Page  00000001 Ornament as Data Structure: An Algorithmic Model based on Micro-Rhythms of Csing6 Laments and Funeral Music Christopher Ariza Graduate School of Arts and Sciences, New York University email: ariza@flexatone.net Abstract This study presents an algorithmic method for creating ornaments linked to skeletal base-notes. In developing this model, a data structure for encoding ornament-types is presented. This data structure employs contour theory, variable harmonic scaling, temporal/iterative parameters, and stochastic noise. In order to tune these parameters, the laments and funeral music of the Csdngd, a music rich with ornamentation and dense heterophony, is used both as a textural model and as a source of quantitative data. This model is implemented in the Python programming language and is integrated into the athenaCL composition system, an open-source, crossplatform program for algorithmic composition in Csound. It is shown that convincing heterophonic textures can result by the combination of algorithmic ornamentations of a single line. 1 Introduction This study presents an algorithmic method for creating ornaments linked to skeletal base-notes. In developing this model, a data structure for encoding ornament-types is presented. This data structure employs contour theory, variable harmonic scaling, temporal/iterative parameters, and stochastic noise This model is implemented in the Python programming language and is integrated into the athenaCL composition system, an open-source, crossplatform program for algorithmic composition in Csound. It is shown that convincing heterophonic textures can result by the combination of algorithmic ornamentations of a single line. The laments and funeral music of the Csang6 are used as a point of departure for this study, providing a musical model of sophisticated heterophony and dramatic ornamentation. Ornament-types, as well as actual temporal measurements from ornaments in recorded Csang6 music are employed in this model. The use of this music is as a textural model and as a source of performative data. This not an attempt to model a style or a performance practice. 2 Music of the Csing6 The Csang6, in some cases a Szekler ethnic group, are found in eastern Transylvania (Kalotaszeg), the Gyimes valley, and Moldavia. The folk music of these people is renowned for its preservation of the most archaic forms of Hungarian folk culture. Intermingled with this population are many Roma (Gypsy); most musicians in these regions are Roma and have contributed significantly to the development of this music. Amongst various Csang6 groups is a tradition of violin duets performed as laments or in association with rites of the dead. This music has regional differences and goes under various names: Keserves (lament), Hajnali (dawn songs), or simply as funeral music. In most situations, two violins perform a descending melodic line in a heterophonic fashion. Each performer provides ornamentation consisting of turns, trills, and detailed passage work. Often trills are combined with other trills or wide vibrato to create a dense, strident spectrum. The harmonic materials are usually diatonic or pentatonic. The rhapsodic, free rhythm often used for this music is often referred to as parlando rubato. Two recordings are analyzed for this study. The first is a stereo recording titled "Dawn Songs And Gypsy Couple Dances" from the album Transylvanian Folk Music From Kalotaszeg, recorded in 1999. The second is a mono recording titled "Lamenting music at the side of the dead with two violins" from the album Hungarian Instrumental Folk Music. For simplicity these recordings will be referred to as A and B respectively. To observe the rapid and detailed ornaments of this music, computer-rendered pitch-tracking graphs were created with the open-source digital audio editor Audacity. These graphs were captured at a resolution of 6.28 milliseconds per pixel (a duration roughly equivalent to a 256th note at quarter equals 120 BPM), providing detailed temporal information. To measure durations, the number of pixels between note-attacks is then counted and converted to seconds. Both the quality of the recordings and the register of the violin contribute to the precision of these graphs. Stereophonic recording additionally

Page  00000002 contributes to this analysis. As each violin is recorded in a sperate channel with a minimum of bleed, an isolated transcription of each part is created. 3 Ornamentation & Heterophony Heterophony, as demonstrated in the music of the Csang6, is the simultaneous presentation of a single skeletal melody by two or more performers, each musician providing unique elaborations to the melody. The use of ornaments is a frequent and functionally important feature. Often improvised, the combination of ornaments adds a micro-polyphony to a line. Ornaments do not have a prescribed duration or rhythm, and thus by their very nature are gestural. With each instance, an ornament-type produces a unique set of pitches and durations. These attributes are amplified when two players perform the same ornament, or two different ornaments, in a heterophonic context. Small variations in timings, tuning, and phrasing result in a complex and conterpuntal result. Recording A provides frequent examples of the same ornament being performed simultaneously by two players. At 0:07 both instruments perform a downward then ascending arc. These ornaments, nearly identical in contour, nonetheless have greatly divergent rhythms and pitch content. This combination of similar ornament-types produces micro-polyphonies between points of melodic unison. In other circumstances, contrasting ornamenttypes are performed