Dary John MIZELLE

Noise is often considered to be a static band of random pulsed events with upper and lower frequency bounds, however, internal nuance of noiselike sounds is possible with complex additive-synthesis techniques. The microcomposition of such nuances may be employed to create nonpitched timbres with an internal "life" as musically interesting as that of many pitched sounds. These nuances may include micro-inflection of individual components by means of different, simultaneous vibrato rates and depths, microtonal placement of adjacent components, and envelope shaping of components ( or groups of components) as well as conventional waveform design (by relative amplitude specification of individual partials). Noiselike timbres composed in this manner often exhibit choric effects and depth characteristics associated with reverberation. Taped examples wil be given from work in progress.

An antecedent for using additive synthesis to generate noise may be found in J. C. Risset's "An Introductory Catalogue of Computer Synthesized Sounds" (Bell Labs, 1970). Catalogue item number 400 is a percussive instrument "...a drum-with and without snares", which consists of three components, a frequency band"...generated by random amplitude modulation of a sine wave...", a sine wave, and an inharmonic spectrum.

"The "inharmonic" spectrum is, in fact, an approximation to an inharmonic spectrum, obtained by playing a wave containing only high order harmonics at a very low frequency". The wave function for this "inharmonic spectrum" contains partials 10, 16, 22, and 23, with no fundamental. The sine wave component also corresponds to the 10th partial (with a different envelope), and the frequency band corresponds to the snare rattle of the drum, which may be subtracted by setting its amplitude to zero.

The present work represents a simplification of Risset's instrument (dropping the noise band and the extra sine wave in most cases) and a broadening of the range of the inharmonic spectrum to include many more adjacent partials. The musical aim was not to work within the framework of an instrumental model, but rather to compose textures of noiselike sounds with internal nuance. Therefore , the challenge did not lie in instrument design, but in the temporal and spatial configuration of the sounds.

The sounds were all computed at the Columbia University Center on the IBM 4341B machine in a VMCMS environment using P. Lansky's MIX software, whih utilyses MUSICIV-like GEN routines. The conventional technique was used to generate the following functions. (All preliminary testing was done with GEN 9.)

Function #	Partial #'s	Range of Band	# of Partials
7	16-32	1 octave	17
8	32-64	1 octave	33
9	64-128	1 octave	65
10	128-136	ca.minor second	9
14	15-18	ca.minor third	4
15	30-34	ca.major second	5
16	60-68	ca.major second	9

These functions were not generally used in their "raw" states, but were treated as basic building blocks to be inflected and combined in various ways. Plots of these waveforms (figure one) reveal pulselike characteristics. Some of the problems encountered in this work are connected with the pulselike nature of the waveforms.

If the specified, missing fundamental (which may be up to seven octaves below the energy spectrum desired) is low enough to be below the audio spectrum, then beats are heard at the fundamental frequency-even though missing. If the phases of the individual partials within a function are properly adjusted, the pulselike nature of the wave function is "smoothed out" and the subspectral beating doesn't occur. I am indebted to John Souza who wrote the GEN 21 subroutine which performs this task by analysing each partial for the peak and then generating the next partial with its trough falling at the peak of the previous partial, through phase adjustment. Figure 2 shows plots of the same functions generated with GEN 21. If the fundamentals of these same functions (generated with GEN 21) are subspectral, then beating doesn't occur and the resulting timbres are smoother.

The functions are played by a simple instrument capable of inflecting them independently in starting time, duration, peak amplitude, attack and decay times, attack and decay shapes, vibrato rate, vibrato depth, vibrato function, and spatial placement in a stereo environment. A provision for glissando has been provided in one version of the instrument. Noiselike timbres wit internal nuance are then built up by the application of composition procedures to control these parameters by writing individual note cards for each function; This is admittedly tedious work, but it provides a sufficiently powerful tool for timbre composition with reasonable efficiency. It should prove possible to automate some of the note-writing tasks if the composition procedures become well-defined algorithms.

Another problem may occur when several of such waves are used simultaneously with different vibrato rates. If the cycle times of the different vibrato rates all come into phase during the duration of the composite note, an amplitude modulation artifact may occur at that time.

