Wavefolding: Modulation of Adjustable Symmetry in Sawtooth And

With many digital samplers available we decided to ture. We puzzled and brainstormed for a period of two choose KONTAKT for composing, because of its wide years and made a lot of adaptations to the instrument and Wavefolding: Modulation of Adjustable Symmetry in options of modifying your digital instrument. Both Gun- music system. This is an ongoing process and to create Sawtooth and Triangular Waveforms awan and me were familiar with this sampler and wanted this instrument we need to communicate a lot in order to to learn more about the software. The scripting editor get understanding for each other. This mentality is vital in allows you to create most things you can imagine. To this cooperation between different cultures. To expand Dr Edward Kelly translate the gamelan set into a MIDI keys, I programmed our mind, I think we have to venture into the unknown. University of the Arts London the notes closest to the actual notes being played. (Figure Here we can discover new possibilities that life has to Camberwell College of Arts 4) offer outside of our comfort zone. I think we should cre- Peckham Road ate more understanding for other people and the things London SE5 8UF we do not know yet. United Kingdom [email protected] The beauty of living nowadays is the technology, with a ABSTRACT frequency modulation (sine-wave modulation) of the laptop I can take my work everywhere. This allows me to waveform results in complex timbre transformations over work outside my home where I receive different impulses The Pulse-Width Modulation (PWM) technique has been time, highly dependent on phase ratios between carrier that inspire me. I tend to search for opinions that are dif- used to generate varying timbres of odd-harmonic spec- and modulator, and a temporal morphology that reflects ferent than mine. It fascinates me how much you can tra from early on in voltage controlled analog synthesis the characteristic shape of the sawtooth wave itself. (Figure 4) learn from people that do not share your world vision. history. Methods for controlling the symmetry of a trian- Slendro 5 is the same tune as pelog 4 and slendro 6 is the This is the main reason I like to working with multicul- gle-to-sawtooth wave have also been devised. This paper 2. THE WAVEFOLDER~ OBJECT same tune as pelog 6. Gunawan uses these notes to switch tural groups. Therefore, as an answer to the question ‘Is discusses a family of objects and techniques for piece- between the different tuning systems. the sky local?’: No, not to me wise waveform manipulation that may be modulated at audio rate, comparing the results with analog equiva- For composing, you want the note you play on your key- 6. CONCLUSIONS lents, and looking specifically at the implications of mod- board to be the actual key. For this reason, we have cho- ulator phase and subtle deviations from integer carri- sen to use the actual notes and keep it structured with one Like Lego, this instrument has the option to grow in vari- er-to-modulator ratios, and fine deviations from these, on tuning in one octave. KONTAKT has the option to use ous shapes and sizes. We can implement different tech- adjustable-symmetry sawtooth waves. Figure 1. The wavefolder~ object generates variable asymme- multiple instruments within one sampler and control them nologies and experiments in realms first unknown to the try sawtooth/triangle waves from a phasor~ (ramp) input. with different midi tracks, within the DAW you use. This gamelan society. We combine our knowledge to develop 1. INTRODUCTION enables the composer to combine sets of instruments in an instrument that can be included in ensembles but also The implementation of an algorithm for converting a the different tuning systems to their liking. serves as a solo instrument. This vision however makes The sawtooth or ramp wave is a fundamental element in ramp wave into a triangle wave or inverse ramp is rela- that almost everything will be possible. In this we have to subtractive synthesis, since it contains both odd and even tively simple. This was initially accomplished as a Pure 1 For performing however we analyze the data coming cut back and search for solutions that are relative and harmonics of the fundamental frequency. It's slightly dull Data[1] (Pd) patch using the sigpack~ library of objects . from the DIGIGAM controller we have to sort out how to functional to gamelan and digital controllers. cousin, the triangle wave, has weak overtones of odd har- More recently this has been created as an external for Pd, control the different articulations and instruments. For monics and sounds much like