simultaneously. For example, in recording A, from 0:03 to 0:04, violin L performs a three-note turn, while violin R performs a two-note trill (figure 5, below). The combination of the two ornaments produces complex timbral and rhythmic interactions. This technique of combining different ornament-types is found throughout recording A. Notice at 0:19 to 0:20, where again a three-note turn is combined with a two-note trill (figure 7 below). With this observed context, heterophony may be seen as a texture which results largely from independent uses of ornamentation. Quntatative temporal data supports this claim: ornaments and heterophony often operate within a similar time scale. In recording A ornament-note durations are often between 30 and 130 ms, while heterophonic notearticulations are often separated by a duration between 40 and 450 ms. 4 An Abstraction of Ornament There are many classification systems for ornaments designed for particular musical styles or performance practices. Labels such as "trill" and "turn" for example are generally understood in Western classical traditions, whereas a wide variety of other ornamental gestures have multiple names, redundant names, or no names at all. In developing an algorithmic system to create ornaments linked to skeletal base-notes, common names and context-specific classifications systems are of little use. Rather, a sophisticated and practical data-structure model of an ornament is required, allowing a wide variety of ornaments to be encoded and generated. The data structure presented here employs contour theory, variable harmonic scaling, temporal/iterative parameters, and stochastic noise. This system categorizes and stores reusable ornament-types that can then be applied to any note in various contexts. This system defines ornamenttypes with three main parameters: position, shape, and style. This model assumes that ornaments operate in relation to a base-note. This relation need not be functional. This paper makes no claim that this is actually how musicians think of ornaments; rather, it claims only that in hearing ornaments, one note may be considered the source, base, or goal of a gesture. Ornaments are thus 'attached' to a base-note by either appearing before or after the base-note, or the basenote being a prominent member of the ornament gesture itself. It is irrelevant that in many instances it is difficult to decide contextually which note is the base-note, for here the base-note functions solely as a point of reference. 4.1 Ornament Position Three terms are used to identify the position of an ornament in relation to the base-note. An "attack" ornament appears at the start of the base-note, a "release" ornament appears at the end of the basenote. An "anticipate" ornament appears before the base-note, but starts before the note's expected (or contextually determined) start-time, beginning in negative time in relation to a base-note starting at time equal to zero. base-note anticipate attack release -t t=0O t=base-note Figure 1. Ornament position in relation to base-note. 4.2 Ornament Shape The shape of an ornament is given by a contour space segment (cseg). Contrary to traditional contour theory (Morris 1987), and for the sake of algorithmic implementation, the base-note pitch of an ornamenttype is assigned the integer 0. Positive and negative integers can thus be used to represent distances above and below the base-note in contour space. This contour, when contextually realized, is scaled by a controlling harmonic language to produce a pitchspace realization. For example, a cseg of <0 1 0 -1> could be scaled by a chromatic harmonic language. With a chromatic scaling, each integer represents a half-step. As shown

Page  00000003 in figure 2, if the base-note is D, the cseý the pitches D, D#, D, C#. Alternatively, the same cseg could be diatonic harmonic language. This meal integer represents a diatonic scale step. note is D, and the local diatonic system the cseg is scaled to D, E, D, C. Diato here, does not necessarily refer to collections, but rather any collection 1l aggregate that is used as a local controllinj Finally, the same cseg could be microtonal interval of any size. This me< integer represents an exact interval, fraction of a half-step. If the base-note i microtonal interval is specified as a qua half-steps, or 50 cents), the contour-form D, DS, D, CO. The following figure sumn g is scaled to durations are scaled to fit within the total-gesture duration. These styles provide a way to classify scaled by a ns that each temporal/iterative relationships. Three styles are used f t b in this algorithmic model: "single", "scale", and Sasr "loop". (1) If a duration for each note of the ornament as C Major,, as used is known, the ornament can be presented once, as a mic, as used major/mir single iteration of the cseg. A "single" ornament major/minor ess ten te derives its total-gesture duration from one iteration of ess then the g harmon the cseg. A mordent is a common "single" ornament, g harmony. Sa y as each instance often uses absoulte durations for scaled by a ns that each each ornamental note. (2) Alternatively, if the totalans that each. given as a gesture duration of the ornament passage is known, a given as a s D, and the scale" ornament can scale the prescribed ornament Sdurations to fit within the total-gesture duration. In rter tone (.5 Sthis case, the absolute duration of the ornament notes translates to are secondary to the proportional relationship narizes these between the ornament's durations. An appogiatura may act as such an ornament, its duration functioning as a percentage of the base-note. (3) Finally, if both resultant the ornament note-duration