Comments about the work being presented at this conference

In this paper, I will discuss the specific issues raised by the piece of music I am presenting at tomorrow's presentation, Composed Spaces Loudspeaker Concert.

Power Chords, Polyphonic Trains and Plain Old Phase is a minimalist work for loudspeaker array that was composed with the several of the above principles in mind. It was composed as a study pertaining to research for a larger compositional project I have been working on.

The work consists of what I think of as a large dynamic frame or bowl of reverberant sonic textures preceded by an introduction and followed by a coda. Within that bowl are numerous musical episodes that follow the dynamics of the bowl.

There is no programmatic intent — the work is entirely abstract.

Sonic materials

Sine waves and square waves

I created a library of sine waves ranging over seven octaves, tuned to a just Aeolian mode based on A. In addition, I generated a much smaller family of square waves, also tuned to that just Aeolian mode. These very simple materials constitute the primary materials used for the piece.

Interestingly, we seldom use “pitches” above 2.1 kHz. (C above high C). In this work, there are sinusoidal pitches as high as 10 kHz.., and it turns out that they have interesting and quite powerful emotional qualities for listeners, representing a fundamentally different quality of pitch than we encounter with acoustic instruments.

Power Chord

I used the attack of a generic recorded electric guitar “power chord” to create the structural frame or bowl of the work.

Processes

Reverberance

Reverberance, in the physical world, is the decay of sonic energy in a reverberant space over time. Aesthetically, reverberance is an extremely powerful and emotion-laden sonic perfume (based, I believe, on safety cues for survival) that provides us with much of our very satisfying sense of envelopment, particularly in a surround sound environment. Electronically, reverberance becomes a highly flexible and versatile sound treatment that can provide us with resonant pitch, spectrally changing texture and spatial dynamism of a sound. Further, in our multichannel environment and with just intonation, reverberance can be used as an agent of what might be called “liquification,” allowing us to immerse ourselves in an active soundfield that is no longer separate or transient but instead becomes the auditory manifestation of the air in which we live and breathe. I find the sensation extremely pleasant, and unique to loudspeaker music.

In my work, the very slow decay of reverberance is a key element. When the reverberation time is several minutes or more, reverberation stops being the transient energy residue of an event and becomes instead, a continuum of sonic energy. And because it is dynamic and constantly changing as a function of its existence, it is of far greater interest to us than are the sonic materials from which it descends.

Beating and rhythms

Beating arises as amplitude modulation derived from sub-audio difference frequencies. When using very simple sine wave intervals, beating rates can be easily controlled. In reverberant fields, beating arising from simple just intervals, especially dissonances (1.250:1.333 or 1.875:2 both are just half-steps, for instance), comparative low pitches yield very beautiful, ambiguous and constantly evolving reverberant pitch classes in addition to the shimmering rhythmic periodicity of the beat rates themselves.

In addition, in this work, I am using quintalets (groups of five), based on the horizontal plane of loudspeakers as a primary rhythmic elements, interspersed with the occasional sextalet (a group of six — which includes the overhead speaker as an accent). More about this below under hockets.

Intonation and modality

Tempered tuning based on the twelfth root of 2 is inherently if only slightly out of tune for all intervals except the octave. This means that all tempered musical intervals will generate beating, and in complex chromatic music that beating will be substantial. At the same time, the consistency of quality of the various tempered intervals more than makes up for the deficiencies caused by beating, particularly when there is little reverberance and a high crest factor in the music.

In my sort of minimalist work, however, where the crest factor has been significantly reduced and reverberance maintains the sonic continuum, tempered intonation proves to be comparatively ugly and disquieting, while more pure and stable musical interval ratios provide a very solid and satisfying set of modal pitch classes.

Power Chords, Polyphonic Trains and Plain Old Phase is modal, based on A and the Aeolian mode (all “white notes” on a musical keyboard). Root and fifth are quite obvious (to me, anyway), and the modal stability of the work over time is an essential ingredient of the work's character. There are no other pitches than those in the mode, except for the quite complex spectral structure of the power chords.

Hockets

Hockets are a common (and ancient) musical device consisting of staccato rhythmic and/or melodic elements alternating among a group of instruments or sound sources. Hockets are extremely idiomatic for loudspeaker music (the “bouncing” tape echo loop that moves in time among speakers in an array, for instance, is both a cliché AND a hocket). In my piece, hocketing is a primary musical process, and almost all melodic sequences are also hockets, in that they “bounce“ note by note from speaker to speaker in clearly defined rhythmic patterns.

The technique is extremely rich in potential for complex rhythmic and polyrhythmic patterns as well as quite interesting contrapuntal lines emerging and moving in both space and time. Hocketing permits the mechanical loudspeaker to have an inherently powerful rhythmic drive and pulse as a function of its technology, a potential that to date has been only partially developed.

Canons

The canon is another traditional polyphonic technique that is extremely idiomatic for loudspeaker music. The “copy and paste” facility of virtually all audio workstations today permit easy generation of canons, while pitch shifting and time compression/expansion permit canons that imitate in augmentation, diminution and modulation to be created easily and in great profusion. I use the technique at numerous points in the work, most audibly in augmentation (the imitations grow longer in time) in the coda.

Other related techniques, not used here

Below are some other techniques (but not all) that I have been working with and developing for this sort of music.

Numerological and physical organizations

The sorts of compositional approaches that I have described also lend themselves to the working out of numerological and physical processes. For instance, in one work I am currently finishing, the convergence of the Fibonacci series with the Golden Section provides the basis for rhythm, meter and a great deal of pitch selection (I use Fibonacci to model the overtone series, for instance).

Similarly, slow physical processes (such as the movement of sunlight) can be realized, where change is not perceptible on an instantaneous basis but is very clear and quite powerful over time. These processes can be dynamic, spectral, temporal and spatial, or complex combinations of some or all of these.

Comb-filter pitches

The derivation of pitch from recombined delayed iterations of noise (for instance, delaying a pink noise signal by 22.73 ms. and recombining it with its undelayed predecessor at unity gain will yield a comb-filtered pitch of A 440) results in some fascinating and quite beautiful and moving timbres. I am beginning to study the effects of these sounds in “choirs” of harmonic arrays.

Musical Dither

Musical dither consists of low level musical content (generally at between-70 and –50 dBFS), usually heavily processed, which serves as a “sonic noise floor” to establish continuity for the piece and as a masking agent to conceal undesirable low-level artifacts that sometimes occur in production. The choice of source for the dither and also its treatment have a profound if subtle effect on the mood and character of the work.