a digital approximation of a along with the wavestretcher~ object. This has simplified this we wrote a MAX patch, this patch has 2 times 7 Although this is an ongoing project, we do have a clear sine wave. Both have their uses in synthesis, but it is pos- the process of converting a ramp from a phasor~ object switches connected to the rim switches. This enables the view on what needs to happen and how we can achieve sible in both analog and digital domains to generate into an adjustable-symmetry waveform, and opened-up user to switch between different articulations and instru- this as a team. We have collected a lot of information waveforms that can be modulated between sawtooth and the possibility of audio frequency modulation of the ments. The upper row pads 1 to 7 control different in- concerning technology, Indonesian music and culture. triangle. Some digital synthesis methods have used this waveform symmetry. struments by activating the channels in Ableton. The Music Technology is slowly developing in Indonesia, principle particularly since the transformation from a The principle is simple. With a ramp waveform from 0 lower row pads control the articulations by pressing the Alexander Dijk and me share our knowledge about tech- sawtooth wave into a triangle wave creates a reduction in to 1, a threshold is set between 0 and 1. Sample-by-sam- rim this enables different MIDI pitch shifters that act like nology with Gunawan and Kyai Fatahilla. We have had harmonic richness similar (but not the same as) subtrac- ple the output is given by: keyswitches. Another patch translates the values of the days when we designed systems together with Gunawan tive filters. Historically, Casio's ill-fated VZ series of syn- O=IF(R>T;R(1/T);1-((R-T)*(1/(1-T)) (1) FSR sensors to data that controls the “sustain and re- and tested the updates. thesizers in the 1980s used a method called IPD or Inter- where O = out sample, R = ramp input and T = threshold. lease” in Ableton. active Phase Distortion, based on the transformation of Divide-by-zero errors are eliminated in a separate func- Gunawan and Kyai Fatahilla are the end users in this and waveforms through progressively sharper sawtooth tion that prevents R from arriving at precisely 0 or 1. This In Ableton I have sorted the notes in separate samplers, we have to customize the design to their logic. A playable shapes. Software glitches with the interface along with object can be found in the ekext library of Pd externals2. because we need the FSR data to damp separate notes. version of the DIGIGAM controller will be made for bad commercial timing (the Korg M1 released at the This is an “instrument rack” for group modifications and them in addition to an original gamelan set and will be same time, which also had a sequencer and drums) led to 3. SPECTRAL CHARACTERISTICS effects, within this is another “instrument rack” with a finished by May 2016 for the LeineRoebana show the withdrawal of Casio from the pro-audio market. maximum of fourteen samplers inside to control the “sus- “Light”. Gunawan and his ensemble need to understand With computer synthesis it is a simple procedure to 3.1 Frequency spectra at static symmetry settings tain and release” of the single notes. The pitch en- how the instrument works. Therefore communication and create an algorithm that generates adjustable symmetry veloppes and pitchbends are connected to Proximity sen- involving them in creative processes remains essential. sawtooth-to-triangle waves that may be modulated at As the waveform is modulated between a setting of 0 sor 2 so it can be controlled by waving your hand over audio frequencies. Empirical research into harmonic (symmetric triangle waveform) and 1 (asymmetric ramp the sensor and modifying the sound. Proximity sensor 2 is Acknowledgments: spectra of such modulations reveals a slightly more waveform), peaks and troughs in the harmonic spectrum connected to sendbus A in Ableton to control an effect. LeineRoebana, Iwan Gunawan, Kyai Fatahilla and Alex- complex morphology of spectra than would be devised are developed (see figures 1-4). This was empirically An additional Korg Nano controller is added to control a ander Dijk formed an essential part in the realization, this using subtractive methods, and the application of single tested in order to establish the relationship between the project isn’t possible without them. looper function. Copyright: © 2016 First author et al. This is an open-access article symmetry of the waveform and the resultant harmonic distributed under the terms of the Creative Commons Reference: spectrum, in order to establish how the functional de- 5. IS THE SKY LOCAL? Attribution License 3.0 Unported, which 1 [1] Henry Spiller -Focus; Gamelan Muisc of Indonesia permits unrestricted use, distribution, and reproduction in any medium, https://puredata.info/downloads/sigpack The strength of this project lays in our differences and provided the original author and source are credited. 2 (second edition, 2008) Latest versions can be downloaded from getting understanding for each other’s discipline and cul- http://sharktracks.co.uk/html/software.html