and the total-gesture pitches duration are known, a "loop" ornament can repeatedly iterate its cseg as a cycle. This is a hybrid of a D D# D C# "single" and a "scale" ornament. Trills, tremolos, and DEDC various vibratos are common "loop" ornaments. The dependence of these styles to durational information D Dý D C# is presented in figure 3: relationships: cseg base-note harmonic language V V <0 10-1> D <0 10-1> D <0 1 0-1> D chromatic diatonic (C-major) microtone (50 cents) temporal information ornament style Figure 2. Cseg shapes scaled to three harmonic languages. As should be clear, the combination of csegs and harmonic languages provides a wide variety of ways to specify an ornament-type. Ornament-types can be redundant when complete information is known. That is to say, with knowledge of the local diatonic system, a diatonic ornament can be constructed by specifying a chromatically scaled cseg with the appropriate number of half-steps for each interval. This redundancy contributes to the flexibility of this system. 4.3 Ornament Style The temporal/iterative structure, or style, of an ornament can be specified in a variety of ways. To account for these temporal/iterative deployments, each ornament-type has parameters for both noteduration and total-gesture duration. Note durations are given as a list of values in seconds; if a cseg demands more durations than provided in the list, the list of durations simply loops. The total-gesture duration is given as a percentage of the base-note's duration. In the case where ornament note-durations are used, information about total-gesture duration is not needed, as the total-gesture duration is calculated from the ornament note durations. Contrarily, in the case where total-gesture duration is used, note single scale loop ornament notedurations total-gesture duration Figure 3. Available ornament styles based on available temporal information. 4.4 Combining Ornament Position, Shape, and Style Combining these three primary parameters provides a way of encoding a wide variety of ornaments. More importantly, similarities between ornaments become readily apparent. For insance, the only formal difference between a trill and a wide vibrato is the choice of harmonic language. Both ornaments may have an "attack" or "release" position, a cseg <0 1> shape, and a "loop" style. A trill, however, uses a chromatic or diatonic harmonic language, while a wide vibrato uses a microtonal harmonic laguage. The same cseg shape, <0 1> can also be conceived of as a turn. In this case the ornament has an "attack" position and a "single" style. The same cseg shape might also be used to create a passing tone gesture to a following note on contourstep 3. In this case the ornament could use a diatonic harmonic language, a "release" position, and a "scale" style.

Page  00000004 4.5 Proportional and Stochastic Parameters In addition to the parameters described above, ornaments have parameters to control stochastic noise. This noise is applied to both the amplitude and duration of each ornament-note. The amplitude of ornamental notes is determined as a percentage of the base-note plus stochastic noise, producing the unpredictable fluctuations common to any gesture. Durations, after determination based on style (described above), are likewise altered with stochastic noise. Normal, exponential, or other continuous distributions may be used. The amount of noise applied to an ornament-note is given as a maximum percentage of variation. For example, if a duration of 100 ms is selected and the ornament-type has a maximum percent offset of.08, or 8%, the distribution is scaled between an offset of -8 and 8 ms. The same procedure is applied to amplitude. The following table presents all attributes of the ornament data structure and their relevant values and units: apply ornaments in a wide variety of contexts. Rather than arbitrarily setting these parameers, this project uses real-values found in recordings of ornamented Csang6 laments and funeral music. Again, the goal of this project is not to imitate a particular performance practice, but rather to use real-values to inform an algorithmic model. The real-value attributes considered here are the duration and micro-rhythms of individual ornament notes. Two representative musical segments will be presented. Examining seconds 3 to 4.5 in recording A, we see the simultaneous presentation of a turn (in violin L) and a trill (in violin R). Duration measurements for succesive notes along with statistical information is presented in the following table: violin L, recording A, 0:03-0:04.5, turn note length time in pixels pixels s L 3-4.5 values/ units example I 16 17 9 16 10 12 8 14 9 9 7 10 maximum 17 median 11 average 11.4 0.0717 minimum 7 0.04396 0.10676 0.06908 ornament position ornament shape (cseg) pitch language ornament style ornament note duration list ornament duration as percent of basenote duration variance percent offset ornament amplitude as percent of basenote amplitude variance percent offset microtone size anticipate attack release scale steps chromatic path set microtone single scale loop <-3 -2 -1> violin R, recording A, note length time in pixels 3-4.5 10 13 5 8 15 0:03-0:04.5, trill seconds.110,.096,.101 unit interval.50 unit interval.08 unit interval.92 unit interval.10 semitones.500 average minimum maximum median pixels 12.6 5 22 12 s 0.07913 0.0314 0.13816 0.07536 10 10 17 10 16 12 15 11 15 22 Figure 4. Ornament data structure parameters. 5 Real-Value Temporal Data Extracted from Pitch-Tracking Analysis This model, based on a contour surrounding a referential pitch, provides a framework with which to Figure 5. Ornament durations. 6.28 ms per pixel.

