mysterybear: tag

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

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

MP3 audio (21.2MB)
Csound unified score file (11KB)

Tags

combination tones, just intonation

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)

Tags

combination tones, drones, just intonation

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