194 Proceedings of the International Computer Music Conference 2016 Proceedings of the International Computer Music Conference 2016 195 scription of a sawtooth or ramp wave is affected by this process. It makes sense to define this relationship in terms of deviation from the sawtooth or ramp waveform toward the triangle, as there is a reciprocal relationship between the troughs in the resultant spectra and the symmetry of the waveform. Furthermore, the reduction in the Figure 7. Superimposed waveforms of modulator and Figure 8. An example of the pulse-width modulated out- magnitude of even harmonics is not linear. resultant waveform at phase = 90º. put from wavefolder~. There is a modulation between the Fourier series of a sawtooth wave: Figure 3. Symmetry setting 0.75. 4.1 Spectro-Morphology at Detuned Modulation Fre- 5. MORE PIECEWISE MANIPULATION quencies 1 1 ∞ sin 2 kft  x saw= − ∑   Thus far this paper has considered static waveforms, and 5.1 Wavestretcher~ 2  k=1 k (2) there is no single result here that cannot be achieved by a A second object uses a similar approach the the wave- and that of a triangle wave: wavetable method of synthesis. But this method begins to folder~ by taking a breakpoint (threshold) and manipulat- yield more interesting results as the modulation wave- ∞ ing the geometric angle of the waveform differently de- 8 sin 2 2k1 ft  form is detuned from integer-multiples of the asymmetric pending on which side of the threshold it is. It is useful to x tri= ∑   2 2 modulated waveform. The phase relationship discussed think of this as a complementary function to the previous  k=0 2k1 (3) above is continually changing, and this results in morpho- object. While the wavefolder~ modulates from a saw- As can be seen from the figures below, the modulation Figure 4. Spectrum and waveform at symmetry setting 0.5. logical transitions between very bright, harsh-sounding tooth input (from phasor~) towards a triangle waveform of the magnitudes of harmonics closely resembles a timbres and softer timbres. using a breakpoint-based algorithm, wavestretcher modu- cosine function of the magnitudes based on the harmonic At a positive detuning away from the frequency of the lates from the sawtooth (or any input waveform for that number, starting at infinity for the ideal saw and starting tri/saw wave, the sweep is from bright-to-soft with a matter) towards pulse-train-style waveforms as shown be- at harmonic 2 for the triangle. Given that, in additive plateau at the brightest point, repeating at a rate equiva- low. synthesis both waveforms' harmonics are alternately lent to the difference in frequency between the carrier opposite in phase to the previous harmonic (1, -2, 3, -4 (tri/saw waveform) and the modulator (sine). The inverse etc and 1, -3, 5, -7 etc) there are clues to how the is true at a negative detuning, that is the sweep in timbre combination of additive sine elements with different is from soft-to-bright. More complex timbres are phase relationships may result in the spectra observed achieved with simple non-integer ratios (1.5, 0.75 etc) below. An exponential relationship between the linear giving inharmonic timbres but with a degree of tonality. asymmetry and the position of the first trough in the Figure 5. Spectrum and waveform at symmetry setting 0 (tri- Figure 9. Stretched sawtooth waveform at breakpoint = angle waveform). Just as with frequency modulation synthesis, the more 0 (middle of absolute value) and stretch factor at -0.5. spectrum is observed, and the interval in harmonics until complex the integer ratio of the carrier to the modulator, the next of these, such that a triangle wave has an absence 4. AUDIO FREQUENCY MODULATION the more inharmonic the timbre produced. of even harmonics (2, 4, 6, 8...interval=2) and figures for Furthermore, since the sweep in brightness is a rhyth- alternative symmetry settings as shown in the table and OF THE WAVESHAPE mic effect, this can be controlled mathematically to be graphical figures below: The shape of the wavefolder~ output is controllable at au- consistent across all integer-ratio carrier-to-modulator dio rate with limits of -1 (saw down) and 1 (saw up) with values, and an object has been created to facilitate this, Figure 10. With the same sawtooth input, breakpoint = Asymmetry Interval a setting of 0 representing the triangle waveform. The re- which will be demonstrated at the conference and made -0.75, stretch factor = -1. 