THE COMPUTER POLYRHYTHMICON

A single polyrhythmicon module

The polyrhythmicon is an original computer hyper-instrument/tool kit designed in the MAX object oriented programming language. The instrument evolved as a means of exploring compositional rhythmic devices and the psychological perception of complex polyrhythmic systems. The creation of this instrument has led to the composition of many works, some of which are discussed here. The polyrhythmicon is a group of tempo modules which, to user-specified degrees, operate independently from one another. Each tempo module creates an independent rhythm and any number of these modules can perform simultaneously (48 simultaneous voices is the maximum used at the present time). The modules are governed by either a global metro object in conjunction with a set clock object or Max's internal millisecond clock, or by individual metro objects allowing greater rhythmic independence between modules.

Each module contains a series of objects working together. The tempo object, working within the metro counter, controls pulse. Crucial to creating an imperceptibly changing tempo, the tempo object is programmed to accept floating point integers by using the beat multiplier argument. Resolution of tempo is calculated by how high the beat multiplier is set (10 is 1/10 of a pulse, 5 is 1/5 of a pulse). In conjunction with the beat multiplier, the tempo in beats per minute and the rhythmic value control the resulting tempo. Due to the amplification of the beat multiplier, the integer sent into the tempo objects 3rd inlet (rhythmic value) is treated as a fractional value. The actual tempo is the result of the rhythmic value (3rd inlet) divided by the beat multiplier (2nd inlet).

Acceleration and deceleration of tempo can be operated manually or used in conjunction with a predefined table. The result of configuring the tempo object in this manner is that the rhythmic pulse of a single module can accelerate or decelerate imperceptibly in any manner specified. Each module also generates its own note number information, amplitude information, note sustain information, and accent placement and accent amplitude. These parameters can also be manually operated or pre-programmed. The patcher accent subpatch is an accent object working in conjunction with a counter object. The counter determines on which beat the accent will fall, and the patcher accent produces the accent by augmenting the original amplitude and routing it to the amplitude slider. The amplitude of the accent can be independent of the overall amplitude allowing pulse and meter accents to be treated separately. In this way, meter (groupings of pulse) is controlled as a separate parameter in the rhythmic texture. The modules work together to create polyrhythms of any possible complexity and interdependency. The instrument was designed to explore two categories of polyrhythm: polytempo and polymeter. These terms are essentially defined in the following manner:

• Polytempo is the qualitative division of time such as 3 in the time of 4, etc.
• Polymeter is the quantitative division of time, cross rhythms such as accents on every 3rd and 4th note of a single tempo pulse.

The polyrhythmicon in 5 Voices

In the earliest stage of working with the polyrhythmicon, in 1994, the audible perception of simple integer-related polyrhythms was studied. An attempt was made to comprehend the rhythmic relationships in the same way that visual patterns can be understood and quantified by the perceptual understanding. Working with polyrhythms such as 2:3:4:5:6 in two and three voices, complexity was increased only as the subjective perception of rhythmic intricacy grew. The results were carefully evaluated and special concentration was given to hearing the characteristic aesthetic relationship between simple polyrhythms.

Accent Subpatch

Next, increased depth of polyrhythmic expression was added by combining tempo and meter polyrhythms. Simple polytempo structures such as 2 : 3 were combined with a polymetric accent structure such as 3 : 4. Through this process I observed that the deeper level of polyrhythmic complexity creates a sense of rhythmic richness not observed in either type of polyrhythm alone. Once these polyrhythmic fabrics became familiar to the ear, the aesthetic characteristics of each polyrhythmic releationship were categorized in terms of the functionality of different combinations. Functionality is the byproduct of a hierarchical system, and in a hierarchical sound structure based on degrees of complexity, one sound can come to imply or necessitate another (McAdams and Bregman 1979). An attempt was made to apply hierarchical structures to rhythmic processes such as the exploration of process-oriented pseudo-harmonic relationships between polyrhythmic fabrics in order to create linear rhythmic progressions which could then underline structural form. In this way rhythm was explored as a way to compliment harmony in respect to formal function.

Following this, transformation as a means of traversing the space between two polyrhythmic areas was explored. Using the tempo tables, each polyrhythmic set can be programmed to change micro-rhythmically from one polyrhythm to another. This is accomplished by each voice moving in similar motion between voices in the two sets. For example, in tempo, a simple 2 : 3 rhythm may change slowly into 4 : 5, the 2 slowly speeding up to 4 (2.01, 2.02, 2.03 etc for example) and the 3 speeding up to 5. Or, in meter, the accents in a voice may be shifted so that attacks on beat 7, gradually become attacks on beat 3 (7, 6, 5 etc.). The points of origin and termination represent degrees of stability on a fluid curve of activity. Exploring these transformations as ways of studying the area between discreet polyrhythms, it was found that in many cases, as the rhythms transmute from one to another, new polyrhythms emerge in the space between the two primary systems as interesting subsets. These areas, termed secondary transition points, can be used functionally in a rhythmic modulation. Secondary transition points can act as points of deviation between larger simple transformations much in the same way that a subdominant key may prepare modulation to a closely related key in tonal music.

These exercises necessarily dealt with the absolute precision of rhythmic differentiation. Musically, however, the resulting rhythms lacked micro-expressiveness, sounding somewhat mechanical and dry. Although this was desirable while trying to formalize a technique of working with these complex rhythms, for extensive musical purposes it was necessary to find ways to increase the level of interpretive expressiveness but retain the perceptibility of the complex rhythmic activity. To this end, several micro-expressive functions were added to the instrument. By using tables to slightly shape the amplitude and duration of the pulses, it is possible to shape a rhythmic phrase over time creating a sense of tension and relaxation. In addition the overall volume of a group of modules can be controlled simultaneously to produce a grouped sense of shaping. Micro-rhythmic transformation in conjunction with the larger macro-rhythmic transformation (such as introducing slight imperfections in the rhythmic pulse) was explored but abandoned because it compromised the perceptible rhythmic integrity of the music.

For live performance the polyrhythmicon was modified in a variety of ways to suit different circumstances. One performance method places all necessary functions under performer control and the performer then reads from a musical score, setting parameters in real time accordingly. Presets are used to jump between sections of the piece. This technique was used in Rend (1995) for snare drum quartet and polyrhythmicon. A cleaner and more automated performance method required placing the rhythmic modules within sub-patchers and leaving only the most basic controls available to the performer. This method is desirable due to its ease and clarity. The performer simply runs a control panel of the work, programmed specifically for each piece, putting him or her in direct control of the specific function desired in the section without cluttering the screen with other boxes and information. This performance method was used in Taruyamaarutet: Twisted Faces (in wood) (1995) for soprano, marimba, bass clarinet, percussion, polyrhythmicon/electronics, movement artist, and projected images. A third applied use of the polyrhythmicon for composition, Symphony in Metal, utilizes the instrument as a means of resynthesising spectral data into performable temporal information. Once the instrument was developed to a state of relative reliability, and the perceptual ability of interpreting the information was evolved, the instrument was used in the creation of several works exploring extended techniques of rhythm. These works illustrate a significant exploration of rhythm in terms of its functioning on both the micro and macro level, and the beginning of a new vocabulary of rhythmic devices.

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