SOLAR ELLIPSE (1984-85)

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for four computer-synthesized soundtracks

Solar Ellipse is a synthesized soundscape in the manner of my earlier "spatial environments," Sonic Landscape No. 3 (1975) and Androgyny (1978). Like its mate, Wave Edge (1983), it is based on a particular type of spatial trajectory and related image. In Solar Ellipse, the trajectory is that of the epicycle, where a spinning sound image (revolving four times per second) travels around an elliptical "orbit" similar to planetary motion. The larger cycles of the eight component stereo tracks (four created with vocal formant-like timbres and four with noise band components) are in the proportions of 6, 8, and 9 which come together and repeat at the mid-point of the piece. However, the tracks are heard in all combinations of 2, 4, 6, and 8 at a time. All are present at the mid-point and only the highest and lowest in pitch at the beginning and end. The image is that of fire whose energy is simultaneously being dissipated yet, like the sun, appears to remain constant.

Solar Ellipse is based on the I Ching hexagram, number 49, Revolution, comprised of the trigrams for fire and lake, the inverse of that of Wave Edge.

Solar Ellipse is available on the Cambridge Street Records and Wergo CD Digital Soundscapes, as well as the Cambridge Street Records album Sequence of Earlier Heaven.

Sound Example available

During a performance of Solar Ellipse in the Academic Quadrangle, SFU, during ICMC 1985 (speakers in the 6th floor balcony corners)

Structural Levels

I. 1/4 second spin, with 6 component events, constant speed, small Doppler shift

II. 4.5 second epicycle, with 18 spatial positions in an ellipse, each with its own timbre (not illustrated in the sound examples)

III. Larger, multiple epicycle constructions:

Four with complex FM carrier (producing vocal formants) and four with complex FM modulator (sine + noise)

A. Slow epicycle (x8 slower) 8 x 4.5 = 36 sec @ 49 and 98 Hz (G) "sol"

B. Pyramid:

C. Parallelogram:

D. Constant frequency (784 Hz) speeding up, slowing down with epicycle durations:

4.5  3.5  2.5  1.5  1.5  1.5  1.5  2.5  3.5  4.5  (= 27 sec)

IV. Phase cycle of 4 epicycle constructions on 8-track tape:

Durations of layers A, B C, D in the ratios:  6 : 8 : 9  which will repeat after 72 repetitions

144 repetitions @ 4.5 sec = 10:48 (duration of the piece)

72 repetitions -- Spiral Construction S -- 72 repetitions

V. 16-track mixdown scheme (to quad):

Tracks (formant version)

Low	1 & 2	1  0  1  0  1  0  1  0  1  0  1  0  1  0  1		1  1  1  1  1  1  1  1  0  0  0  0  0  0  0
	3 & 4	0  1  1  0  0  1  1  0  0  1  1  0  0  1  1	S	1  1  1  1  0  0  0  0  1  1  1  1  0  0  0
	5 & 6	0  0  0  1  1  1  1  0  0  0  0  1  1  1  1	S	1  1  0  0  1  1  0  0  1  1  0  0  1  1  0
High	7 & 8	0  0  0  0  0  0  0  1  1  1  1  1  1  1  1		1  0  1  0  1  0  1  0  1  0  1  0  1  0  1

Tracks (noise version)

Low	1 & 2	0  0  0  0  0  0  0  1  1  1  1  1  1  1  1		1  0  1  0  1  0  1  0  1  0  1  0  1  0  1
	3 & 4	0  0  0  1  1  1  1  0  0  0  0  1  1  1  1	S	1  1  0  0  1  1  0  0  1  1  0  0  1  1  0
	5 & 6	0  1  1  0  0  1  1  0  0  1  1  0  0  1  1	S	1  1  1  1  0  0  0  0  1  1  1  1  0  0  0
High	7 & 8	1  0  1  0  1  0  1  0  1  0  1  0  1  0  1		1  1  1  1  1  1  1  1  0  0  0  0  0  0  0

where 1 = track present in the mix; 0 = track absent in the mix; duration = ~ 20 sec

Read vertically, the mixing scheme represents the binary numbers from 1 to 15, and is the equivalent of the rule:

No track is heard in combination before being heard alone, e.g.

A, B, A + B, C, C + A, C + B, C + A + B, D, D + A, D + B, D + A + B, D + C, D + C + A, D + C + B, D + C + A + B

Note: Sound examples of the various elements of the piece are available on the WSP Database (truax@sfu.ca for guest access).

Spectrogram of the opening of the work

Reference:

B. Truax, "Sequence of Earlier Heaven: The Record as a Medium for the Electroacoustic Composer," Leonardo, 20(1), 1988, 25-28.

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Technical Note:

Solar Ellipse was realized with the composer's PODX system for computer sound synthesis and composition in the Centre for the Arts at Simon Fraser University using the DMX-1000 Digital Signal Processor. The synthesis technique used is that of frequency modulation (FM) of arbitrary waveforms. A spatial trajectory program developed by the composer was used to map specific paths for the various layers in binaural stereo.