0 (triangle) 2 lationships between the phase of the modulation signal available on the author's website. Positive values of the stretch factor allow the modula- 0.5 4 (in this case a simple sinusoidal waveform) and the phase tion between triangular or sawtooth waveforms through 0.75 8 of the asymmetry modulation are important to the result- 4.2 Pulse-Width Modulations of the Modulated trapezoidal waveforms until a square wave or clipped 0.875 16 ing timbre. With a modulating sine function at the same Asymmetric Waveform sawtooth waveform results. 0.9325 32 frequency, at 270º there are more corners to the wave- 1 (sawtooth) Nyquist (SR/2) The wavefolder~ object has an extra inlet and outlet at form, and more high-frequency harmonics are generated audio rate allowing for the modulated waveform to have a Table 1. Asymmetry settings and their correspondent (fig. 7), whereas at 90º between trisaw and sine the wave- troughs in the harmonic spectrum. process of pulse-width modulation applied to it. Since the form is more like a distended triangle wave and the har- waveform shapes of a modulated asymmetric waveform monic spectrum is less bright (fig. 6). are geometrically complex, a set of timbres are available from the object that are more varied than those of tradi- Figure 11. With the same sawtooth input, breakpoint = -0.5, tional PWM. When this is combined with the detuning of stretch factor = 0.7. the modulator discussed above, the timbre evolution of The use of both objects, with the output of the asymmetric waveform is transferred to the pulse wavefolder~ feeding into wavestretcher~ affords a situa- waveform with the potential for modulations of the PWM tion where a large repertoire of complex timbres may be Figure 6. Superimposed waveforms of modulator and threshold to create further evolutions in timbre. generate using a highly compact, efficient structure. It is resultant waveform at modulator phase = 270º with re- possible to emulate timbres of subtractive synthesis with- Figure 2. Spectrum and waveform at symmetry setting spect to the tri/saw wave. out the use of filters, but with a greater degree of flexibil- 1 (ramp waveform). ity in terms of timbre control3.

3 It must be stated that there is no way to reproduce high-Q resonant peaks without the use of audio filters in this system, although a phase- distortion-type equivalent may involve added resonant circuits to one portion of the waveform.

197 Proceedings of the International Computer Music Conference 2016 Proceedings of the International Computer Music Conference 2016 198 scription of a sawtooth or ramp wave is affected by this process. It makes sense to define this relationship in terms of deviation from the sawtooth or ramp waveform toward the triangle, as there is a reciprocal relationship between the troughs in the resultant spectra and the symmetry of the waveform. Furthermore, the reduction in the Figure 7. Superimposed waveforms of modulator and Figure 8. An example of the pulse-width modulated out- magnitude of even harmonics is not linear. resultant waveform at phase = 90º. put from wavefolder~. There is a modulation between the Fourier series of a sawtooth wave: Figure 3. Symmetry setting 0.75. 4.1 Spectro-Morphology at Detuned Modulation Fre- 5. MORE PIECEWISE MANIPULATION quencies 1 1 ∞ sin 2 kft  x saw= − ∑   Thus far this paper has considered static waveforms, and 5.1 Wavestretcher~ 2  k=1 k (2) there is no single result here that cannot be achieved by a A second object uses a similar approach the the wave- and that of a triangle wave: wavetable method of synthesis. But this method begins to folder~ by taking a breakpoint (threshold) and manipulat- yield more interesting results as the modulation wave- ∞ ing the geometric angle of the waveform differently de- 8 sin 2 2k1 ft  form is detuned from integer-multiples of the asymmetric pending on which side of the threshold it is. It is useful to x tri= ∑   2 2 modulated waveform. The phase relationship discussed think of this as a complementary function to the previous  k=0 2k1 (3) above is continually changing, and this results in morpho- object. While the wavefolder~ modulates from a saw- As can be seen from the figures below, the modulation Figure 4. Spectrum and waveform at symmetry setting 0.5. logical transitions between very bright, harsh-sounding tooth input (from phasor~) towards a triangle waveform of the magnitudes