbers, twin primes, warren burt

Law of Octaves

Posted 12 August 2008, 13:29

Description

A third take on the idea in I first explored in Drift Dhikr, with a richer timbre and harmonic texture.

Duration: 9:03

Background & Technical Details

As I indicate above, this is my third attempt at expressing a rather simple idea: a simple chord, augmented by continuously-generated difference and summation tones, that glides from a starting consonance to an ending consonance via a long gradual glissando. The first piece used simple sine waves; the second piece used a form of FM synthesis. This one is back to plain old oscillators, but with some other refinements:

a more complex waveform, built from the first seven unique partials in the Fibonacci sequence (1, 2, 3, 5, 8, 13, 21)
a more complex chord — the original chord plus the indentical one tranposed to the just perfect fourth (4/3) in a lower octave
movement in space by panning from the center to both sides.

I like the results better than the two previous pieces, and hope that you do as well. I won’t get into an explication of the title, which you can discover for yourself if so inclined.

Copyright & Licensing

Files/Downloads

MP3 (21MB, 48K/16-bit, 320kpbs)
Csound project file (102KB)

Tags

combination tones, drones, just intonation

Second Sleep

Posted 14 July 2008, 19:10

Description

A waking dream — an
empty bowl by a still pond
lit by the full moon.

Duration: 7:53

Background & Technical Details

Second Sleep returns to the harmonic material I first started exploring in Aurora. In this piece, I move from one pentatonic scale (introduced as a slow, rising arpeggio and prolonged as a chordal drone) to another pentatonic scale, and back again. The continuous background drone consists of the “root” (1/1) pitch shared by both pentatonic scales, along with three other pitches that do not appear in either of the scales.

The first pentatonic scale (expressed as ratios) is:
1/1 9/8 151/128 3/2 25/16

The second pentatonic scale is:
1/1 37/32 21/16 49/32 7/4

The drone is built from the pitch set
1/1 65/64 43/32 57/32

The pentatonic scales/chords use a modified version of a Csound/blue instrument called Resonant Rhythm by Atte André Jensen. Atte describes his instrument as an “animated, resonant pad/drone/bass instrument with tempo sync”. As he designed it, it produces a steady pulse at a given rate, with randomized filtering applied to each successive note. I modified it for my own nefarious purposes in a couple of different ways:

I made the articulation of the beat-to-beat transitions much “softer”, so that the beats aren’t really perceived as such;
I used nine oscillators with very small pitch offsets rather than one, similar to the Risset harmonic arpeggio technique, to make the sound richer, giving it an almost horn-like quality.

In all instances of the modified Resonant Rhythm (MRR) instrument, I used a pulse-width modulated square wave.

Parts of the background drone (1/1 in three octaves) also use the MRR instrument. The other three pitches use a Risset harmonic arpeggio instrument with a waveform built from the the first eleven harmonics from the Fibonacci sequence (i.e., 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, and 144).

Copyright & Licensing

Files/Downloads

MP3 (18MB, 44.1K/16-bit, 320kpbs)
blue & Csound project files, Scala files (12KB)

Tags

drones, just intonation, kraig grady, meta-slendro, mount meru

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)
blue & Csound project files, Scala files (23KB)

Tags

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

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)
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

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

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

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

Tags

drones, just intonation, la monte young

Drone Instrument - Sruti Box

Posted 8 January 2005, 13:28

Description

A realtime Csound instrument with a graphical interface, intended for use in live performance with other instruments (acoustic and/or electronic). For use with CsoundAV (and Csound5, once it is released).

Features:

One to four voices
Tunable base pitch by frequency
Each voice tunable as a ratio plus an octave displacement relative to the base pitch
Nine selectable waveforms (1 sine, 2 sawtooth, 2 square, 2 prime, 2 Fibonacci)
Optional Risset harmonic arpeggio effect
Built-in reverb

Performance Notes

The are four drones, each one arranged in a column. The button at the top turns the drone on or off. The two controls belows the on/off button are the numerator and denominator that specify the tuning ratio for the drone. For example, for the interval 2/1 (octave), set the upper control to 2 and the lower one to 1. The small arrow changes the setting by 1; the double arraw changes the setting by 10. The ratio control will accept any whole number up to 1500.

The next control down sets the octave displacement of the drone relative to the base pitch: 0 means that the drone is in the same octave as the base pitch, 1 means one octave up, -1 means one octave down, etc. Under the octave control is a “mute” switch, so that you can exclude one or more drones, which is useful if you want to turn them on or off as a group.

In the middle is control that sets the frequency of the base pitch against which the drones are tuned. The single arrow moves in increments of .05 Hz; the double arrow is in increments of 5 Hz. (If you would like a version with finer-grained control, let me know.)

The next set of buttons selects the waveform that will be used by all the drones. See the next section for details.

The bottom row contains the Play and Stop buttons, which turn all (unmuted) drones on or off, respectively.

Finally, the Harmonic arpeggio control activates the Risset effect that is described in the next section.

Background & Technical Details

Since I don’t own or have regular access to a tamboura, and have been dissatisfied so far with the reed-and-bellows or electronic sruti boxes I’ve tried, I decided to make one of my own. As a student of just intonation, I decided to make the drones tunable using ratios. The default settings match one of the typical tamboura tunings: 1/1 (Sa), 3/2 (Pa), 2/1 (Sa’), 2/1 (Sa’), but of course you are free to use whatever ratios you wish. For example, a very nice set of ratios incorporating the septimal seventh is 1/1, 3/2, 7/4, 2/1. Or replace the 2/1 with a septimal whole tone (8/7) or a major whole tone (9/8). The possibilities are endless.

I’ve included a range of waveforms. The sawtooth and square waves are probably the closest to most existing electronic sruti boxes. The “prime” wave is a waveform built up prime-numbered partials through 23; the “Fibonacci” wave is built up from partials in the Fibonacci sequence through 89. The sawtooth, square, prime and Fibonacci waves have two variants each. In the first instance of each wave, the strengths of the partials are calculated as 1/n (where n is the partial number). The alternative versions use the formula 1/n + 1/(n-1), which results in slightly richer harmonic content.

The optional Risset harmonic arpeggio effect is a technique discovered by the pioneering electronic composer Jean-Claude Risset. By combining an oscillator with eight other oscillators at slight frequency offsets, a complex interference pattern is created that sweeps through the component harmonics of the original waveform. This is the best way I’ve found so far to produce a sound that suggests the characteristic buzzing sound of a tamboura string.

I will likely revise this instrument over time with different effects, waveforms, and controls, possibly even a “rhythmic” version that simulates a plucked tamboura. I am certainly open to suggestions, so please add a comment to this page or send me email if you have any ideas, requests, or bug reports.

This is dedicated to Art Hunkins, from whom I have been learning a lot about realtime Csound, including some techniques that greatly improved the design of this instrument.

Copyright & Licensing

Files

Csound unified score file (text, 14KB)

Tags

drones

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)

Tags

combination tones, drones, just intonation

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