This phenomenon is a function of the vibrato rates and note length. For example, if eight waves (such as function 7) are played simultaneously with their missing fundamentals specified within a whole tone, for two seconds-and they have vibrato rates of 11 Hz., 12 Hz.,...18 Hz; they will fuse to form a composite noise with an amplitude modulation artifact at one second after the attack. This problem can be avoided by specifying the vibrato rates in smalller increments than even cycles per second (such as tenths of cycles per second) so that they don't come into phase during the duration of the note.

The generated function components in a composed noiseband are typically arranged in the vertical dimension along equally-spaced, generally microtonal intervals. The inflections of each wave are controlled independently in envelope shape, vibrato rate, spatial placement, etc. Typically, a composite noise complex would be composed internally as shown below.

Vibrato rates: in increments of.1 Hz to 1 Hz depending on duration of composite note

Mixing techniques: overlapping of pitch and noise complexes to create continuously- evolving timbral sequences

overlapping or cross-fading noise complexes with conventional waveforms to color the noise

Timbral fusion of composed-waveform complexes happens automatically when the missing fundamentals all lie within a critical band; however, to attain a blend of sine waves and noise complexes is very difficult, if not impossible. If the sine wave is played at a low enough amplitude to fuse with the noise, it is masked;if it is played at a high enough amplitude to be heard as an entity, it contrasts greatly with the noise. The cross fading techniques were used to test this phenomenon. The concept of pitch/noise index was developed to analyse this dimension. See below.

The concept of musical interval may apply in a general way between successive noise complexes, even though there is pitch ambivalence or no perceivable pitch. This phenomenon arises because of the vertical placement of the noise complexes within the audio spectrum - and may be quite general and vaguely defined, depending on the size of the noise bands (bandwith) and the amount of vertical displacement between successive complexes. Thus, a "melody" of noises is possible in several ways. One possibility is analogous to conventional pitch melodies: a noise band with constant bandwith and internal characteristics moves vertically in the spectrum. Another possibility is analogous to klangfarbenmelodie on a single pitch: this is a succession of noise complexes with the same bandwith and changing internal characteristics and densities. A third possibility would be analogous to compound melody : a patterned configuration of successive noises in two or more different areas of the spectrum. It would be possible to combine these methods of noise interval configuration as well as applying conventional analog techniques of varying the bandwith and center frequency. Further, in some cases, pitch/noise anomalies arise which could probably be composed in certain musical contexts. Psychoacoustical studies by Fastl and Bilsen have found that noise bands of less than 1/5 octave give rise to pitch perceptions in the center of the band, while those of greater bandwith give rise to pitch perceptions at the low and high cutoff frequencies.

The choric effect may be broadly defined as the effect of several sounds of the same general type sounding simultaneously. This is a complex acoustical phenomenon and not well understood by psychologists. It is probably the result of "...small random variations in pitch, loudness, timbre, and precision of attack; but another aspect of the effect is perceptible as the size of the sound source, its dispersion, especially on the horizontal plane." (R. Erickson, Sound Structure in Music, Univ. of California Press, 1975). My musical experiments have resulted in choric effects when there are several different vibrato rates within a noise complex. The effect seems to be enhanced when sine waves are used which glissando together and apart; sometimes this practice leads to the perception of a sound complex of changing size.

Likewise, an interesting experience of depth or room size akin to reverberation may be perceived in many of the noise complexes. It is not entirely clear whether this phenomenon is related to multiple points of projection in the stereo space, the sheer number of sounds present, interaction of the different vibrato rates, or perhaps some combination of these factors.

In order to deal compositionally with the materials described above, it became necessary to develop some theoretical concepts for the analysis and synthesis of timbre. One such conception postulates two different scales related to pitch and noise. The first scale is called pitch/noise index and defines a continuum divided into ten areas. Area one contains all pitched sounds with no perceivable noise content; area two through nine contain relative changing mixtures of perceivable pitched and noise components. Area ten contains all sounds with no perceivable pitch content. The second scale is open ended and is constructed at each of the ten areas of the pitch/noise index continuum. This second scale measures the internal complexity of the sound and consists of the sum of the partials times the number of internal inflections. It then becomes possible to construct "melodies" of successive timbres in either (or both) of these scales. This conception is not based on any formal psychoacoustical research, but represents a working model for compositional use. This model assumes a nonhierarchical nature of the different perceptual parameters which constitute the sound object. This assumption may not hold in the "real" world, since many listeners have preconceived ideas about what constitutes meaningful musical experience, however, for the purposes of the present work, no hierarchies are assumed. "I don't think there's an absolute hierarchy; parameters can take each other's function in polyvalent composition." (J. Cott Stockhausen Conversations with the Composer, Picador 1974)