of harmonics closely resembles a timbres and softer timbres. using a breakpoint-based algorithm, wavestretcher modu- cosine function of the magnitudes based on the harmonic At a positive detuning away from the frequency of the lates from the sawtooth (or any input waveform for that number, starting at infinity for the ideal saw and starting tri/saw wave, the sweep is from bright-to-soft with a matter) towards pulse-train-style waveforms as shown be- at harmonic 2 for the triangle. Given that, in additive plateau at the brightest point, repeating at a rate equiva- low. synthesis both waveforms' harmonics are alternately lent to the difference in frequency between the carrier opposite in phase to the previous harmonic (1, -2, 3, -4 (tri/saw waveform) and the modulator (sine). The inverse etc and 1, -3, 5, -7 etc) there are clues to how the is true at a negative detuning, that is the sweep in timbre combination of additive sine elements with different is from soft-to-bright. More complex timbres are phase relationships may result in the spectra observed achieved with simple non-integer ratios (1.5, 0.75 etc) below. An exponential relationship between the linear giving inharmonic timbres but with a degree of tonality. asymmetry and the position of the first trough in the Figure 5. Spectrum and waveform at symmetry setting 0 (tri- Figure 9. Stretched sawtooth waveform at breakpoint = angle waveform). Just as with frequency modulation synthesis, the more 0 (middle of absolute value) and stretch factor at -0.5. spectrum is observed, and the interval in harmonics until complex the integer ratio of the carrier to the modulator, the next of these, such that a triangle wave has an absence 4. AUDIO FREQUENCY MODULATION the more inharmonic the timbre produced. of even harmonics (2, 4, 6, 8...interval=2) and figures for Furthermore, since the sweep in brightness is a rhyth- alternative symmetry settings as shown in the table and OF THE WAVESHAPE mic effect, this can be controlled mathematically to be graphical figures below: The shape of the wavefolder~ output is controllable at au- consistent across all integer-ratio carrier-to-modulator dio rate with limits of -1 (saw down) and 1 (saw up) with values, and an object has been created to facilitate this, Figure 10. With the same sawtooth input, breakpoint = Asymmetry Interval a setting of 0 representing the triangle waveform. The re- which will be demonstrated at the conference and made -0.75, stretch factor = -1. 0 (triangle) 2 lationships between the phase of the modulation signal available on the author's website. Positive values of the stretch factor allow the modula- 0.5 4 (in this case a simple sinusoidal waveform) and the phase tion between triangular or sawtooth waveforms through 0.75 8 of the asymmetry modulation are important to the result- 4.2 Pulse-Width Modulations of the Modulated trapezoidal waveforms until a square wave or clipped 0.875 16 ing timbre. With a modulating sine function at the same Asymmetric Waveform sawtooth waveform results. 0.9325 32 frequency, at 270º there are more corners to the wave- 1 (sawtooth) Nyquist (SR/2) The wavefolder~ object has an extra inlet and outlet at form, and more high-frequency harmonics are generated audio rate allowing for the modulated waveform to have a Table 1. Asymmetry settings and their correspondent (fig. 7), whereas at 90º between trisaw and sine the wave- troughs in the harmonic spectrum. process of pulse-width modulation applied to it. Since the form is more like a distended triangle wave and the har- waveform shapes of a modulated asymmetric waveform monic spectrum is less bright (fig. 6). are geometrically complex, a set of timbres are available from the object that are more varied than those of tradi- Figure 11. With the same sawtooth input, breakpoint = -0.5, tional PWM. When this is combined with the detuning of stretch factor = 0.7. the modulator discussed above, the timbre evolution of The use of both objects, with the output of the asymmetric waveform is transferred to the pulse wavefolder~ feeding into wavestretcher~ affords a situa- waveform with the potential for modulations of the PWM tion where a large repertoire of complex timbres may be Figure 6. Superimposed waveforms of modulator and threshold to create further evolutions in timbre. generate using a highly compact, efficient structure. It is resultant waveform at modulator phase = 270º with re- possible to emulate timbres of subtractive synthesis with- Figure 2. Spectrum and waveform at symmetry setting spect to the tri/saw wave. out the use of filters, but with a greater degree of flexibil- 1 (ramp waveform). ity in terms of timbre control3.

