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Page 00000001 A COMPOSER'S AMANUENSIS FOR THE WEB Matthew Malsky Clark University Department of Visual and Performing Arts 950 Main St. Worcester, MA 01610-1477 mmalsky @ clarku.edu Abstract: This paper describes MIDI composition software that facilitates a transformative algorithmic method. After a brief discussion of the compositional model and objectives, these tools are examined in detail and their operations explicated by way of an extended musical example. The paper ends with a discussion of the Internet as a means to store the software's output, and to foster exchange among composers using the software. 1. Introductory Notes This paper begins with a description of a collection of MIDI software tools that facilitate a generative algorithmic compositional method based on principles of musical variation or transformation (Rowe 1993, Winkler 1998). After a brief discussion of a compositional model and objectives, the two principle of these tools will be examined in detail: a data structure for an abstract representation of a theme or 'musical object' and a template for composing variations (or transformations) upon musical input. These tools are written in the graphical programming language Max, and are presented as an application within the frame of a Max 'patcher.' In the second section of this paper, the musical utility and operations of this method will be examined through a short musical example. Seven transformations (variations) on a musical object show the design of transformative functions and their musical results. This section will conclude with a discussion of means provided for the combination of these resulting transformations. In conjunction with a standard web browser, musical objects and transformations may be stored independent of the original Max 'patch,' as part of a database on an Internet-accessible server. The third section of the paper will describe the use of the Internet as a storage medium. 2. The compositional method These tools will allow a composer to build new, consanguineous musical "objects" from existing ones. These objects, the building blocks from which a composition may be built, are the progeny of Pierre Schaeffer's objets musicaux, Varesian 'sound masses' and Ralph Shapey's 'graven images.' An object, as a self-identical form, has the potential to be altered (varied, embellished, dissected, juxtaposed, overlaid, enlarged, and fragmented) while still retaining its essential, ontological musical identity. These material building blocks are created through a cyclical process of statement and modification/variation, and are then combined into a larger form. Within the scope of operations of this algorithmic environment, musical objects are statements to be shaped and combined to meet the requirements of this larger context, the compositional design, which makes demands upon its component parts. Good fit, a composer's judgment in light of a "programmatic clarity" of a composition, is a necessary property. Form, or a composition's logical internal constitution, results from clarity in using a compositional language (Alexander 1964). 3. The data structure and transformation engine At the core of this composing method are two principle software tools. A data structure is an object which abstracts a MIDI representation of a musical object into a matrix of parameters for processing, collectively called transformation data. Second, a tranformation engine can be used to design and compute alterations to transformation data, and return a new object. Through the data structure object, MIDI input (either in the form of a Standard MIDI file or a live performance) becomes array of events and relationships, the grist for the transformational mill. Transformation data describes the events in an object in terms of two classes of musical parameters, STATIC and DYNAMIC. There are five STATIC classes: PITCH, VELOCITY, GATETIME, RELEASE and POSITION. There are four DYNAMIC classes: APITCH, AVELOCITY, AGATETIME, and ARELEASE. The STATIC parameters are concerned with the measurable musical characteristic of each given event of an object while DYNAMIC parameters measure aspects of the movement between successive events. Pitch and velocity are both notated in CSound's octave point pitch-class form (Vercoe 1993). Timing information is notated as beats plus parts of beats. Additionally, editable object constants include STEP SIZE, the resolution of the quarter note (default is 480), MIDI CHANNEL (which is initially set according to the original input), and TEMPO. INITIAL PITCH and INITIAL VELOCITY are used as starting points for DYNAMIC calculations.
