The Nature of Musical Time and SPANDA

The Nature of Musical Time and the Composition of SPANDA

Structure in my music follows a model borrowed from physics. I apply this system to the structuring of both time and sound. There are up to 12 hierarchical levels of structure in this system. They are from smallest to largest:
1.) particle/wave, 2.) atom, 3.) element, 4.) cell, 5.) field, 6.) subzone, 7.) zone, 8.) world, 9.) system, 10.) galaxy, 11.) cluster, and 12.) superstring. Each level of structure is at least one order of magnitude larger than the previous level, and will contain several elements from the next lower level.

Musical time exists in at least three domains of perception. In the audio spectrum (roughly 20 Hz. to 20 kHz.) we may perceive the qualities of pitch, timbre, noise, loudness, etc. I will call this the domain of pitch and timbre. In the next domain of time (roughly 20 Hz. to about 10 seconds) we perceive the rhythmic aspects (durations and patterns of relative duration between sounds) and internal changes in the pitch, timbre and loudness envelopes (growth and decay aspects) of sounds, as well as the shorter aspects of musical ideas (motives, melodies, short phrases, harmonic successions, motion of sound in space and accents of various kinds). I call this the domain of musical rhythm. In the next time domain (from about 10 seconds to about one hour) we perceive the larger structural aspects of music (longer phrases, periods, sections, movements, etc.) in which the musical forms and the development of ideas take place. I call this the domain of musical form.

Stockhausen has pointed out* that each of these domains is about eight to ten “octaves” in size. (An octave being a 2 to 1 ratio of time duration, whether measured in frequency (cycles per second or Hertz) or in duration (micro seconds, milliseconds, seconds, minutes, hours, etc.). For example, the interval between pitches with the fundamental frequencies of 220 Hz. to 440 Hz. constitutes an octave in the pitch domain; the difference between the two tempi MM 60 and MM 120 constitute an “octave” in the rhythmic domain, and the durations 30 seconds and one minute have the ratio of an “octave” in the structural domain of musical time.) Different perceptions of time (pitch, timbre, rhythm and duration) take place in these different domains because our nervous systems process the temporal data differently as the sound materials cross the perceptual thresholds between each phenomenon. Musical composition consists mainly of the ordering of sonic configurations of the different musical elements in these three different temporal domains. So the composer must master the configuration of time in several different ways. Within each domain there are many different parameters of sound to be ordered and configured.

I conceived the complex of 198 compositions titled SPANDA in 1989 using this understanding of musical time. SPANDA is a Sanskrit word borrowed from the yogic philosophy of Kashmir Shaivism, which means the ‘creative throb of Consciousness’ (which creates the entire universe and everything in it). The duration of the entire complex was derived from the pitch of the first sound of the first composition in the complex. That pitch is a Bb with the fundamental frequency of 116.54 Hz. When this frequency is transposed downwards by 27 octaves, it passes out of the domain of pitch and timbre, through the domains of rhythm and musical form, and into the next domain of time in which we live our lives and experience our education and life experience. The former Bb now forms a “wave” one cycle of which has the duration of 13 days and almost eight hours. (See table one below.)




116.5409…Hz. Bb

58.27947…Hz. Bb (one octave lower)

29.13523…Hz. Bb lowest Bb on the conventional piano keyboard

14.56761…Hz. below the audio spectrum
Into the domain of musical rhythm

7.2838……Hz. (four octaves lower)

3.6419……Hz. (3.6 cycles a second or .2745 seconds per
cycle)
.5491” (duration of one cycle measured in seconds)

1.098…”

2.196…” (eight octaves lower)

4.393…”

8.786…”

17.573…” (no longer short enough to be perceived as rhythm)

35.146…” (12 octaves lower)

70.292…” (1minute 10.29” per cycle)

2’ 20.58…”

4’ 41.17…”

9’ 22.34…” (16 octaves lower)

18’ 44.68…”

37’ 29.372…”

1 hr. 14’ 58.745…” (out of the domain of musical form
into the temporal realm of education and life experience)

2 hrs. 29’ 57.49…” (20 octaves lower)

4 hrs. 59’ 54.98…”

9 hrs. 59’ 49.961…”

19 hrs. 59’ 39.92…”

1 day 15 hrs. 59’ 19.84…” (24 octaves lower)

3 days 7 hrs. 58’ 39.694…”

6 days 15 hrs. 57’ 19.898”

13 days 7 hrs. 54’ 38.77” (27 octaves lower)

Table One

The full theoretical duration of SPANDA is thirteen days, seven hours, 54 minutes and 38.77 seconds. (In reality this duration will vary somewhat with individual interpretations of tempo and rubato interpretations of different performers.) Each day of the cycle was subdivided according to different principles of division, and embodies a different “rhythm” of durations based on the principles of each day of the cycle. The collective proportions (of the durations of the 198 pieces) constitute the coherent macrostructure of the complex. I proceeded in this fashion according to my understanding that a numinous world of hyperspace exists under the aspect of patterned relations,** in this case the pattern of relative durations of the compositions in the complex, a kind of higher order of temporal macrostructure. I sometimes refer to this as the architecture of the complex.

SPANDA Macrostructure

13 days 7 Hours 54' 38.77" = Bb 116.54Hz / 2 27 times ( = a wave one cycle of which is 13 days 7hrs 54' 38.77")

Day principal sound structural principle # of time zones Title

1 Bb noise entropic 27 Symphonies of Sound

2 F logarithmic spiral 19 Symphonies of Time

3 Ab spatial 8 Symphonies of Space

4 E exponential 11 Symphonies of Energy

5 D polyphonic overlapping 7 Symphonies of Earth

6 G expansion from a point 5 Symphonies of the
Light of Consciousness

7 F# linguistic, microcosmic 13 Symphonies of the Word

8 A aperiodic different speeds 7 Symphonies of Love

9 D# biomorphic 10 Symphonies of the Seed

10 B games and play 15 Symphonies of the Children

11 Db linear growth and decay 11 Symphonies of the Vine of
Life and Death

12 C isomorphic with inversion 26 Symphonies of the
Universe

13 Bb serial 37 Symphonies of
Transmutation and Metamorphosis

14 Bb silence seamless Postlude (7 hrs. 54’ 38.77”)


Each composition of the 198 constitutes an individual “time zone” of a specific duration whose internal structure is subdivided according to different numerical principles into “time fields” which are in turn subdivided into different “time cells” with specific internal structure which contain the sonic materials. These different levels of temporal hierarchy constitute the macrostructural, middle level, rhythmic, and microstructural forms of the compositions. In this way of working, the fundamental dichotomy between form and content disappears since the content is determined by the form and the form may be determined by an analysis of the content. Furthermore, the principles which determine the rhythm may also be used to determine the melodic, harmonic and timbral materials.