196 Proceedings of the International Computer Music Conference 2016 Proceedings of the International Computer Music Conference 2016 197 6. ANALOG REALIZATION gle OTA may be used, and in this realization it is a CA3080 – the chip designed by RCA that was vital to the Towards an Aesthetic of Instrumental Plausibility for Mixed Electronic Music 6.1 Sawtooth to Triangle Wave Modulation creation of early voltage-controlled synthesizers (the RCA Mk1 and Mk2) which, as the footnote below shows There are some implementations of this idea available on is now available again, albeit in lots of 100 ICs. Richard Dudas Pete Furniss synth-DIY sites by Hoshuyama [2]. Tillmans [3] and This circuit should perform in exactly the same way as CREAMA Reid School of Music Gratz [4]. All of these articles observed by this author the digital algorithm, with a threshold voltage determin- Hanyang University Edinburgh College of Art come with the caveat that they are “untested” e.g.[2] al- ing the asymmetry of the resultant waveform. Effectively Seoul, Korea University of Edinburgh, UK though this seems unlikely given the knowledge and ex- though, every analog implementation of this principle, [email protected] [email protected] perience of those contributing this knowledge, since such from the low-frequency oscillator of the Korg MS20 to features exist in Moog and MFB synthesizers (Moog the switched OTA concept described above, uses the Voyager, MFB Dominion) and it would be naive to as- same principle of threshold-switching the separately am- to simulate a human approach, but rather create something sume that the potential of these systems was overlooked4, ABSTRACT plified non-inverted and inverted portions of the ramp pragmatic that draws on human musical nuancing. especially given the ubiquity of PWM in commercially waveform on either side of the switching threshold. The implementation of live audio transformations in mixed The desire for a plausible instrumental transposition re- successful forms of popular electronic music and elec- electronic music raises the issue of plausibility in real-time quired addressing the way that audio effects can modify tronic dance music (EDM) over the past four decades. 7. CONCLUSIONS instrumental transposition. The composer-performer col- the perception of instrumental resonance in uneven ways. However only the Moog Voyager XL appears to offer a laboration described in this paper deals with two of the While resonant filter banks have been used frequently to fully patchable (and hence audio rate) modulation of the This project was driven by curiosity into a way of gener- composer’s existing pieces for solo instrument and com- simulate instrumental resonance where sound synthesis is waveform shape. ating complex timbres from simple means, and how puter, addressing issues of timbre and intonation in the concerned [1, 2], here they were employed to provide a Of particular interest for its simplicity is the design and pushing methods from analog experimentation by synthe- output and adapting the existing software with improve- homogeneity within the transposed material. Furthermore, article by Don Tillmans [2], published in 2000 and re- sis enthusiasts into the digital domain may open new ap- ments informed by both the physical resonating properties the recent move to 64-bit has brought subtle improvements vised in 2002, providing a simple circuit for analog wave- proaches (asymmetry modulation) to timbre modulation of musical instruments and by instrumental ensemble prac- to clarity in audio signal processing that become musically shaping of a sawtooth wave using two operational of basic synthesis waveforms. The conceptual process of tice. In preparing these pieces for publication, wider per- significant in multi-layered musical and sonic textures. It transconductance amplifiers. A certain amount is left to development for the analog circuit was realized by under- formance and further instrumental transcription, improve- was therefore necessary to make updates at the code level the circuit-builder to figure out in this article. As the orig- standing that through some lateral transposition of the ments stemming from both compositional and performa- to some project-specific software. Finally, it was decided inal circuit uses hard-to-find CA3280 chips5 efforts are principles of the digital implementation, an analog real- tive considerations were implemented to address this issue to break from an exclusive use of equally tempered semi- ongoing to adapt the circuit to use a readily available ization could be created based on the same principles as of plausibility. While not attempting to closely simulate tones as a subtle step in an attempt to impart a chamber LM13700 dual operational transconductance amplifier the digital object. A conceptual loop can be observed a human approach, the authors worked towards a prag- music aesthetic to the computer processed output. (OTA) integrated circuit (IC), although a new solution is where code-based digital methods and analog electronics matic heuristic that draws on human musical nuancing in The work undertaken on instrumental transcription and detailed below, based on the wavefolder~ algorithm. can be created in parallel, and where understanding from concert practice. Alternative control options for a range interface design represents a continuation of the authors’ earlier research on Prelude I.