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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.
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