Page 00000002 In a single transformation, there are three levels of nested function definitions which are enacted sequentially. A first order transformation definition returns a chosen transformation data parameter altered by an arithmetic expression applied to this specified parameter. Additionally, at this level of transformation, the values for one parameter may be mapped onto another. For example, an object' s APITCH values be converted into VELOCITY information to create dynamic and timbral changes which are analogous to the motions of the object' s interval progression. Second order functions are expressions which use the parameter POSITION as an index. The effect of second order functions increases (or decreases) as a function of the sequential position of events in an object. Finally, third order functions are expressions which can utilize multiple parameters simultaneously. By nesting the first and second order functions within this final superior level, a complex expression may be created. The syntax for third order functions are identical to first order expressions except that whenever there is a first or second order expression modifying a parameter defined in the third order expression, the result of the lower order function are evaluated first and the resultant number becomes the input for the higher order function. At each of these levels, a limiting BIAS may be applied to either the index or to the data itself. Several subsidiary objects support the two discussed above, and round out the functions of the application. Objects are included to convert the data structure back to MIDI (and audible output), support graphical viewing and editing of the variations, create a 'score' to control timing for combining individual variations, and direct input from either a live performance or from a sequence stored as a Standard MIDI file. 4. Operation by way of musical example This object, taken from my composition, The Ballad of the Strange Strand, will serve here as the basis for creating a short musical example which will demonstrate this process of transformations. The musical events notated yield the following transformation data: Ipos I pitch vet I ate ret A pitch Aye! A gate A re! RT I 1 I 5.01 5.04 0.360 0 ___ """"Ii I 2 I 5.02 6.03 1 0.059 0 0.01 1.04] -0.301 0 0.360 I 3 I 4.03 5.04 1 0.107 0.060 1 0.01 -toil1 0.048 0.060 1 0.119 I 4 I 6.04 5.04 0.096. 0.012.!. 0.01. 0.01! -0.011..-0.048.!. 0.119 I 5 I 3.05 5.04 1 0.082 0.023 1 0.01 0 ]~-0.014 0.0111 0.119 I 6 I 7.06 5.04 1 0.082 0.014 1 0.01 0 ]~0 -0.009 1 0.096 17 1 2.07 5.04 0.289. 0.014! 0.01. 0 * 0.207. 0.1 0.096 I 8 I 6.08 7.06 1 0.82 -0.194 1 0.01 2.0 ]~-0.207 -0.208 1 0.096 I 9 I 4.09 5.04 1 0.047 0.0141 0.01 -2.02] -0.035 0.208 1 0.096 I 10 I 5.1 5.04 0.051. 0.169!1 0.01. -0.02! 0.004. 0.155.!. 0.216 I ii I 4.11 5.04 1 1.0 * 0.068 1 0.01 0 -1.051 -0.1011 0.060 I 12 I 5.00 4.02 1 0.191 * 0 1I 0.01 -1.0 -1.191 -0.068 1 1.0 The process of building this musical example began with experimentation. This object was used as the basis for creating, through trial and error, a large collection of new but associated objects. They share a common set of transformation data. Each variation is defined by its transformation definitions.
Page 00000003 C8 Cl Ill IIlii IllIl - - - - - - -- - 0- - -;1860 Il 111 44 sCO GT = 2 * GT REL = REL + 0.005 Object Two Object2 is a rhythmic augmentation of the original. Two first order functions alter the GATETIME, doubling the original GATETIME, and scaling the articulative space between notes (RELEASE) exponentially. The result is an object which is slightly longer than the original, more expansive with a little more space between notes. RUNNING TIME is recalculated so that the changes in GATETIME are reflected as melodic rather than harmonic alterations. CS ------- ------------------------ ------- -------- C1 E--------------------------- ------- 0 480 %0 1440 19W 2C) 280 APIT = APIT * (-0.1) GT = GT * (1.3) REL = REL * (1.1) Object Three In Object3, all interval directions are inverted (APITCH) The object now consists of a descending chromatic scale beginning, again, on C#4. The octave displacements are preserved. In addition, GATETIME and RELEASE are augmented slightly, the first by 30%, the second by 10%. RUNNING TIME is recalculated. -8 ---------------- ii---- - - - - - C1 0 40..90. 144w 19 Is AGT * (-1) AREL <-- (AGT * (-1)) BIAS limits this function to events 4 - 9 Object Four bO 2860
Page 00000004 A chord is created in the middle of Object4 by inverting AGATETIME and mapping those returned values to ARELEASE for events 4 through 9. The range of application of these functions is determined through a BIAS applied to the AGATETIME and ARELEASE, limiting the effect of the transformation to only the middle of the object. When RUNNING TIME is recalculated using the new AGATETIME and old RUNNING TIME values for the ninth event, a slight gap, a silence is created immediately following the chord. C 8 - - - - - - - - - - - - - - - - - - - - - - - -- O 19---------- % 11,) CC FIRST ORDER: AGT = AGT * (1) REL = ((-4) * REL) - 0.5 SECOND ORDER: AGT = AGT + (0.05 * POS) Object Five In Object5, as in Object2, the result of the transformations is a rhythmic augmentation of the original object. AGATETIME is altered in two steps. First, all of the AGATETIME values are inverted using a first order function; increases in GATETIME between contiguous events become decreases of equivalent size and vice versa. The rhythmic value of the first event (C#4) serves as the starting point for this transformation but remains unchanged. Additionally, AGATETIME is scaled using a second order function which, operating on the results of the first order transformation, arithmetically increasing the GATETIME of each successive event by multiples of 24 pulses. Working against the inherent rhythm of the original object, this increases rhythmic values over the course of the object. RELEASE is also scaled and inverted using a first order function. The result of switching the sign of each RELEASE value, the method of producing inversion, is to create overlaps between adjacent pitches but with no more than a dyad sounding at any given time. C1 1 1 L L I 15 ~ 3 6 1 1 4 01 I1 I.19.01II1I114!4V 119 FIRST ORDER: APIT = APIT * (-0.1) GT = GT * (1.3) / REL = REL * (1.1) SECOND ORDER: AVEL = AVEL + (-1 * POS) Object Six Object6 is a variant similar to Object3. In addition to the changes in the previous example, VELOCITY is transformed here. A second order function on AVELOCITY increases the change to VELOCITY between adjacent events over the course of the object, creating a crescendo effect.