[3] Improvements to the in- The analog circuit designed by Don Tillmans (cited by one branch of electronic music can be adapted to function of concert spaces were also implemented, including the configuration of user input and output at interface level terface and audio processing chain were implemented in Gratz[3]) uses an equivalent equation to that in the digital using the same principles in another. in order to manage common performance-related contin- order to address the configuration of user input and out- object wavefolder~ expressed in a form more mathemati- Acknowledgments gencies. put for the management of common contingencies in the cally elegant than the coding algorithm expressed in part performance space. The existing user interface was further 2 above, thus: This project was devised and researched by the author, adapted to provide a diversity of options for control either and I am deeply grateful to the University of the Arts 1. INTRODUCTION 1 1 onstage by the performer or offstage by a technical assis-  =1 London, and particularly Nick Gorse and Jonathan Kear- x −x Following several years of collaboration on the perform- tant. 1e 1e ney for releasing funding for its presentation. A great deal (4) ance of mixed electronic music, the authors decided to re- of credit for understanding analog circuits in voltage-con- turn to two existing pieces, Prelude I for Clarinet 2. RESONANCE AND FORMANT FILTERING where x is equivalent to the control voltage in the analog trolled synthesis should be given to Thomas Henry, Ray circuit, and the threshold/breakpoint value in the digital and Computer and Prelude II for Clarinet and Computer, Wilson, Ian Fritz and Don Tillmans. in order to modify and update their technological compo- The two pieces referred to here each employ real-time trans- algorithm of wavefolder~. This accurately reflects the ex- nent. The primary motivation behind this was simply to formations of the live input, including transposition both ponential relationship between the wavefolder~ threshold 8. REFERENCES make the audio processing “sound better” for the purposes within and beyond the actual range of the instrument(s) to value and the harmonic modulations detailed in table 1, of including them on a published sound recording. The create the effect of a virtual ensemble. Where these trans- and figures 2-5. [1] Puckette, M, Pure Data: another integrated second motivation was to prepare the pieces for wider dis- positions extend beyond a perfect fifth in either direction, Given that an exponential multiplication of a signal is computer music environment, Proceedings, Second semination, including transcription of one of the pieces for the question of plausibility becomes an issue [4] in respect the reciprocal of a division by a linear increase or de- Intercollege Computer Music Concerts, Tachikawa, a variety of other instruments, through publication of the of an overall ensemble aesthetic. In the case of the Pre- crease of the denominator, an alternative method can be Japan, pp. 37-41, 1996 score and technical materials. Both motivations necessi- lude I, transcription of the original solo flute part to both devised for an analog circuit using the principles of the violin and viola had led the composer to adapt the software [2] Hoshuyama, O, Wave-Shaper (Variable Slope-Ratio tated an updating and refinement of the underlying audio original wavefolder~ algorithm. An analog switch IC re- processing. Improvements to the audio signal processing to string instruments by first filtering out the fixed formant Triangular), structure of the resonating instrumental body using notch places the IF statements, and differential amplifiers are http://www5b.biglobe.ne.jp/~houshu/ were geared toward the implementation of a plausible in- used to generate reciprocal control voltages for a voltage- strumental transposition – one that is informed by physical filters before transposition, and later adding the formants synth/WvShp0306.gif, 2003. controlled amplifier against a reference voltage. Both the resonating properties of instruments and by instrumental back into the transposed sound through the use of resonant filtering. This creates a greater sense of homogeneity, since input ramp wave and its inverted counterpart are switched [3] Tillmans, D, Voltage Controlled Duty Cycle ensemble practice. In doing this, we were not attempting the formants remain stable when the sound is transposed. alternately using a comparator, along with the control Sawtooth Circuit, www.till.com, 1999, 2002. (Refer to Sound Example Set 1 via the link provided at the voltages to an exponential converter into an OTA. A sin- Copyright: c 2016 Richard Dudas et al. This is an open-access article [4] Gratz, A, Triangle / Sawtooth VCO with voltage end of this paper.) distributed under the terms of the Creative Commons Attribution License 4 controlled continously variable symmetry, In comparison to stringed instruments, the spectral en- These articles are all over a decade old at the time of publication. 3.0 Unported, which permits unrestricted use, distribution, and reproduc- 5 http://synth.stromeko.net/diy/SawWM velope of woodwind instruments is heavily dependent on These are now being manufactured by Rochester Electronics: tion in any medium, provided the original author and source are credited. both pitch and volume (this is especially true of the clar- http://www.rocelec.com .pdf, 2006.

199 Proceedings of the International Computer Music Conference 2016 Proceedings of the International Computer Music Conference 2016 200