Page  00000005 3.0 4.0 violin L, recording A, 0:19-0:20, turn note length time in pixels p 19-20 7 average 1 18 minimum 7 11 maximum 1 17 median 1 11 17 8 13 10 9 10 17 ixels 2.3 8 1 s 0.07745 0.04396 0.11304 0.06908 violin R, recording A, note length time in pixels 19-20 10 10 12 13 0:19-0:20, trill average minimum maximum median pixels 12.5 8 17 12 s 0.07874 0.05024 0.10676 0.07536 Figure 6. Pitch tracking analysis of recording A, seconds 3 to 4.5. Notice that in the case of the turn the durations alternate between larger (12-17 pixel) and smaller (8 -10 pixel) durations. The longer durations align with the base-note, while the shorter durations align with the surrounding scale steps 1, -1. In the case of the turn, there appears a micro-rhythm emphasizing the base-note. The trill in violin R, on the contrary, shows no similar organization, moving unpredictably from values between 5 and 22 pixels. In the case of the trill, there appears no directed durational change. Seconds 19-20 again demonstrate the combination of a turn (in violin L) and a trill (in violin R): 14 11 17 10 14 8 12 17 15 Figure 7. Ornament durations. 6.28 ms per pixel. 19.0 20.0;:.*:; *<,?-: *:...............................................................................................................:-: Figure 8. Pitch tracking analysis of recording A, seconds 19-20. Notice that violin L again presents a turn in a distinct micro-rhythm, alternating between long and

Page  00000006 short durations in order to provide greater durational weight to the base-note. The trill in violin R is likewise consistent: there appears an average duration of around 80ms, no ordered use of durations, and no directed change in tempo. The particular contstruction of ornaments described above is part of larger collection of realvalue data obtained from recordings A and B for this study. In addition to the measurement of ornament note-durations and micro-rhythms within ornaments, pitch movement of specific ornaments is translated to the appropriate csegs and harmonic laguages. The collection of this data enables the creation of a repertory of ornament-types and parameters. The table below gives the names and parameters of threesample ornaments in this repertory. parameter values common name ornament position cseg pitch language ornament style ornament note duration list (s) ornament duration as percent of base-note (%) duration noise maximum percent offset (%) ornament amplitude as percent of base-note (%) amplitude noise maximum offset (%) trill turn appoggiatura release anticipate anticipate <1 0> <0 1 0-1> <-1> diatonic diatonic diatonic loop.090,.096,.094,.092, single.110,.070,.105,.076.6 n/a.10.06 single.088 n/a.08.960.022 6 Implementation in athenaCL This model of ornament-types is integrated within the athenaCL algorithmic composition system, allowing the easy deployment and sonic realization of these ornaments. This software has three features that support the use of this ornament model. First, in athenaCL a musical part is conceived of as a texture. A texture is any way of organizing musical parameters into a single musical part. Textures are implemented as object instances created from a TextureModule. Any number of texture instances can be combined within athenaCL, each functioning as an independent part. Second, textures take as a primary organizing parameter a "path". A path is an ordered collection of pitch sets. These sets can be of any size, can contain redundancies, and can simultaneously be interpreted as ordered or un-ordered and as operating in pitchspace, pitch class space, or set-class space. The use of paths allows athenaCL to determine two types of diatonicism for any given pitch: a local diatonicism based on the total pitch collection in a pitch's set, and a global diatonicism based on the total pitch collection of the entire path. When using ornaments within athenaCL, the user can choose between either of these two diatonicisms for each ornament-type. Third, textures within athenaCL can be assigned a variety of temperaments, unique tunings for each of the twelve tones. Some temperaments model historical temperaments such as mean-tone and Pythagorean tunings. Other temperaments provide varying degrees of noise upon twelve-tone equal temperament, simulating humanistic deviations. A TextureModule can be used to control the choice of when to apply an ornament and which ornament to apply. A simple method is presented here, implemented in the TextureModule "MonophonicOrnament". First, a repretory of ornaments is created as a collection of ornament datastructures. The texture, for each new note generated, then decides whether or not an ornament should be created based on a user-defined probability. If the texture chooses to create an ornament, an ornament is randomly selected from the repretory using a uniform distribution. A future TextureModule could make ornament choices based on specialized contextual information concerning previous and next pitches, position within the set and path, or the rhythmic value of the basenote. Applications using Markov chains or formal grammars are also equally viable. In the example provided here, base-notes are chosen in-order from a path with a single set, the set providing the skeletal melody of recording B. Base note amplitudes are kept within a narrow range. Tempo and rhythms are given so as to create a rhapsodic, parlando rubato pulse. The following figure shows the TextureInstance View command of.910.010.940.025 Figure 9. Example parameters for common ornaments Notice that the trill has a distributed list of durations and high value of durational noise, promoting the generation of durations similar to those seen above. The turn, likewise, has weighted durations to produce the observed alternating rhythm.