In 1980, J. Dashow proposed a theory (Spectra as Chords, Computer Music Journal, Vol.4, #1) based on a timbral model in which "...the nonharmonic domain of frequency relationships may in some way contain a necessary system of hierarchical structural functions." His approach utilised various modulation techniques as a beginning point for generating "...a group of chords that have meaningful and possibly necessary functional relationships..." rather than have to "...choose among the infinite combinations produced by additive synthesis."Despite his lack of distiction between "chord" and "timbre", I feel that the root assumption of Dashow's theory is sound, but could be expanded to include additive synthesis techniques and noise bands.Thus, an important area of timbre synthesis in electronic and computer music could be dealt with.

The missing (or present) fundamentals of noise complexes could be considered as part of the generating diads or triads of Dashow's theory. In any case, missing fundamentals are often perceived as second order effects (fundamental tracking) through neural processing.(J.Roederer, Introduction o the Physics and Psychophysics of Music, Springer-Verlag 1973) If a harmonic spectrum is perceived as inharmonic (because of the closeness of its adjacent partials) it is irrelevant if the partials are integral multiples of a missing fundamental or are inharmonically related to some present fundamental, which is then used as acarrier for modulation.

The question of the infinity of possibilities available with additive synthesis is an important one, however, and is reminiscent of Stravinsky: "I experience asort of terror when, at the moment of setting to work and finding myself before the infinitudeof possibilities that present themselves, I have the feeling that everything is possible to me ... Will I have to lose myself in an abyss of freedom?... I have no use for theoretic freedom. My freedom will be so much greater the more narrowly I limit my field of action and the more I surround myself with obstacles. Whatever diminishes constraint diminishes strength."(I.Stravinsky,Poetics of Music, Harvard Univ. Press, 1956)

In dealing with theories which are to be used to support musical composition, some simplifying assumptions need always be made just to begin to bring the infinity of possibilities within the realm of human (and computer) endeavor. The two scales of timbre mentioned above represent such an attempt. Other theoretical models are being developed which lie outside the scope of this paper.

Illustrated are the first two minutes of the work in progress, Dream of the Vacationers, a theatre piece for tape, four instrumentalists (flute, percussion, piano and contrabass), and three singer/actors. The present approach to noise synthesis was developed for this piece. The compositional strategy of this work involves composition of the threshold between pitch and noise along the continuum mentioned above. This is accomplished through mixing noise bands with different widths and internal activity, mixing sine waves, and integrating various instrumental timbres and textures with the computer sounds. (Taped example )

Since timbre is a multidimensional phenomenon, and since it is now possible to specify such precise and subtle changes in sound with computer technology, some of which are unperceivable, simplifying assumptions are necessary for composition. A multidimensional approach to timbre composition could reasonably deal with variability of the pitch /noise continuum as a primary form-generating parameter. Erickson (Op. cit.) lists the following nine characteristics of timbre:

The first of these categories are considered when composing or analysing for pitch/noise index and the fourth through ninth are considered when dealing with inflectional possibilities of the internal complexity. The strategy for timbre composition postulates the configuration of elements along the pitch/noise continuum and the internal complexity as the primary pattern-building feature.

Since virtually any sound world may be used as the basis for music making, and almost any perceivable parameter may be varied as a generating principle for (hierarchical or nonhierarchical) musical structure, a systematic method for making musical choises becomes necessary. Attempts to define a theory for electronic and computer music which would specify "necessary" parameters for variation are inherently and could lead to strait-jacketing a vigorous new art form. While it is recognized that some form of limitation is necessary before creative activity can begin, these limitations are practical rather than absolute. "Whatever diminishes constraint diminishes strength" is true in a musical sence; its opposite seems to be true in a theoretical sense -- that is the more possibilities a theory presents, the more different kinds of music can be composed or analysed using its principles. Microcomposition of noise with additive synthesis techniques represents a useful method of timbre composition which is constrained in technique, but also open-ended in compositional possibilities.