Page 00000005 C8 ------- ----------- - --- - - -- - - - - - 40 t 19 2 14A40 2 c 0 AGT * (-1) AREL <-- (AGT * (-1)) NO BIAS Object Seven Finally, Object7 is a variant of Object4. The only difference lies in the BIAS applied to the returned values of AGATETIME and ARELEASE. There is no BIAS and so the effect is to alter the RUNNING TIME of every event, creating a twelve note chord beginning at RUNNING TIME 0 whose voicing is determined by the octave displacements of the original object and whose length is set by the rhythmic value of its constituent notes. Now, to put it all together. The design of this musical example began once a larger vocabulary of objects had been constructed. The compositional intent was to strike a balance between two extremes: the repetitive statement of recognizable objects, both the initial and the related, derived objects, and the creation of a larger "ensemble" with a musical cohesiveness through a partial synthesis of these same objects. The following is a graphic representation of the examples discussed: the original object and the six variant forms arranged through time. Each object appears in this diagram as a diamond indicating, roughly, its registral shape and approximate length in relation to its fellow objects. This is how the components are organized and positioned. 2.4088 36.159 Each transformation produces an editable sequence of its results. A score object provides a common clock for the playback of transformed objects. This musical example has been constructed principally with concern for the alignment of the entrances of each object. The original object begins the example. Object2 begins with the attack of Objectl's lowest note (Gl) which has been designated as an anchor. Object3 and Object2 end together. Object4 is concatenated with Object3, following immediately after its last note. Object5 and an exact repetition of Object1 (the original) commence in rapid succession on the tenth and eleventh notes of Object4 respectively. Dyads are created at these points of conjunction; Bb4-C#4 and B3-C#4. Object6 begins on the tenth event of Object5, creating a dyad Bb4 at the end of Object5 with a C#4 which starts Object6. Finally, the cluster of Object7, accentuates the attack of the penultimate note of the musical example. Although the entrances (and, in one case, the exit) of these objects are contrived to form a logical progression from one to the next, the musical surface of this example, as a continuous stream, is less exactingly formulated. When objects overlap, there is often a compound rhythm and harmonic content which was not specified in either of the component objects. These surface shapes can only be evaluated in terms of an original compositional notion of what this musical excerpt should be. The compositional combination of objects to form an interesting and coherent surface is integral to this compositional paradigm.
Page 00000006 5. Internet application [Internet server/client structure] This project uses the Internet to distribute the client software, store the output of data structures and transformations, and foster interaction among composers using the software. In effect, the software described above serves as a helper application; the Internet site is a means for distribution and storage of its products. Using any frame-compliant web browser, composers may (using the ftp functions of the web server and the client's web browser) upload data structures and transformations to this central storage facility. A relational database is the means for organizing these Max patches. Files created on individual composer's client computers may be cataloged by composer and composition (i.e. objects and transformations can be marked as part of a particular composition and belonging to a particular composer), and descriptive notes added. The database may be searched, and stored files downloaded for further work or study. Citations: Alexander, C. (1964). Notes on the synthesis of form. Cambridge, Harvard University Press. Rowe, R. (1993). Interactive music systems: machine listening and composing. Cambridge, MIT Press. Vercoe, B. (1993 ). CSound: A Manual for the Audio Processing System and Supporting Programs. Cambridge, Media Lab, MIT. Winkler, T. (1998). Composing Interactive Music. Cambridge, MIT Press.