Page  00000007 a MonophonicOrnament texture from within athenaCL. [PI(phraseA-nonPart6)TI(wer)]:: tiv TI: wer, TM: MonophonicOrnament, TC: (0), TT: TwelveEqual PitchMode: pitchSpaceSet, PolyMode: set 0/+: + (i)nstrument 50 (guitarNylonNormal) (t)ime range 001.00--041.00 (b)pm 'staticBeat', 76.00 (r)hythm 'loop', ((4,4,+),(4,5,+), (4,4,+), (4,7,+), (4,9,+), (4,7,+),(4,12,+)) (p)ath phraseA-nonPart6 (12,11,9,12,14,11,9,11,9,9,11,9,9,11,9, 9,9,7,7,5,2) 40.00(s) local (f)ield 'basketGen', 'orderedCycl ic', local (o)ctave (a)mplitude pa(n)ing au(x) pfields t(e)xture eO el (0) 'basketGen', 'randomChoice', (7) 'cyclicGen', 'linearUpDown', 89.00, 90.00, 0.12 'constant', 0.25 none 'loopWithinSet', 'off' 'ornamentLibrary', 'diatonicGroupA' to select ornaments based on higher levels of contextual data. This would included information such as temporally adjacent base-notes, position in the set and path, and the rhythm of the base-note. Alternatively, a TextureModule could be created that simultaneously generates both musical parts of a heterophonic texture, coordinating each part's choice in ornament and producing a more refined heterophony. Open Source Software Resources athenaCL <www.athenacl.org> Python <www.python.org> Audacity <audacity. sourceforge.net> Recordings "Hajnali Csirdis Es Szapora A Ciganyoknak / Dawn Songs And Gypsy Couple Dances" (track 1) on Kalotaszegi N6pzene / Transylvanian Folk Music From Kalotaszeg. 1999. Budapest. {Recording A} "Lamenting music at the side of the dead with two violins" (tk 41) on Hungarian Instrumental Folk Music Nos 1-2. 1977. Budapest: Hungaroton Classic. {Recording B} References Morris, Robert. 1987. Composition with Pitch Classes: A Theory of Compositional Design. New Haven: Yale University Press. Paksa, Katalin. 1992. "Connection of style and dialect in the ornamentation of Hungarian folksongs." Studia Musicologica Academiae Scientiarum Hungaricae, 34(1-2): pp. 73-80. Paksa, Katalin. 1987. "Line starting ornaments in the Hungarian folk Song." Studia Musicologica Academiae Scientiarum Hungaricae, 29(1-4): pp. 219-36. Szirmai, Palma. 1967. "A Csango-Hungarian lament." EthnoMusicology, 11(3): pp. 310-25. Figure 10: athenaCL TextureInstance View display The realized algorithmic examples demonstrate various arrangements of this texture within athenaCL, using a simple Csound instrument. Each rendering of a TextureInstance employing ornaments is unique due to both the choice of ornaments and the application of stochastic noise. These differences result in dramatic changes in the timing and character of the resultant line. When two TextureInstances are combined, both with the same rhythms and skeletal melody, the result is a thick heterophony. The timing of base-note articulations are shifted due to varying "attack" ornament durations, and "release" ornaments create varying combinations of sustained ornamental textures. Even when both textures use the same ornament-type, variations due to stochastic noise produce appropriate deviations. During moments between base-notes, thick ornamental micropolyphony is obtained. In order to obtain the necessary timbral distinctions between instruments, each texture can be tuned to a slightly different temperament. The resultant pitch differntiation produces a timbrally thicker sound and a greater independence between parts. 7 Conclusion The ornament model presented here, even when employed with a simple generator, demonstrates a flexible and powerful way of algorithmically conceiving and deploying ornaments. Additionally, the results obtained suggest that in some cases heterophony may actually result as a product of choices in ornamentation alone, rather than specific considerations of timing and leader/follower relationships. Future work with this system will develop more sophisticated TextureModules designed