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

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

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

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

Files

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

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

http://mysterybear.net by Dave Seidel is licensed under a
Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 Unported License.